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1 Moist static energy budget of the MJO during DYNAMO
∗ 2 Adam Sobel
Department of Applied Physics and Applied Mathematics, and
Lamont-Doherty Earth Observatory, Columbia University, New York, NY
3 Shuguang Wang
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY
4 Daehyun Kim
Department of Atmospheric Sciences, University of Washington, Seattle, WA
∗Corresponding author address: Columbia University, Dept. of Applied Physics and Applied Mathemat- ics, 500 W. 120th St., Rm. 217, New York, NY 10027 USA. E-mail: latex@[email protected]
1 5 ABSTRACT
6 The authors analyze of the moist static energy budget over the region of the tropical Indian
7 ocean covered by the sounding array during the CINDY/DYNAMO field experiment in late
8 2011. The analysis is performed using the sounding array complemented by the Objectively
9 Analyzed air-sea Fluxes for the Global Oceans (OAflux) and Clouds and the Earth’s Radiant
10 Energy System (CERES) data for surface turbulent fluxes and atmospheric radiative heating
11 respectively. The analysis is repeated using the ERA Interim Reanalysis for all terms. The
12 roles of surface turbulent fluxes, radiative heating, and advection are quantified for the two
13 Madden-Julian oscillation (MJO) events that occurred in October and November using the
14 sounding data; a third event in December is also studied in the ERA Interim data.
15 These results are consistent with the view that the MJO’s moist static energy anomalies
16 grow and are sustained to a significant extent by the radiative feedbacks associated with
17 water vapor and cloud anomalies associated with MJO convection, and that propagation of
18 the MJO is associated with advection of moist static energy. Both horizontal and vertical
19 advection appear to play significant roles in the events studied here. Horizontal advection
20 strongly moistens the atmosphere during the buildup to the active phase of the October event
21 when the low-level winds switch from westerly to easterly. Horizontal advection strongly dries
22 the atmosphere in the wake of the active phases of the November and December events as
23 the westerlies associated with off-equatorial cyclonic gyres bring subtropical dry air into the
24 convective region from the west.
1 25 1. Introduction
26 Though the Madden-Julian oscillation (MJO) was first discovered over four decades ago
27 (Madden and Julian 1971, 1972), its basic dynamics remains unexplained to the collective
28 satisfaction of the research community. There is no fundamental agreement on what kind of
29 dynamical entity the MJO is.
30 We have been pursuing the notion that the MJO is a moisture mode. At the broadest
31 level, we mean by this a mode of variability which would not exist in any mathematical
32 model that does not contain a prognostic equation for moisture. At this level of generality,
33 the idealized models of Sobel and Maloney (2012, 2013) depict moisture modes, as do those
34 of Fuchs and Raymond (2002, 2005, 2007), Majda and Stechmann (2009) and Sugiyama
35 (2009a,b), Sukhatme (2013), and perhaps others.
36 More specifically, we have been led by analysis of observations and comprehensive models
37 to the view that the interaction of the MJO’s convection and circulation anomalies with en-
38 ergy fluxes at the boundaries — surface turbulent fluxes and radiative fluxes — is important
39 to its growth and maintenance (e.g., Sobel et al. 2008, 2010; see also, e.g., Emanuel 1987;
40 Neelin et al. 1987; Raymond 2001; Bony and Emanuel 2005). This view follows earlier
41 theoretical and modeling studies which posited that the MJO might be driven by feedbacks
42 involving surface turbulent fluxes (Emanuel 1987, Neelin et al. 1987) or radiative fluxes
43 (Raymond 2001, Bony and Emanuel 2005). Since these processes are sources and sinks of
44 column-integrated moist static energy or moist entropy, this view suggests that it may be
45 useful to view the observed MJO through column-integrated budgets of these conserved vari-
46 ables. It is also a durable principle in the physical sciences that it is often useful to study
47 any phenomenon from the point of view of those variables that are most nearly conserved.
48 In this study, we analyze the column-integrated moist static energy budget of a region
49 in the tropical Indian ocean during a single season of MJO activity, namely that of the
50 CINDY/DYNAMO field campaign (Zhang et al., 2013, Yoneyama et al., 2013, Gottschalck
51 et al., 2013). We choose this period because of the availability of high-quality radiosonde
2 52 observations from the array put in place for the campaign. Also, however, there is value
53 in focusing on a small number of events, even though the conclusions necessarily lack the
54 generality associated with statistical analyses of longer records.
55 Our expectations, based on previous work (e.g., Sobel et al. 2008, 2010; Maloney 2009;
56 Kiranmayi and Maloney 2011; Ma and Kuang 2011; Andersen and Kuang 2012; Kim et al.
57 2014) are the following:
58 i. precipitation and column-integrated moist static energy are in phase;
59 ii. radiative heating is approximately in phase with both column-integrated moist static
60 energy and precipitation (Lin and Mapes 2004);
61 iii. surface turbulent fluxes (latent being the dominant one, sensible being small) are pos-
62 itively correlated with moist static energy, but with some phase lag;
63 iv. vertical advection is approximately out of phase with moist static energy; since positive
64 moist static energy anomalies are associated with ascent, this implies that the gross
65 moist stability (Neelin and Held 1987; Raymond et al. 2009) is positive.
66 v. horizontal advection leads moist static energy, perhaps being close to in quadrature,
67 so that it has the effect of aiding propagation. That is, we expect horizontal advection
68 to provide moistening ahead (to the east) of the active phase, drying behind (to the
69 west of) the active phase, or both;
70 vi. neither vertical nor horizontal advection are positively correlated with MSE itself, while
71 radiative and turbulent fluxes are; thus radiative and turbulent fluxes are responsible
72 for the growth and maintenance of the MSE anomalies associated with the MJO.
73 Of these expectations, the last two, involving advection, are the most uncertain. The
74 gross moist stability is difficult to estimate from observations, even in sign, and even in the
75 climatological mean (e.g., Back and Bretherton 2006). Raymond and Fuchs (2009) obtain
76 better MJO simulations in models whose gross moist stabilities are negative, and infer that it
3 77 is negative in the real atmosphere. Benedict et al. (2014) similarly found that stronger MJOs
78 were simulated in models with small or negative GMS, but also found evidence that these
79 small or negative GMS values are inconsistent with observations. While negative NGMS
80 would allow vertical advection to induce or maintain MSE anomalies and thus strengthen
81 the MJO, vertical advection may also play a role in propagation. If frictional convergence
82 is important to the MJO (e.g., Wang 1988) it is likely to be associated with shallow ascent
83 and moist static energy import in the easterly region, leading the active phase to the east
84 and inducing its eastward propagation.
85 Our analysis uses observations from the field program as well as routinely available data
86 sets to estimate terms in the moist static energy budget for the region of the CINDY/DYNAMO
87 array for a three-month period during the experiment. Plots of the time series of these terms
88 from ECMWF Interim Reanalysis (Dee et al. 2011) are also examined. Discussion of these
89 time series is complemented by synoptic maps of satellite-derived column water vapor, pre-
90 cipitation, and low-level horizontal flow.
91 2. Data and methods
92 a. Data
93 The averaged atmospheric state variables derived from the CSU array-averaged analysis
94 products (version 1, Johnson and Ciesielski, 2013, Ciesielski et al., 2013) are used here
95 to compute the horizontal and vertical advection terms of column-integrated moist static
96 energy. We analyze data from the northern sounding array (NSA) , located mostly north
97 of the equator in the central equatorial Indian ocean (see fig. 1 and table 1 of Johnson
98 and Ciesielski 2013) as that was the site of greater variability in deep convection during the
99 course of the experiment than was the southern array.
100 The boundary fluxes of MSE at the surface and top of the atmosphere are estimated
101 from two independent datasets: (1) radiative fluxes averaged over the sounding array from
4 102 the 1 degree daily CERES (Clouds and the Earths Radiant Energy System, Wielicki et al.,
103 1996, Loeb et al., 2012) SYN1deg data; (2) daily 1 degree surface enthalpy fluxes from the
104 OAFlux data (Objectively analyzed air-sea Fluxes for Global Oceans, Yu et al., 2008).
◦ 105 For comparison, the ECMWF-Interim reanalysis 2.5 dataset (Dee et al., 2011) is also
106 used to compute the column-integrated MSE budget terms, as well as the gross moist sta-
107 bility.
◦ 108 Two precipitation data sets are used: the 3-hourly 0.25 TRMM 3B-42 version 7A, and
109 the daily GPCP (Global Precipitation Climatology Project, Adler et al. 2003; Huffman
110 et al. 2009) product. Total precipitable water estimated from satellite observations — a
111 combination of the SSM/I (Special Sensor Microwave Imager) and TMI (Tropical Rainfall
112 Measuring Mission’s Microwave Imager) — is compared against sounding array values and
113 the ECMWF-Interim reanalysis dataset.
114 b. Methods
115 The budget of the column-integrated MSE is computed as: ∂(c T + L q) ∂h h p v i = −hu · ∇(c T + L q)i−hω i + E + H + R, (1) ∂t p v ∂p
116 where h denotes moist static energy,
h = cpT + Lvq + gz
−1 −1 117 with T temperature, q specific humidity, cp dry air heat at constant pressure (1004 J K kg ),
6 −1 118 Lv latent heat of condensation (taken constant at 2.5 × 10 J kg ); u and ω horizontal and
119 pressure vertical velocities, respectively; hi represents mass-weighted vertical integration
120 from 1000 hPa to 100 hPa; E and H, turbulent latent and and sensible heat fluxes; and R,
121 column net radiative heating, defined as the difference between the net fluxes at the bottom
122 and top of atmosphere (thus we neglect any net radiative heating above 100 hPa).
123 Note that the partial time derivative and horizontal advection terms in (1) are applied not
124 to h, but to cpT + Lvq, omitting the gz term. This is consistent with the primitive equations
5 125 (Neelin 2007). On the other hand Betts (1974), without appealing to the primitive equations,
126 shows that neglecting kinetic energy generation (an assumption also required to derive (1)
127 and assuming hydrostatic balance together with the first law of thermodynamics results in
128 retention of the gz term in the tendency and horizontal advection. We have tried both forms,
129 and found only small differences. The form (1) leads to slightly better closure of the budgets,
130 discussed further in the presentation of figs. 8 and 9 below.
131 The dry static energy equation is
∂s ∂s h i = −hu · ∇si−hω i + H + R + L P, (2) ∂t ∂p v
132 where s = cpT + gz is dry static energy and P is precipitation.
133 The total normalized gross moist stability (e.g., Raymond et al. 2009), here denoted M˜ t
134 may be directly estimated as hω ∂h i + hu · ∇hi ˜ ∂p Mt = ∂s . (3) hω ∂p i
135 Our choice of column-integrated vertical advection of dry static energy in the denominator
136 follows Sobel and Maloney (2012, 2013); Raymond et al. (2009), for example, normalize
137 by the moisture convergence. In practice the difference is minor. By either definition, M˜ t
138 quantifies the relationship between the precipitation and the net column forcing of MSE
139 (surface fluxes plus radiation) in steady state, with smaller NGMS giving greater steady
140 -state precipitation for a given net positive forcing. If we assume steady state and neglect
141 horizontal advection of dry static energy in (2), then that equation together with (1) can be
142 solved for precipitation using the definition of M˜ t:
˜ −1 LvP = Mt (E + H + R) − R − H. (4)
143 In the transient case, smaller NGMS leads to a greater positive tendency of hhi for a
144 given positive forcing, while negative M˜ gives a positive tendency of hhi even when forcing
145 is negative. We use the subscript t to indicate that (3) defines the ”total” normalized gross
146 moist stability, including both horizontal and vertical advection terms in the numerator.
6 147 Horizontal and vertical components may be defined separately by retaining only one or the
148 other in the numerator. The quantity denoted M˜ in Sobel and Maloney (2012, 2013) is the
149 vertical component.
150 The direct use of equation (3) requires computation of the advection terms. The vertical
151 advection term in particular is delicate. It depends closely on the vertical motion profile,
152 which is a relatively highly derived quantity containing considerable uncertainty, and there
153 is generally significant cancellation in the vertical integral. We complement this direct cal-
154 culation by an alternate method in which we ignore time tendency and horizontal advection
155 of dry static energy in (2) but retain the tendency and horizontal advection terms in (1),
156 and then estimate the NGMS indirectly as
∂ E + H + R −h( ∂t + u · ∇)(cpT + Lvq)i M˜ t = . (5) H + R + LvP
157 3. Results
158 We first examine several time series that provide useful context to our investigation of the
159 MSE budget. In each case more than one data set is used, to give a sense of the observational
160 uncertainties.
161 Fig. 1 is a Hovmoeller plot of column-integrated water vapor (mm), precipitation from
162 GPCP (mm/d), and anomalous zonal wind at 850 hPa (arrows), all averaged between 10S
163 and 10N, as functions of time and longitude. Three MJO events are readily apparent as
164 eastward-propagating maxima in the water vapor and precipitation. The first two occurred
165 during the operation of the sounding array. Further discussion of the large-scale context and
166 synoptic evolution of these events can be found in, e.g., Yoneyama et al. (2013), Gottschalk
167 et al. (2013), Johnson and Ciesielski (2013), and Kerns and Chen (2014) . The properties
168 of the cloud populations as characterized by radar and other observations are presented in
169 Powell and Houze (2013) and Zuluaga and Houze (2013). In each event a shift to more
170 eastward zonal winds during the passage of the water vapor and precipitation maxima is
7 171 apparent, as expected during MJO active phases. At the longitudes near the array between
172 70-90E the easterlies beginning after October 16, preceding the first active MJO phase, were
173 themselves preceded by westerly anomalies in the first half of the month; these westerlies,
174 unlike those of the MJO events to follow, were not associated with significant precipitation.
175 Fig. 2a shows time series of precipitation averaged over the northern sounding array.
176 Data from the Global Precipitation Climatology Project (GPCP), Tropical Rainfall Mea-
177 suring Mission (TRMM) 3B42 data set, the rainfall deduced from budget analysis of the
178 sounding array, and the ERA-Interim reanalysis are shown. There is broad agreement, but
179 there are significant discrepancies in detail. The ERA-I is the largest outlier, with precip-
180 itation values greater than those in the other data sets during the suppressed periods and
181 considerably smaller than the others during the first active phase in late October.
182 Fig. 2b shows column-integrated precipitable water retrieved from the SSM/I-TMI
183 microwave satellite data sets, as well as that computed from the soundings, from ERA-I.
184 Again, there is qualitative agreement, but quantitative differences. The sounding values are
185 highest for most of the record while the ERA-I values are lowest, with differences exceeding 5
186 mm in early October. It is interesting that ERA-I has simultaneously the driest atmosphere
187 and the most precipitation during suppressed periods.
188 Fig. 2c shows column-integrated moist static energy from the soundings and ERA-I.
189 Time variation of the column-integrated moist static energy closely matches that of precip-
190 itable water, indicating that the variations in the latent heat term Lvq are much larger than
191 those in the temperature term cpT or the geopotential gz.
192 Figs. 3 and 4 show time series of terms in the column-integrated moist static energy bud-
193 get of the DYNAMO northern array. In fig. 3, the advection terms are computed from the
194 sounding array data, the surface turbulent fluxes from OAFLUX, and the column-integrated
195 radiative heating (surface flux minus top-of-atmosphere flux, shortwave and longwave com-
196 bined) from CERES. In fig. 4, all terms are computed from the ERA Interim Reanalysis. In
197 each figure, the column-integrated moist static energy itself is also shown for reference, as is
8 198 its time derivative.
199 Figs. 3a and 4a show the total surface turbulent heat flux (latent plus sensible), the
200 column-integrated radiative heating, and their sum. The sum varies approximately in phase
201 with the MSE itself, in quadrature with the tendency. In the first MJO active phase, the
202 radiative heating anomaly is much larger than the surface turbulent flux anomaly. In the
203 second, the anomalies in the two are comparable. In this second event, the increase in radia-
204 tive heating is more gradual, and begins earlier than, the increase in MSE itself, suggesting
205 that radiation contributed significantly to the buildup of the active phase. Similarly gradual
206 increases of column-integrated radiative heating (decrease of radiative cooling) were found
207 during TOGA COARE by Johnson and Ciesielski (2000). One plausible cause for the in-
208 crease (R. Johnson, pers. comm.) could be the increase in cirrus which has been found,
209 in recent satellite observations, to precede active MJO phases (Virts and Wallace 2010; Del
210 Genio et al. 2012). Such an increase could contribute to the buildup of moisture prior to
211 active phase onset by reducing the rate of radiatively-controlled subsidence drying in clear
212 skies (e.g., Chikira 2013).
213 Figs. 3b and 4b show column-integrated horizontal advection and vertical advection of
214 MSE, as well as their sum. The sum varies approximately in phase with the tendency of
215 column-integrated MSE, close to in quadrature with the MSE itself. In the first half of Oc-
216 tober, horizontal advection increased dramatically, during the period of anomalous low-level
217 easterly winds. The subsequent decrease in total advection (horizontal plus vertical), over
218 the course of the active phase in late October, was in large part due to vertical advection. In
219 the second MJO event, vertical advection contributed more of the increase in total advection
220 just before the active phase in the sounding data (fig. 3b) while an advective contribution
221 to the increase then is difficult to detect in the ERA (fig. 4b). In both data sets, both
222 horizontal and vertical advection contributed to the strong decrease after the peak MSE.
223 Figs. 3c and 4c compare the sum of the surface fluxes and radiative heating with the
224 sum of vertical and horizontal advection, as well of the sum of all these terms. In Fig. 3c, the
9 225 sum is similar to the actual tendency in the second event, both in structure and amplitude,
226 though the amplitude is slightly low compared to the actual tendency. In the first event,
227 the sum does not explain the sharp peak in the tendency before Oct. 16, corresponding to
228 the rapid increase in MSE during that time, although it does capture the steady decrease
229 after that. In Fig. 4c, there is more of a maximum in early October in the sum, but less of
230 a clear decrease after that. In November, the buildup is less well-captured than in Fig. 3c,
231 but the drying in the decline of the active phase is about equally evident, again modestly
232 weaker than the observed tendency.
233 Fig. 4c also shows the third MJO event (not captured in the sounding data) in the ERA
234 interim data. In that event, surface fluxes and radiation both vary in phase with MSE,
235 peaking near the peak of MSE itself, while advection drives the decrease late in the active
236 phase. There is again a conspicuous gap between the actual tendency in the buildup and
237 the sum of sources and advection, particularly in early December. As with the second event,
238 the radiative heating appears to begin increasing early, contributing to the buildup; in this
239 case, however, surface turbulent fluxes increase during that time as well.
240 Fig. 5 compares individual terms computed from the observational data sets with
241 those from the ERA-Interim Reanalysis. The agreement broadly is good. The advection
242 terms show the greatest differences, particularly in the first event. The horizontal advection
243 increases earlier and the vertical advection decreases earlier in the Reanalysis; the minimum
244 in the vertical advection is stronger as well as later in the sounding data. The turbulent flux
245 is greater in the Reanalysis than in OAFLUX, particularly in early October, but has very
246 similar temporal structure. Radiative cooling in the two data sets agrees very well.
247 Figs. 6 and 7 show time-height plots of pressure vertical velocity (a); vertical advection
248 of MSE (b); horizontal advection of moisture (c); and zonal velocity (d), in the sounding and
249 Reanalysis data, respectively. These plots lend some insight into the flow structures which
250 produce the changes in advection over the course of the events.
251 The vertical velocity shows deep ascent early in both active phases, in late October and
10 252 November. In both events, the ascent becomes more concentrated in the upper troposphere
253 towards the end, around November 1 and December 1. The vertical advection during the
254 active phases tends to be positive in the lower troposphere and negative in the upper tro-
255 posphere, as expected in ascending motion from the mean structure of MSE with its middle
256 tropospheric minimum. Though it is perhaps not so easy to discern by eye, the upper tro-
257 pospheric negative advection becomes stronger relative to the lower tropospheric positive
258 advection as the ascent becomes more concentrated in the upper troposphere late in each
259 event. This corresponds to a more positive gross moist stability, shown more explicitly below.
260 The horizontal advection variations are dominated by the layer roughly from 900-600
261 hPa in both data sets. Both show strong drying by westerlies in that layer in early October,
262 moistening in mid-October as the easterlies descend into the lower mid-troposphere and the
263 westerlies near the surface weaken, followed by a return of drying around Nov. 1. Both show
264 a similar pattern in the second event; the horizontal advective moistening is not as dramatic
265 in late November as in mid-October, but there is at least a reduction in advective drying;
266 later in the event, just before December 1, the intense westerly wind burst brings very strong
267 advective drying through a deep layer, from 400 hPa down to near the surface (reaching the
268 surface, in fact, in the sounding data).
269 Figures 8 and 9 analyze the moist static energy budget using the normalized gross moist
270 stability (NGMS), defined and discussed in section b. The NGMS has horizontal and vertical
271 components, in which only the horizontal or vertical component of MSE advection is used in
272 the numerator; the total NGMS is the sum of the two. Each column shows the horizontal,
273 vertical, and total NGMS as a function of time. The column-integrated MSE itself is also
274 shown for reference, to indicate the active and suppressed MJO phases.
275 Figure 8 computes the NGMS from the sounding data and other observational data sets.
276 Two curves are shown for NGMS in each panel. In one, the NGMS is derived directly from
277 the advection terms computed with the sounding data, while in the other, it is computed
278 as a budget residual. The difference is one measure of the degree to which the analyzed
11 279 MSE budget closes. In the budget residual calculation, the OAFlux and CERES data are
280 used for the surface turbulent fluxes and radiative fluxes respectively, while the tendency is
281 computed from the sounding data. Points at which the denominator is less than one-fifth
282 of the numerator in absolute value are not shown, in order to avoid the neighborhoods near
283 zero crossings of the denominator, at which NGMS is not well defined. Figure 9 shows
284 an analogous set of calculations from the ERA Interim data. In all cases, both numerator
285 and denominator are smoothed with a 5-day running mean time average. In both sets of
286 calculations, both components of the NGMS increase from the suppressed phase to the active
287 phase. The increase in the vertical component is weak in the ERA Interim when computed
288 directly, strong when it is computed as a budget residual.
289 In fig. 1 we introduced the overall large-scale evolution of the MJO events. Now, having
290 analyzed the moist static energy budget and seen that horizontal advection plays a signif-
291 icant role, we present a further depiction of the horizontal structures in the low-frequency
292 component of the flow to illustrate the large-scale flow patterns responsible for the horizontal
293 advection. Figure 10 shows a series of maps, each one representing a 7-day mean, of column
294 water vapor, 850 hPa horizontal vector wind, and precipitation. Precipitation is contoured
295 only at intervals of 10 mm/d, to make more apparent when and where the active phases of
296 the MJO occur. In showing 850 hPa wind, we take this to be representative of the lower-level
297 wind which is responsible for the majority of the horizontal advection.
298 We focus on the bands of latitude in which the MJO’s variations in convective activity
299 are most prominent, which lie somewhat north of the equator in October and November,
300 proceeding to south of the equator by December. In these latitude bands, the maps show
301 relatively westerly flow during suppressed phases, particularly in the central and eastern
302 longitudes of the Indian ocean basin — October 10-16, November 7-13, December 4-10 —
303 compared to the following phases, in which the moisture is increasing. As the active phases
304 mature in the succeeding weeks, strong westerlies re-develop in response to the convection,
305 again bringing in tongues of dry air from the west in October 31-November 6, November
12 306 28-December 3, and December 25-31 (in the last case, the dry air appears to come more
307 directly from the north than west).
308 The strong westerlies just north of the equator bringing dry air eastward are apparent
309 in October 10-16; the cyclonic flow pattern suggests that the source of the dry air is the
310 subtropical Arabian Sea, Indian Subcontinent, and south Asia. Very moist air is present in
311 the Bay of Bengal and South China Sea at this time; the zonal gradient of water vapor north
312 of the equator is strongly positive (increasing eastward). In October 17-23, the westerlies
313 remain in the western Indian ocean, but change to easterlies in the eastern Indian ocean;
314 one has the impression that as the monsoon westerlies relax, easterlies bring the moist air
315 west into the central Indian ocean. This allows precipitation to increase, maximizing around
316 the Maldives in October 24-30; during that period, however, the strongest westerlies are
317 found only in the western part of the basin. In October 31-November 6, the westerlies reach
318 across the near-equatorial Indian ocean, pushing dry air over the Maldives and suppressing
319 convection. In November 7-13, the monsoon over, strong westerlies are found only in the
320 eastern part of the basin. Column water vapor is relatively low (though still fairly high by the
321 standards of the earth as a whole, with values in excess of 50mm around the Maldives) and
322 precipitation is suppressed over the entire equatorial Indian ocean. On the equator, the zonal
323 gradient of column water vapor is positive. In November 14-20, stronger easterlies again relax
324 the zonal gradient, bringing moist air westward, preceding the onset of strong convection
325 during November 21-27. Strong westerlies in November 28-December 3 again bring dry air
326 (whose source again appears to be subtropical, associated with strong equatorward flow near
327 the longitude of the east African coast in both hemispheres) eastward, re-establishing the
328 zonal gradient of water vapor. A similar sequence plays out again in December.
13 329 4. Conclusions
330 We have analyzed the moist static energy budget over the sounding array from the
331 CINDY/DYNAMO field campaign, using sounding data, complementary large-scale data
332 sets for surface turbulent fluxes and radiative fluxes, and ERA Interim Reanalysis data.
333 Three MJO active phases are analyzed, though sounding data are only available for the first
334 two.
335 The results show some significant differences between the different MJO events, as noted
336 by Johnson and Ciesielski (2013); however, some commonalities are also apparent.
337 In all events, column water vapor, column moist static energy, and precipitation are
338 strongly correlated, as expected. Column radiative heating is also strongly correlated with
339 those variables. Surface turbulent enthalpy fluxes (predominantly latent heat flux) are also
340 correlated with those variables, with some lag on average as expected. The magnitude of
341 turbulent flux variations is more variable from event to event than is the magnitude of
342 radiative flux variations, and is smaller than radiative flux variations in two out of the three
343 events.
344 In all events, horizontal advection is relatively moistening (that is, more positive than
345 before or after; in some cases positive in absolute value) in the build-up to the active phase.
346 Horizontal advection is drying in the later part of the active phase itself. Large moistening
347 by horizontal advection occurs in the build-up to the October event, while large drying by
348 horizontal advection occurs during the rapid decay of the November event. Both of these
349 are consistent with a significant role for horizontal advection in the eastward propagation of
350 the MJO, but in different ways (advection ahead vs. drying behind). The December event
351 is not captured in the sounding data, but appears more similar to the November event in
352 the ERA Interim data.
353 The horizontal advection variations result largely from variations in zonal advection of
354 moisture in the 600-900 hPa layer, although the ultimate source of the dry air appears (by
355 inspection of maps) to be subtropical. In the wake of the December active phase, the dry
14 356 advection appears to be more meridional than zonal. To the extent that the source of the
357 dry air is subtropical in either case, and due to off-equatorial cyclonic gyres lagging the
358 active phase, this suggests that the fundamental mechanism is the same whether the zonal
359 or meridional wind accomplishes the advection. The relative magnitudes of horizontal and
360 vertical advection also vary across the MJO events, but the picture that emerges overall is
361 of a significant role for both in MJO propagation. Analysis of the normalized gross moist
362 stability shows particularly clearly the increase in vertical advection from suppressed to peak
363 active phase. This appears to result from a deepening layer of ascent as the active phase
364 matures.
365 Overall, these results support the view that the moist static energy anomalies associated
366 with the MJO are maintained by radiative feedbacks, with surface flux feedbacks also playing
367 a significant but perhaps secondary role; and that those anomalies propagate because of
368 advection. Though the advection is both horizontal and vertical, we speculate on theoretical
369 grounds that the horizontal advection plays a more fundamental role in determining the
370 direction of propagation. The β effect breaks the symmetry between east and west, and that
371 is most clearly evident in the horizontal flow field — e.g., as manifest in the response to
372 a stationary heat source (Webster 1972; Gill 1980) to which the MJO’s flow pattern bears
373 some broad resemblance. While the increase of the vertical NGMS with time during the
374 course of an MJO active phase (shown in figs. 8 and 9) also is associated with relative
375 moistening during onset and relative drying during decay of the active phase, and thus aids
376 propagation, we see no inherent reason why that same progression could not occur for a
377 westward-propagating disturbance.
378 Acknowledgments.
379 SSM/I and TMI data are produced by Remote Sensing Systems and sponsored by the
380 NASA Earth Science MEaSUREs DISCOVER Project. Data are available at www.remss.com.
381 We thank Richard Johnson and Paul Ciesielski for the sounding data and for discussions.
15 382 This work was supported by National Science Foundation grant AGS-1062206 and Office of
383 Naval Research grant N00014-415 12-1-0911.
16 384
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21 492 List of Figures
◦ ◦ 493 1 Hovm¨oller diagram of 10 S −10 N averaged precipitable water (mm, shaded),
−1 −1 494 precipitation (mm d , contour), and 850 hPa zonal wind (m s , arrows) dur-
−1 495 ing the CINDY/DYNAMO period. The first contours represent 10 mm d ,
−1 496 while contour interval is 10 mm d . 23
◦ ◦ −1 497 2 Area-averaged (73 − 80 E, Eq. − 5 N) time-series of a) rainfall (mm d ), b)
7 −2 498 precipitable water (mm), and c) column-integrated MSE (×10 Jm ). For
499 rainfall, data from GPCP (black), TRMM (red), budget calculation over
500 the DYNAMO northern array (green), and ERA-I (blue) are used. For pre-
501 cipitable water, SSM/I-TMI (black), the DYNAMO northern array (green),
502 and ERA-I (blue) are displayed, while the sounding array (green) and ERA-I
503 (blue) are shown for column-integrated MSE. All variables are 5-day moving
504 averaged. Note that the column integration means a mass-weighted integra-
505 tion from 1000 hPa to 100 hPa. 24
506 3 Column-integrated MSE budget terms derived from the DYNAMO northern
507 sounding array. a) Source terms: surface turbulent flux (red), column in-
508 tegrated radiative flux (green), and their sum (blue). b) Advective terms:
509 horizontal advection (red), vertical advection (green), and their sum (blue).
510 c) Source and advective terms: sum of all source terms (red), sum of all ad-
511 vective terms (green), and sum of all source and advective terms (blue). All
512 variables are 5-day moving averaged. Dotted black and solid curves in each
513 panel represent column-integrated MSE (with the vertical axis on the right)
514 and its time derivatives, respectively. 25
515 4 Same as Figure 3, except for those derived using ERA-I. 26
22 −2 516 5 Column-integrated MSE budget terms (W m ) derived from the DYNAMO
517 northern sounding array (solid), and ERA-I (dashed). a) Surface turbulent
518 flux, b) column-integrated radiative flux, c) horizontal advection, and d) ver-
519 tical advection term. All variables are 5-day moving averaged. 27
−1 520 6 Time series of a) pressure velocity (hPa h ), b) vertical and c) horizontal
−1 −1 −1 521 advection of MSE (Jkg s ), and d) zonal wind (ms ) from the DYNAMO
522 northern sounding array. All variables are 5-day moving averaged. 28
◦ ◦ 523 7 Area-averaged (73 − 80 E, 0 − 5 N) time series of a) pressure velocity (hPa
−1 −1 −1 524 h ), b) vertical and c) horizontal advection of MSE (Jkg s ), and d) zonal
−1 525 wind (ms ) from ERA-I. All variables are 5-day moving averaged. 29
526 8 Estimated GMS using the DYNAMO northern sounding array. a) Horizontal,
527 b) vertical, and c) horizontal plus vertical component. Blue solid curve de-
528 notes GMS directly estimated from the advection terms, while red solid curve
529 denotes GMS indirectly estimated from the budget residual. Black dashed
7 −2 530 curve shows column-integrated MSE (×10 Jm ). All variables are 5-day
531 moving averaged. 30
532 9 Estimated GMS using ERA-I. a) Horizontal, b) vertical, and c) horizontal plus
533 vertical component. Blue solid curve denote GMS directly estimated from
534 the advection terms, while red solid curve denotes GMS indirectly estimated
535 from the budget residual. Black dashed curve shows column-integrated MSE
7 −2 536 (×10 Jm ). All variables are 5-day moving averaged. 31
537 10 Map view of weekly mean column water vapor (mm, shaded), 850 hPa vector
−1 −1 538 wind (arrows), and precipitation (mm d , contour interval 10 mm d ; lowest
−1 539 contour value shown 10 mm d ). 32
23 Fig. 1. Hovm¨oller diagram of 10◦S − 10◦N averaged precipitable water (mm, shaded), −1 precipitation (mm d , contour), and 850 hPa zonal wind (m s−1, arrows) during the − CINDY/DYNAMO period. The first contours represent 10 mm d 1 , while contour interval −1 is 10 mm d .
24 −1 Fig. 2. Area-averaged (73 − 80◦ E, Eq. − 5◦N) time-series of a) rainfall (mm d ), b) precipitable water (mm), and c) column-integrated MSE (×107Jm−2). For rainfall, data from GPCP (black), TRMM (red), budget calculation over the DYNAMO northern array (green), and ERA-I (blue) are used. For precipitable water, SSM/I-TMI (black), the DYNAMO northern array (green), and ERA-I (blue) are25 displayed, while the sounding array (green) and ERA-I (blue) are shown for column-integrated MSE. All variables are 5-day moving averaged. Note that the column integration means a mass-weighted integration from 1000 hPa to 100 hPa. Fig. 3. Column-integrated MSE budget terms derived from the DYNAMO northern sound- ing array. a) Source terms: surface turbulent flux (red), column integrated radiative flux (green), and their sum (blue). b) Advective terms: horizontal advection (red), vertical ad- vection (green), and their sum (blue). c) Source and advective terms: sum of all source terms (red), sum of all advective terms (green), and sum of all source and advective terms (blue). All variables are 5-day moving averaged.26 Dotted black and solid curves in each panel represent column-integrated MSE (with the vertical axis on the right) and its time derivatives, respectively. Fig. 4. Same as Figure 3, except for those derived using ERA-I.
27 Fig. 5. Column-integrated MSE budget terms (W m−2) derived from the DYNAMO north- ern sounding array (solid), and ERA-I (dashed). a) Surface turbulent flux, b) column- integrated radiative flux, c) horizontal advection, and d) vertical advection term. All vari- ables are 5-day moving averaged. 28 fME(Jkg MSE of l aibe r -a oigaveraged. moving 5-day are variables All Fig. Pres(hPa) Pres (hPa) Pres(hPa) Pres(hPa) 1000 1000 1000 1000 800 600 400 200 800 600 400 200 800 600 400 200 800 600 400 200 .Tm eiso )pesr eoiy(P h (hPa velocity pressure a) of series Time 6. 01/Oct 01/Oct 01/Oct 01/Oct
(a) Omega(hPa/h) (d) Zonalwinds(m/s) (c) − (b) − − 1 V Ω⋅ s − ⋅∇ dh/dp (J/Kg/s) 1 ,add oa id(ms wind zonal d) and ), Q (J/Kg/s) 15/Oct 15/Oct 15/Oct 15/Oct 01/Nov 01/Nov 01/Nov 01/Nov − 1 29 rmteDNM otensudn array. sounding northern DYNAMO the from ) − 1 15/Nov 15/Nov 15/Nov 15/Nov ,b etcladc oiotladvection horizontal c) and vertical b) ), 01/Dec 01/Dec 01/Dec 01/Dec 15/Dec 15/Dec 15/Dec 15/Dec
−10 −5 0 5 10 −0.05 0 0.05 −0.05 0 0.05 −10 0 10 R-.Alvralsae5dymvn averaged. moving 5-day are variables All ERA-I. )vria n )hrzna deto fME(Jkg MSE of advection horizontal c) and vertical b) Fig. Pres(hPa) Pres (hPa) Pres(hPa) Pres(hPa) 1000 1000 1000 1000 800 600 400 200 800 600 400 200 800 600 400 200 800 600 400 200 .Ae-vrgd(73 Area-averaged 7. 01/Oct 01/Oct 01/Oct 01/Oct
(a) Omega(hPa/h) (d) Zonalwinds(m/s) (c) − (b) − V Ω⋅ ⋅∇ dh/dp (J/Kg/s) Q (J/Kg/s) 15/Oct 15/Oct 15/Oct 15/Oct − 80 ◦ ,0 E, 01/Nov 01/Nov 01/Nov 01/Nov − 5 ◦ )tm eiso )pesr eoiy(P h (hPa velocity pressure a) of series time N) 30 15/Nov 15/Nov 15/Nov 15/Nov − 1 s − 1 ,add oa id(ms wind zonal d) and ), 01/Dec 01/Dec 01/Dec 01/Dec 15/Dec 15/Dec 15/Dec 15/Dec −
1 from ) − −10 −5 0 5 10 −0.05 0 0.05 −0.05 0 0.05 −10 0 10 1 ), Fig. 8. Estimated GMS using the DYNAMO northern sounding array. a) Horizontal, b) vertical, and c) horizontal plus vertical component. Blue solid curve denotes GMS directly estimated from the advection terms, while red solid curve denotes GMS indirectly estimated from the budget residual. Black dashed curve shows column-integrated MSE (×107Jm−2). All variables are 5-day moving averaged.
31 Fig. 9. Estimated GMS using ERA-I. a) Horizontal, b) vertical, and c) horizontal plus vertical component. Blue solid curve denote GMS directly estimated from the advection terms, while red solid curve denotes GMS indirectly estimated from the budget residual. Black dashed curve shows column-integrated MSE (×107Jm−2). All variables are 5-day moving averaged.
32 Fig. 10. Map view of weekly mean column water vapor (mm, shaded), 850 hPa vector wind (arrows), and precipitation (mm d−1, contour interval 10 mm d−1; lowest contour value shown 10 mm d−1).
33