African Easterly Waves, Observations and Theory

African Easterly Waves, Observations and Theory Nick Hall LEGOS / Univ. Toulouse Stephanie Leroux LTHE / Univ. Grenoble George Kiladis ESRL NOAA, Boulder Chris Thorncroft - SUNY, Albany

Three questions How do easterly waves grow? How are they initiated? How do they interact with convection?

The birth of hurricane Alberto

The West African monsoon TEJ AEJ Hadley Cell E H R Θe

Climatology of transient disturbances shading: OLR contours: wind and standard deviation of OLR and vorticity

<6-day Perturbation kinetic energy: 10-120 day filtered (shading) P KE = u 2 + v 2 2 700 mb 850 mb (a) mean PKE 700 mb and EOF1 (8.6 %) (b) mean PKE 850 mb and EOF1 (9.1 %) EOF1 1 2 1 1.5 0.5 1.5 1 0.5 - EOF2 (5.1 %) - EOF2 (4.6 %) EOF2 0.5-6 -4-4 6-1 -0.5-1 -0.5-6 -4-4 6 0.5 fig3

Zonal wind 600 mb June-Sept NCEP2 1980-2006 -4 (a) Mean Jun-Sep. non filt. zonal wind 600 mb -6-8 -2-6 -4-4 6-4 -8-10 -6 Climatology (b) Jun-Sep. non filt. zonal wind 600 mb EOF1 (16.2 %) -2-3 -1 1-4 -6-4 - 4 6 (c) Jun-Sep. 0-120d filt. zonal wind 600 mb EOF1 (6.6 %) 1-3 -6-4 - 4 6 (d) Jun-Sep. 10-120d filt. zonal wind 600 mb EOF1 (10.2 %) -1 1-6 -4-4 6 2 1 2 EOF2 (6.6 %) -6-4 - 4 6 1 2 EOF2 (5.7 %) -6-4 - 4 6 1 EOF2 (8.5 %) -6-4 - 4 6-1 -1 Unfiltered EOFs 0-120 day filtered EOFs 10-120 day filtered EOFs fig 1

Space-Time Spectrum of JJA Antisymmetric OLR, 15S-15N Wheeler and Kiladis 1999

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 0 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 01 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 01 2 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 01 23 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 01 23 4 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

Regression Analysis OLR and 850mb streamfunction regressed against space-time filtered OLR (TD band) at 10N,10W : June-Sept 79-93 Day -5-4 -3-2 -1 01 23 45 OLR anomaly > < 10 W/m2, streamfunction ci=2x105 m2/s

NCEP2 2-6d filtered V700mb JJAS.2006 2006 2-6 day filtered 700 mb meridional wind - NCEP2 10-120 day filtered PKE NCEP2 PKE 10-120d 10-120d filtered filtered pke700mb JJAS.2006 JJAS.2006 270 270 265 265 260 255 260 255 250 245 250 245 240 240 235 230 235 230 225 220 225 220 215 215 210 205 210 205 200 200 195 190 195 190 185 180 185 180 175 170 165 160 155 175 170 165 160 155 P KE = u 2 + v 2 2-60 -50-40 -30-20 -10 0 10 20 30 40 50 60 longitude -60-50 -40-30 -20-10 0 10 20 30 40 50 60 longitude -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 filtered V700mb (m/s) -12-11-10 0 1-9 -8 2-7 -6 3-5 -4 4-3 -2 5-1 60 1 72 3 84 5 96 7 10 8 9 11 10 11 12 filtered PKE (m^2.s^-2)

A brief history of ideas on African transient disturbances In the beginning, there was GATE: Eady/Charney, Burpee,... Thorncroft and Hoskins... etc.

A brief history of ideas on African transient disturbances In the beginning, there was GATE: Eady/Charney, Burpee,... Thorncroft and Hoskins... etc. then came Stone. Farrel, etc - and their ideas applied to the African easterly jet: but the AEJ is also short, and variable

Possible Jet - Wave relationships: instability hypothesis simple triggering T T variable jet triggering T T can we see these ideas at work in the observations?

Regression of 10-120 day 600 mb zonal wind (m/s) onto 700 mb PKE index -6-4 - 4 6 8 10 1 Day -6 Day -4 Day -2-0.2-0.2 DAY 0 Day+2 Day+4 Day +6-0.4-0.2-0.4-0.2-0.4 0.2-0.4-0.2-0.4-0.2-0.2-0.4-0.2-0.2-0.2-0.2-0.2 0.4 0.2-0.6-0.6-0.4-0.6-0.4-0.4-0.2-0.6-0.4-0.2-0.4-0.2-0.4-0.6-6 -4-4 6 8 10 1-0.2 m/s 1 N Σα i X i 1 N Σα2 i αi is the PKE index in the box Xi is the zonal wind fig8

E vectors Regression of 10-120 day E-vectors onto 700 mb PKE index (vectors ~ 1 m 2 /s 2, contours of div E every 10-6 ms -2 ) ) E = (u 2 v 2, u v E vectors converge where easterlies are accelerated by transients. An eastward pointing E vector has north-south elongated eddies. A westward pointing E vector has east-west elongated eddies. A southward pointing E vector has NE-SW oriented eddies

PV gradient -6-4 - 4 6 Regression of 10-120 day 320K PV gradient onto 700 mb PKE index (contours 10-10 K m Kg -1 s -1 ) Day -6 Day -4 Day -2 DAY 0 Day +2 Day +4 Day +6-6 -4-4 6 fig10

Relationship between convection and transients Regression of 10-120 day NOAA OLR (W m -2 ) onto 700 mb PKE index -6-4 - 4 6 8 10 1 Day -6 Day -4 Day -2 DAY 0 Day+2 Day+4 Day +6-1 -2-1 -1-1 -6-4 - 4 6 8 10 1 1 1 2-4 -3-1 fig11

Try it the other way round Regressions onto OLR index (a) 10-120d filt. OLR -6-4 - 4 6 Day -6 Day -4 Day -2 DAY 0 Day+2 Day+4 Day +6-4 -6-6 -2-4 -2-4 -2-2 -6-4 - 4 6-2 -2 PKE (b) 10-120d filt. PKE at 700 mb -6-4 - 4 6 Day -6 Day -4 Day -2 DAY 0 Day+2 0.1 0.2 0.2 Day+4 0.1 0.2 Day +6-0.1 0.1 0.1-0.2 0.3-0.2 0.2 0.1 0.2 0.2 0.4 0.2 0.3 0.1 0.3-6 -4-4 6 fig12

Conclusions so far... - Prior to increased transient activity, the upstream AEJ is reinforced. - Afterwards, the downstream AEJ is shifted to the north. - Eddy momentum forcing from transients is consistent with this AEJ development. - Increased transients over W. Africa are associated with increased convection on intraseasonal timescales. - Increased transient activity tends to follow peaks in convective activity in an upstream location.

generalized development Generic equation for the development of a nonlinear system q t = Lq.vq + f introduce a state vector Φ =( v, q,...) this becomes dφ dt = LΦ +Φ QΦ + f where Φ is the diagonal matrix that contains the elements of Φ

basic state separation: 1 specify a basic state that is a solution of the equations Φ =Φ 0 + Φ 1 dφ 0 f = f 0 + f 1 dt and LΦ 0 + Φ 0 QΦ 0 + f 0 =0 so =0 dφ dt = LΦ +Φ QΦ + f dφ 1 dt = LΦ 1 + Φ 1 QΦ 0 + Φ 0 QΦ 1 + Φ 1 QΦ 1 + f 1 or to put it another way dφ 1 dt = L 0 Φ 1 + O(Φ 2 1)+f 1 ADVANTAGE: eddy development independent of separation DISADVANTAGE: basic state unrealistic so nonlinear term large - linearization of questionable relevance

basic state separation: 2 specify a realistic basic state (for example, the time mean flow) but this time in fact we have and Φ = Φ +Φ f = f + f LΦ + Φ QΦ + f 0 dφ dt =0 mean advection LΦ + Φ QΦ + Φ QΦ + f =0 dφ transient eddy forcing dt = LΦ + Φ QΦ + Φ QΦ + dφ dt = LΦ +Φ QΦ + f [Φ QΦ Φ QΦ ] ADVANTAGE: realistic basic state so meaningful linearization possible DISADVANTAGE: linear development equation not independent of time mean transient forcing + f or to put it another way dφ dt = L meanφ + [ ] O(Φ 2 ) O(Φ 2 ) + f

a perturbation model So much for theory. How do we solve these equations? We use a dynamical model. We can appeal to data to deduce the appropriate forcing functions: data dφ dt = LΦ +Φ QΦ + f(t) model dψ dt = LΨ +Ψ QΨ + g We now define g using data, so that if we initialize the model with Φ it will not develop. so g = LΦ Φ QΦ We can easly find g by integrating the unforced model from Φ for just one timestep. From the time-mean budget equation we also see that this definition of g gives g = f + Φ QΦ So this forcing represents the time mean diabatic forcing plus the mean transient eddy forcing. These are the two processes that maintain the time-mean circulation.

stability analysis With our data-derived forcing, for small perturbations, integrating dψ dt = LΨ +Ψ QΨ + g is equivalent to integrating dψ dt = L mean Ψ We use the dynamical model to analyse the linear growth problem for normal modes of Lmean L mean e n (x, y, z) =λ n e n (x, y, z) for a single mode λ n = σ + iω Ψ n = e n (x, y, z)e (σ+iω)t in general en is complex so the solution takes the form Ψ =[A(x, y, z) sin ωt + B(x, y, z) cos ωt] e σt

response to forcing We can use our dynamical model to find the response to a perturbation forcing f dψ dt = L mean Ψ + f (and if we keep f small the response is linear) Start with another example from African easterly waves. This time we use a (convective) heating anomaly as f, to trigger a response. The response still looks like the normal mode that we found before. But it decays in time.

explicit transients: a simple GCM Let s reconsider the definition of our forcing function g. Recall the development equations: data dφ dt = LΦ +Φ QΦ + f(t) model dψ dt = LΨ +Ψ QΨ + g If we set g = f g = LΦ Φ QΦ Φ QΦ then this is the same as setting i.e. we have subtracted out the time-mean forcing due to the transients. Again, we can calculate this forcing by initializing the unforced model from a series of values of and then taking the time-average. Φ Φ If the model is now initialized with it will develop in time. In fact we hope it will develop its own explicit transient activity. And we hope that it will be realistic. But there is no guarrantee that this simple GCM will have a realistic climatology. The only thing that is guarranteed is that: LΨ + Ψ QΨ + Ψ QΨ = LΦ + Φ QΦ + Φ QΦ

nudge nudge Another way of forcing a model is to push it towards a desired climatology in a restricted region, and look at the effect on the solution outside that region. This is called nudging. dψ dt = LΨ +Ψ QΨ + g + ( ) Φn Ψ Nudging involves an additional constant forcing term and a damping term. In a linear experiment, the appropriate model is: τ dψ dt = L mean Ψ + ɛ ( ) Φn Φ Ψ τ τ This can be useful technique for diagnosing climate anomalies or simulating other people s GCMs with a simple model.

Previous work

The African Easterly Jet sector mean 60W-60E slice at Greenwich slice at 12N Thorncroft 1995 - Which (if any) zonal section is appropriate? - Are these basic states unstable? - Is instability important? - Which structures are the most efficient at extracting energy from this flow? 650 mb zonal wind NCEP JJAS mean 68-98

Effect of low level damping on modal growth rate Hall and Sardeshmukh 1998

Normal Mode Structures: Zonal Basic State Horizontal streamfunction at 850 mb and 12N Greenwich Slice Growth rate: 0.473 days-1 Period: 4.88 days

Normal Mode Structures: Zonal Basic State Horizontal streamfunction at 850 mb and 12N Sector Greenwich Mean 60W-60E Slice Growth rate: 0.473 days-1 Period: 4.88 days

Normal Mode Structures: Zonal Basic State Horizontal streamfunction at 850 mb and 12N Sector Greenwich Mean 60W-60E Slice Growth rate: 0.473 0.144 days-1 Period: 4.88 5.44 days

Normal mode structures: 3D basic state Growth rate: 0.272 days-1 Period: 5.56 days

Normal mode structures: 3D basic state Add damping below 800 mb: 2 days on momentum, 4 days on temperature Growth rate: -0.003 0.272 days-1 Period: 5.51 5.56 days

Observations Model

Fluxes through the looking glass Low Low High C PV W - + W C - Easterly waves transport heat southwards (away from the Saharan heat source). - But they still have convergent momentum transport, so they deplete the African easterly jet.

Eddy Fluxes Maritime decay region Wave maximum region Wave inception region 60-30W 30W-0 0-30E northward temperature flux v't' momentum flux u'v'

model 0-30W average regression 10W 17.5W 500mb 500mb 500mb 500mb EQ 30N EQ 30N EQ 30N

Some wave properties

basic state damped modal structure d-1 Some more basic states.33 Growth rates are given for undamped experiments. Damped modes are all close to neutral.25.25.20 Active year.17 Quiet year.23 650mb zonal wind ci=2 m/s 850 mb streamfunction and vertical motion

Initial value problems - If normal mode solutions are neutral they can tell us about efficient structures. - But we still lack a complete theory for the generation and intermittence of AEW events. heat for one day in an elipse with a cosine squared bell shaped distribution and various vertical profiles

An influence function for heating experiments shallow convective profile H 0 =5σ 4

Sensitivity to size and profile deep convective deep convective with low level evaporation [ ] H 0 = π(1 σ) sin(π(1 σ)) H 0 = 9π2 3π (1 σ) cos (1 σ) 2(3π + 2) 2 shallow convective radius 5 deg shallow convective radius 7 deg H 0 =5σ 4 H 0 =5σ 4

Are triggered waves sensitive to a varying easterly jet? 10-day averaged basic states NCEP II reanalysis (1979-2006) >> 336 jets >> 336 perturbation experiments zonal wind at 650 mb

Are triggered waves sensitive to a varying easterly jet? 10-day averaged basic states NCEP II reanalysis (1979-2006) >> 336 jets >> 336 perturbation experiments zonal wind at 650 mb day 2 day 5 day 8 stream-function at 850 mb

A measure of the intensity of the wave response: stream-function at 850 mb - day 10 Root mean square stream function anomaly at 850 mb, averaged from day 1 to day 18. How does the basic state influence the intensity of the response?

Dependance of wave response on spatial EOFs of basic state 650 mb zonal wind? 30 1st mode of variation (35%) EOF1 (35%) 20 10 0!60!30 0 30 60 30 2nd mode EOF2 of variation (12%) (12%) 20 10 0!60!30 0 30 60

Dependance of wave response on spatial EOFs of basic state 650 mb zonal wind? 30 1st mode of variation (35%) EOF1 (35%) 20 10 0!60!30 0 30 60 1st Principal Component 100 50 0!50!100!50 0 50 2nd Principal Component bottom 20% weakest wave responses (blue dots) top 20% strongest wave responses (orange dots) The strongest waves are mainly associated with jets that are strong in the south and west. 2nd mode EOF2 of variation (12%) (12%) 30 20 10 0!60!30 0 30 60

Composite jets for strong and weak responses 40 30 20 10 zonal wind at 650 mb!4!8 4 40 30 20 10 zonal wind at 650 mb!4!8!8 4!4 0!4!8!10!60!40!20 0 20 40 60!4 0!10!60!40!20 0 20 40 60!4 Composite jet for the top 20% strongest wave responses Composite jet for the bottom 20% weakest wave responses

Some more conclusions... - Taking account of the jet entrance/exit structure of a realistic AEJ, even in a linear model analysis can take us a lot further towards explaining the 3-d structure of observed AEW composites. - A modest amount of surface damping with a realistic 3-d basic state produces neutral modes. We therefore need to reexamine the traditional instability hypothesis for the timing of AEW growth. - Instead, we look for finite amplitude perturbation events to initiate AEWs. - The strength of the wave response is sensitive to the position of the finite amplitude trigger - convection over the Darfur region is the most efficient. - The response is also very sensitive to the state of the AEJ, as suspected from the observational analysis, although the details differ. however... - The modelling results shown so far do not take into account two-way wavejet interacitons. - Neither do they take into account tropical - extratropical interactions

Use the simple GCM (perpetual JJAS mode) June-September 1979-2006 NCEP2 reanalyses Simple GCM Climatological zonal wind (contours 5 m/s)

< 120 day transient covariances momentum flux c.i. 10/5 m 2 /s 2 temperature flux c.i. 3/2 K m/s EKE c.i. 50/15 m 2 /s 2 Reanalyses Model

zoom over the African easterly jet shading shows standard deviation

momentum flux c.i. 0.5/0.3 m 2 /s 2 temperature flux c.i. 0.3/0.2 K m/s EKE c.i. 1/0.25 m 2 /s 2

eastward propagating disturbances: reanalysis meridional wind anomaly and 10-120 day filtered EKE (contours)

eastward propagating disturbances: model

regression analysis from model <120 day filtered streamfunction regressed onto <10 day filtered meridional wind at base point 9.5N 7.5W

standard run transients suppressed north of 30N Contours of zonal wind. EKE shaded in green and yellow transients suppressed south of equator transients suppressed north of 30N and south of equator transients suppressed east of 45E in the NH

regression analysis from model 0-120 day filtered variables regressed onto AEW activity index 650 hpa streamfunction zonal wind

regression analysis from reanalysis 0-120 day filtered variables regressed onto AEW activity index 650 hpa streamfunction zonal wind

Last set of conclusions - A convection-free model with explicit transient activity can reproduce observed transient activity, albeit with a reduced amplitude. - It can also produce realistic African easterly waves with an amplitude that is stronger than our simulations triggered by convective heat sources. - The easterly waves it produces again resemble linear modes of the AEJ. - However, they disappear entirely if variability is restricted to the tropical band, shedding further doubt on the idea that small perturbations can grow on the AEJ. - The simulated AEWs also show intermittency, without the need for intermittent upstream heating. - Experiments show that the Atlantic storm track is crucial for the existence of these intermittent AEWs. - In the model, statistical precursors appear to originate in the Atlantic storm track, but it is difficult to corroberate this finding from the observations.