Haurwitz Memorial Lecture

Transcription

1 Haurwitz Memorial Lecture Scale InteracAons and the GeneraAon of Low- Frequency Variability in the Atmosphere Dennis L. Hartmann Department of Atmospheric Sciences University of Washington AOFD MeeAng Spokane, Washington June 15, 2011

2 Bernhard Haurwitz Born 14 August 1905, Glogau, Lower Silesia Studied at U's of Breslau, and GöUngen PhD under Ludwig Weickmann at Leipzig, 1927 Inferred the veracal structure of midlaatude storms from balloon measurements Joined Rossby at MIT in 1932 Studied the effect of cloud type on solar radiaaon from measurements (Manabe and SAckler, 1964) Deduced from theory the compensaaon depth of hurricanes to be ~10km, and the eyewall to be funnel- shaped. Haurwitz(1936)

3 Bernhard Haurwitz Carnegie Fellow at U. of Toronto , visiang lecturer unal 1941 supported by Canadian Met. Service Three classic papers on dynamic meteorology, > Rossby- Haurwitz Waves Published Dynamic Meteorology in 1941 Associate Professor MIT, July 1941 Chair of Dept. of Meteorology at NYU 1947 Moved to University of Colorado and HAO 1959 Moved to NCAR in 1964 Lectured at U. of Alaska Fairbanks Lectured at Colorado State University

4 Rossby- Haurwitz Wave Theory Haurwitz (1937) The OscillaAons of the Atmosphere, Gerlands Beitrag. Geophys. 51, Rossby and Collab. (1939) RelaAon between variaaons in the intensity of the zonal circulaaon of the atmosphere and the displacements of the semi- permanent centers of acaon, J. Mar. Res. 2, 38- " c = U 1! L2 % $ 2 ' L s = 2( U # L s & ) Haurwitz (1940a) The moaon of atmospheric disturbances, J. Mar. Res. 3, 35 extended Rossby (1939) to finite- width channel with fricaon. Haurwitz(1940b) The moaon of atmospheric disturbances on a spherical Earth, J. Mar. Res. 3, some of his soluaons on a sphere to the barotropic equaaons are exact, and people refer to that soluaon as the Rossby- Haurwitz Wave, which has been used to test dynamical codes (e.g. Bourke (1972) and Hoskins (1973)).

5 Rossby- Haurwitz Wave Theory " c = U $ 1! L2 2 # L s % ' L s = 2( U & ) c = U! " 4# 2 L2 For fixed c, L increases with U For fixed c and U, L increases as beta decreases

6 Outline IntroducAon to Eddy- Driven, Self- Maintaining Jets on Earth and in Earth- Like models Variability of Eddy- Driven Jets Barotropic models of eddy driven jet variability. Localized jets and Eddy Feedbacks Rossby Wave Scales and jet laatude

7 Annual Momentum ERA- 40 From the mass- averaged zonal- mean momentum balance, it seems the only way to induce midlaatude westerly jet is with meridional eddy momentum transport.!! u [ ]!t " #! $ "!y u* v % * & # ' KD $ u & % sfc '

8 Why Eddies move Momentum We now relate meridional eddy momentum flux to the generaaon, propagaaon and breaking of Rossby waves. Rossby waves are generated preferenaally in the Extratropics, primarily by baroclinic instability. Rossby waves propagate away from their source regions, and flux momentum in the opposite direcaon toward the wave source region. Rossby waves propagate preferenaally toward the Tropics and they break there as they approach criacal lines deduced from linear theory. AcceleraAon of zonal momentum in the same direcaon as the rotaaon in regions of wave generaaon is required when a gradient in absolute voracity is present.

9 Barotropic Cartoon

10 Eddy, Mean- Flow Jet StabilizaAon Conceptual Model Wave Breaking - Easterly AcceleraAon Wave Source in Jet Westerly AcceleraAon Wave propagaaon out of jet Haurwitz Lecture 2011

11 !u!t = "!!y u 'v' = v'# ' Wave Breaking - Easterly AcceleraAon! + Wave Source in Jet Westerly AcceleraAon! " Wave propagaaon out of jet Haurwitz Lecture 2011

12 Eddy- Driven Jets Eddies must have source in jet e.g. conversion from potenaal to kineac energy as in baroclinic instability thermal gradient is largest under jet, or in Tropics, convecaon. Eddies must be able to propagate out of jet, mostly meridionally, and break elsewhere in order to move momentum around permanently.

13 Panena (1993) Broad, Baroclinic, doubly periodic - plane U top U bonom Flow organizes into strong westerly jets, separated by weak easterlies Temperature and PotenAal VorAcity gradients maximize in these jets, heat flux more uniform. Jets persist and slowly move around in laatude in presence of highly turbulent flow.! " # "y u* v $ * % & f [v] In upper layer momentum balance is between eddy momentum flux convergence, driving jet, balanced by mean meridional circulaaon. In the lower layer (not shown here) the balance is between mean meridional circulaaon and drag.

14 Observed Zonal Flow in Southern Hemisphere Eddy- Driven jet is characterized by Surface westerlies, Is clearly disanguished from the Hadley- driven subtropical jet, And is present in all seasons. First EOF is robust and represents a meridional ship of the jet posiaon. Hartmann and Lo, 1998

15 Southern Annular Mode Expressed as EOF of zonal mean wind The first EOF is a ship with laatude: larger variance and more persistent. The Second EOF is an intensificaaon (pulse) of the climatological jet at 50S: less persistent. Hartmann and Lo, 1998

16 Southern Hemisphere Eddy- Driven Jet. First EOF represents N- S ship of eddy driven jet. 1.5 standard deviaaon of PC- 1 corresponds to 10 laatude ship of surface westerlies. Hartmann and Lo, 1998

17 Southern Hemisphere Eddy- Driven Jet. Momentum Budget of Meridional Eddy- Jet Meandering Transformed Eulerian Mean FormulaAon Residual Circ. Barotropic Baroclinic aka Form Drag Drag determined as residual Hartmann and Lo, 1998

18 Momentum Budget of Meridional Eddy- Jet Meandering Barotropic Baroclinic aka Form Drag Total Eddy Forcing Residual Circ. Drag determined as residual Hartmann and Lo, 1998

19 Residual CirculaAon and Self- Maintenance of Anomalies f [!v] Eddy momentum flux at top drives residual circulaaon that sustains surface zonal wind anomalies against drag ~!K D [u] Poster 19 Xia, Guo & Chang diabaac damping AdiabaAc heaang associated with residual circulaaon supports meridional temperature gradient against eddy heat flux convergence. Hartmann and Lo, 1998

20 Self- Maintenance and Eddy Feedback Eddy- Driven jets are self- maintained, and Eddies can feed back on zonal flow anomalies to enhance them and enhance the persistence of anomalies Counter argument: The diagnosacs are just showing dynamical consistency and its all random, zonal flow is more persistent because it is weakly damped.

21 QuanAficaAon of Eddy Feedback Lorenz and Hartmann (2001) Demonstrate net posiave eddy feedback for first EOF meridional ship of jet. Feedback accounts for about half of the low- frequency variance of this mode of variability. Demonstrate no feedback for second EOF pulsing of strength of jet. Strong high- frequency eddy feedback Slightly weaker negaave feedback by other eddies not as strongly sourced in jet and are refracted into jet.

22 Linear System Simple Model of PosiAve Eddy Feedback dz dt = m! z " M=- d/dy(u v ) Assume part of momentum forcing depends on zonal wind. m =!m + bz Choose b to explain long- term memory, then z without feedback can be computed. d!z dt = z!m!! " b. High- frequency eddies produce low- frequency forcing, because they respond to zonal flow. Lorenz & Hartmann, 2001

23 Zonal Asymmetry Eddy feedbacks drive climatological zonal- mean wind jets and add persistence to north- south shiping anomalies. But atmosphere has zonal asymmetry. Repeat analysis, but ship to analysis of voracity, rather than zonal- mean wind. Simple scalar budget Doesn't assume structure

24 Geographic View of AAO/SAM Subtropical Jet MidlaAtude Jet Shading = Climatological zonal wind Contours = SAM Structure SAM is meridional ship of zonal wind, slightly downstream of eddy- driven midlaatude jet. Barnes & Hartmann, 2010b JAS Haurwitz Lecture 2011

25 Eddy Feedback CalculaAon Since we are not taking zonal averages, it is easier to use the voracity budget, which is a scalar quanaty, with a handy conservaaon equaaon. Haurwitz Lecture 2011

26 Eddy VorAcity Flux Feedback in Southern Hemisphere AAO/SAM VorAcity Structure at upper levels! ' SAM ~ 2.5 days " ( V '! ') Synoptic SynopAc eddy voracity flux convergence associated with SAM Barnes & Hartmann, 2010b, JAS Haurwitz Lecture 2011 (all definiaons based on EOF of sea level pressure)

27 Does forcing panern match response? Transient eddies provide a voracity flux that reinforces voracity signature of jets. Amplitude is sufficient to replace voracity anomaly in less than a week. Is voracity forcing that is in- phase with voracity anomaly efficient for reinforcing the panern? (e.g. would forcing in shape of mean panern actually reinforce panern or produce some other panern, like a Rossby wave downstream?) Haurwitz Lecture 2011

28 Barotropic response to VorAcity Dipole 5- day linear drag Steady VorAcity Dipole forcing = F dipole Random Red Noise added = F VorAcity Forcing VorAcity Response Zonal Wind Response Haurwitz Lecture 2011 Zhu & Hartmann 2011

29 Eddy Feedback in 3- D Eddies flux voracity into voracity maximum VorAcity input at upper levels is balanced by a divergence term VerAcal moaon to support upper level divergence a. Cools center of voracity anomaly. b. Supports convergence at lower levels to balance drag. VorAcity anomaly is more persistent than it would be in the absence of high- frequency eddies. Haurwitz Lecture 2011 Barnes & Hartmann 2010a

30 Eddy Feedback Jet Self- Maintenance Robinson (2000, 2006) Baroclinic eddies are generated They propagate away and dissipate elsewhere, leaving a barotropic westerly wind anomaly Surface drag generates baroclinicity (residual circulaaon is involved here) Baroclinic eddies are generated Assumes conanued forcing of broad baroclinic zone

31 Is a Movable Wave Source Necessary? Meridional eddy propagaaon seems criacal, and this is determined by horizontal wind shear, not baroclinicity. VerAcal eddy flux seems less criacal to the variaaon than meridional eddy flux. A Barotropic model with fixed eddy sarring of voracity explains most of the interesang features (Vallis et al 2004; Barnes et al. 2010)

32 RelaAve change of u'v' much bigger Contour interval 1.5 m/s/day Contour interval 0.4 m/s/day Hartmann and Lo, 1998

33 Barotropic Model SArring of eddies voracity in broad envelope in mid laatudes produces an eddy driven jet that has many of the characterisacs of observed annular variability in data and baroclinic models (Vallis et al. 2004). Eddy Wind Wind EOF Zonal Wind Zonal Wind Eddy SArring

34 Observed Features that the Barotropic model produces Shiping and Pulsing Modes (Vallis et al '04) Shiping mode has persistence similar to observaaons (Vallis et al 04) Shiping mode has posiave eddy feedback, pulsing mode does not. (LH'01, Barnes et al '10) NegaAve skewness of the shiping mode more persistent when jet is displaced toward the equator. Change from ship to pulse as the jet moves poleward Less eddy feedback and persistence as the jet moves poleward Weakened shiping mode enhanced pulsing mode as eddy- driven jet moves closer to subtropical jet (BH'11)

35 Barotropic Model LaAtude and Scale SAr as in Vallis et al. (2004), but move eddy forcing across laatude from 30 to 40 to 50. Scale of the resulang eddies is larger for higher laatudes. Zonal Wind Wind EOF Zonal Wind Scale of Eddy Forcing Scale of Eddy Response Barnes & Hartmann, 2011

36 Barotropic Model LaAtude and Scale Total wavenumber and zonal scales as a funcaon of eddy- driven jet laatude, and quasi- linear theory. Kidston et al jet ship scale increase. Zonal Wind Wind EOF Zonal Wind Total Wavenumber Scaling Zonal Length Scale Barnes & Hartmann, 2011

37 Barotropic Model LaAtude and Scale Quasi- Linear model: reduce wave amplitude by factor of 100 and increase momentum flux by corresponding factor - > linear waves, but comparable magnitude of eddy momentum flux to nonlinear integraaon. Zonal Wind Wind EOF Zonal Wind 30- degree Jet 50- degree Jet Barnes & Hartmann, 2011

38 Barotropic Model LaAtude and Scale Phase speeds and wind speeds are similar for the 30- and 50- degree jets, so the scale change seems mostly related to laatude. Zonal Wind Wind EOF Zonal Wind 30- degree Jet 50- degree Jet VorAcity Power spectra as funcaon of zonal wavenumber and phase speed Barnes & Hartmann, 2011

39 Increase in eddy scale with more poleward eddy- driven jet Since zonal wind and phase speed don t change much, it must be primarily laatude that causes the increase in scale, in these barotropic experiments.

40 SpaAal Scales in ERA- 40 Reanalysis EsAmate scale through the one point correlaaon map of voracity anomalies, aper removing mean seasonal cycle from daily instantaneous fields. Haurwitz Lecture 2011 Barnes & Hartmann, 2011

41 Scales of Weather Transients MidlaAtude Zonal Length scales are about 20-30% greater in the Southern Hemisphere than the Northern Hemisphere Haurwitz Lecture 2011

42 Scales of Weather Transients Haurwitz Lecture 2011

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50 Zonal and Meridional VorAcity Scales Zonal Meridional DJF JJA

51 VorAcity Scales at 50mb

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54 Eddy- Driven Jets and Change The troposphere is almost inviscid, but waves can move momentum around because they can propagate and break efficiently. Eddy feedback produces internal modes of low- frequency variability, notably meridional jet shiping. This gives large natural internal atmospheric variability that is unforced, but can respond to relaavely modest external forcings (e.g. QBO, stratospheric ozone loss or greenhouse gas warming). Haurwitz Lecture 2011

55 Thank You You for your anenaon AOFD for this honor Grad Students (especially Libby Barnes and Brian Smoliak) Colleagues for ideas, encouragement and inspiraaon

56 Quasi- Biennial OscillaAon Downward propagaang oscillaaon of tropical stratospheric zonal winds on the equator

57 Tropospheric Response to QBO 50 mb Tropopause PBL Haurwitz Lecture 2011 Garfinkel & Hartmann, 2010

58 Tropospheric Response to QBO Dry GCM No Eddies Steady response to QBO momentum forcing Haurwitz Lecture 2011 Garfinkel & Hartmann, 2010

59 Eddy InteracAon with QBO anomaly 50 mb C E W Rossby Wave Flux PBL Garfinkel & Hartmann, 2010 Haurwitz Lecture 2011

60 Tropospheric Response to QBO Days 5-25 Days Jet core Dry GCM With Eddies Transient response to QBO momentum forcing Eddies move easterly QBO anomalies downward by shiping jet Haurwitz Lecture 2011 Garfinkel & Hartmann, 2010

61 Observed response of zonal wind to QBO Oct- Nov Dec- Jan Feb- Mar AR- 40 Pacific WACCM Pacific Haurwitz Lecture 2011 AR- 40 AtlanAc Garfinkel & Hartmann, 2010

62 Eddy- Driven Jets and Feedbacks A very interesang problem in large- scale dynamic meteorology Very important for understanding the intraseasonal and interannual variability of the General CirculaAon Very important for understanding the response of the general circulaaon to natural and human influences. Thank You!

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64 Wave PropagaAon Theory If the jet- eddy feedback explains extratropical jets and their variability, we should be able to use wave propagaaon theory to explain some of their observed behavior. K * # = q y!cos 2! & % ( $ u " c ' 1/2 k < K* propagate, K* - > 0 turning laatude for all waves, waves are refracted toward larger K*, poles in K* indicate criacal lines and wave breaking Haurwitz Lecture 2011

65 Bernhard Haurwitz - Sources Bernhard Haurwitz , Julius London, NaAonal Academy of Sciences, Biographical Memoire, 1996 BAMS, 1985, Meteorology in the 20 th Century A ParAcipants View, Bernhard Haurwitz 4 parts Meteorology and Atmospheric Physics, 1988, vol 38, no 1-2 Bernhard Haurwitz Memorial Volume, Eds. Julius London and P.D. Thompson Contains complete publicaaon list InteresAng papers in which P.D. Thompson and J. Tribbia reflect on the contribuaons of Rossby and Haurwitz to the theory of Rossby- Haurwitz waves Would someone like to consult these references and write a Wikipedia page for Bernhard Haurwitz?

66 NAO SLP and VorAcity Anomalies Haurwitz Lecture 2011 Barnes & Hartmann 2010a

67 NAO VorAcity Anomalies and High- Frequency, SynopAc, Eddy Forcing. High- frequency eddy voracity flux convergence projects very well onto low level voracity anomaly. Haurwitz Lecture 2011 Barnes & Hartmann 2010a

68 QuanAficaAon of Eddy Feedback using Southern Hemisphere Lorenz and Hartmann (2001) Focus on veracal average momentum balance and meridional wave propagaaon. Then reduce to first EOF of U, call it Z, and corresponding structure in eddy momentum forcing, call it M, then consider the system,!z!t = M " Z # Lorenz & Hartmann, 2001

69 Linear model of Annular Mode!Z!t = M " Z # Z = amplitude!of! first!eof!of![u]! M = corresponding!!! " "y [u!*v*] Fourier Cross- Spectra of Z and M behave like linear equaaon is a good model. Lorenz & Hartmann, 2001

70 PosiAve Eddy Feedback Z=u M=- d/dy(u v ) b. synopac = 2-7 days Clues a. a. M remembers Z b. High- frequency eddies produce low- frequency forcing. Lorenz & Hartmann, 2001

71 Eddy Fluxes and Zonal Momentum Consider a non- divergent, barotropic fluid Enstrophy EquaAon![u]!t! = "v "x # "u "y!!t # 1 $ % 2 " *2 = "! [u *v*] = [v *#*]!y!u!x +!v!y = 0 & ' ( + ) eff [v *"*] = [F *"*]! eff [v *"*] = [F *"*] Up- gradient eddy voracity flux Source of eddy enstrophy

72 Steady Enstrophy EquaAon SArring Eddies to Generate Zonal Flow! eff [v *"*] = [F *"*] If voracity source F* adds enstrophy, eddy voracity flux must be up- gradient (normally northward) to maintain steady state. Zonal Wind EquaAon![u]!t + K D [u] = "!!y [u *v*] = [v *#*] = $ "1 eff [F *#*] So that a source of wave enstrophy can support a westerly zonal mean wind against fricaon in the presence of a posiave gradient of mean voracity. Also: Meridional Wave PropagaAon c gy! "[u *v*]