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O ^IThe UTCS Project Towards Unified Turbulence - Shallow Convection SchemeRJ$3e3e3e73e3eI ZOOutline$  VTowards a unified treatment of shallow convection and turbulence  possible alternatives The importance of turbulence potential energy A key issue  parameterization of non-local transport due to convection Coupling with microphysics and radiation schemes A few words about tuning Conclusions ,, , rtuVA Unified Treatment  Possible Alternatives,,  , =Mass-Flux Schemes (e.g. Lappen and Randall 2001, 2005): Missing components (e.g. pressure terms in the ADHOC1 model) are modelled using second-order closure ideas Hybrid Schemes (e.g. Soares et al. 2004): A combination of down-gradient diffusion approximations and mass-flux updraught models Second-Order Closure Schemes (e.g. Mellor and Yamada 1974, Nakanishi and Niino 2004): Missing components, most notably, a parameterization of non-local convective transport, are borrowed from the mass flux approach and translated into the language of the second-order closure z>3e3ev8  [  9  U   T   a-Turbulence Schemes Based on the TKE Equation :., . mh A Missing Component  Turbulence Potential Energy J51 5 Transport equation for turbulence potential energy (<q 2>, <q 2> and <q q > ), Q 4   Q dBudget of < 2> in convective boundary layer from LES (Mironov et al. 2000). Red  mean-gradient production/destruction, green  third-order transport, blue  dissipation of the temperature variance.    >)F*     y v,The UTCS  An Outline    wlA Key Issue  Parameterization of Non-Local Transport (75 7 xzi The Tuning      A good few of dimensionless constants, however & A number of constants appear only in combinations with other constants and are not required per se Some constants may (and should!) be estimated a priory using independent empirical and numerical data and physical constraints (tensor invariants, symmetry, realisability) Only the remaining constants should be  tuned Recalling George Orwell s  Animal Farm &  All constants are tunable, but some constants are more tunable than others. >v  23 = / 1-N&5    k Conclusions     The COSMO Priority Project UTCS is initiated with the aim to parameterize boundary-layer turbulence and shallow non-precipitating convection in a unified framework As the unified framework, the (two-equation) second-order closure scheme that prognostically treats both the TKE and the TPE holds considerable promise The missing components, most notably, parameterization of non-local convective transport, are borrowed from the mass flux approach and translated into the language of the second-order closure The implementation of UTCS is expected to result, among other things, in a better coupling between turbulence, convection and radiation 8ACGCb  !      lsTPosing the turbulence-convection problem & ++ +  & & &   |{$The Two Alternatives - Pros and Cons%%&   /0[,?DIKLMSTUVWXY[\]`aP'  ` ̙33` 3` 3333f` 999MMM` f` f3` 3>?" ddFx? 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F ,$@ 0P 4 s *޽h ?"` f"___PPT10..r-+ZbD' = @B D' = @BA?%,( < +O%,( < +DS' =%(%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =-s6Bwipe(left)*<3<*4 D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =-s6Bwipe(left)*<3<*4 Dy' =%(D!' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =-s6Bwipe(left)*<3<*4 D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 4 %(D' =-s6Bwipe(left)*<3<* 4 D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* 4 %(D' =-g6B fade*<3<* 4 D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* 4 %(D' =-g6B fade*<3<* 4 D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4 %(D' =-g6B fade*<3<* 4 D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4 %(D' =-g6B fade*<3<* 4 ++0+4  ++0+4  ++0+ 4  ++0+ 4  +( U  D (  D " D s *3@`@B 0B 0 D s *3`@B 0B 0 D TZ1?,$@ 0 V"Splitting (artificial separation of processes and scales) causes a lot of problems that become severe as the resolution is increased. Quoting Arakawa (2004, The Cumulus Parameterization Problem: Past, Present, and Future, J. Climate, 17, 2493-2525), It is rather obvious that for future climate models the scope of the problem must be drastically expanded & to  unified cloud parameterization or even to  unified model physics. A less ambitious task is  A Unified Parameterization of Turbulence and Shallow Convection . 2 p?  hh88B D s *޽h ? f___PPT10..r-+D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*D %(D' =-g6B fade*<3<*D D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*D %(D' =-g6B fade*<3<*D +e V ph L (  L  L s *`pcx <$ 0   @ L s *p]\+<$ 0  ,@ @`" L s *3@`@B 0B 0 L s *3`@B 0B 0B L s *޽h ? f___PPT10u..r-+D=' = @B +  ?    x O (  x  x s *Pp<$ 0   @ x 0 C z0e0eA m?p?"?;v m  x 0 c 0e0eA j? ?p?"? . j " x s *3@`@B 0B 0 x s *3`@B 0B 0R  x T1?h NThe third-order transport term is parameterized as a down-gradient diffusion, 4O 253e O hh88| x Txڿ1? z  xEquations for the Reynolds stress and for the turbulent scalar fluxes are reduced to down-gradient algebraic relations, 4y 2U!3e y hh88P x T1?  NOnly one second-order equation is carried in its full form, the TKE equation, 2Ol0 iFZ3e1 O hh88 x 0 c 0e0eA  p? ?p?"?b  p 1 x TX1?pR 5Unable to account for non-local convective transport!,6(25 6 hh88B x s *޽h ? f___PPT10u..r-+D=' = @B +/ M   @(     s *pg   @  s *`p(@  ,@ @`  0 C z0e0eA r?p?"?|0H r "  s *3@`@B 0B 0  s *3`@B 0B 0j  T1?x,$  0 4Production = Dissipation & yields the down-gradient formulation for the temperature variance (implicit in all models that carry the TKE equations only) 2 2n(  hh88  T1? ``,$@   0 The neglect of third-order transport TPE TKE conversions are not described satisfactorily (convection!) No way to get counter-gradient diffusion in convective flows (the ad hoc inclusion of counter gradient fluxes leads to a negative scalar variance dissipation!) Poor input for the (statistical) sub-grid scale cloud scheme (<q 2> and <q 2> are strongly underestimated!) & 2T 2*@  ! z hh88*  Z1?"` p ,$@   0 ^  hh88B  TD)?r <,$@ 0B  TD)?2d,$@ 0B  TD)?t ,$@ 0B  TD)?*@,$@ 0  Tf&1?"`P ,$@ 0  Tf&1?"` (,$@ 0B  s *޽h ? f___PPT10..r-+7TD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D ' =%(D ' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* &%(D' =-s6Bwipe(left)*<3<* &D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* &l%(D' =-s6Bwipe(left)*<3<* &lDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* l %(D' =-s6Bwipe(left)*<3<* l D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* z%(D' =-s6Bwipe(left)*<3<* z+p+0+  ++0+  + D-K0   * P(     s *l*p$ i     Tx1?b \(2  hh88  T1? e (2  hh88  s *3`@B 0B 0"  s *3@`@B 0B 00  ZR1?  8Temperature Variance Budget in Boundary-Layer Convection998  hh88  # ~0e0eA pbalTT_CC,    Tc1?Xhx  -eT:(2   hh88pB  HDF8c?(   Tf1?0 ."- <u 3  2>/x3(2  &   hh88pB  @ HD8c?ph 08  T̆1? @ F&-<u 3 > <  >/x3(2 @   hh88pB  @ HD8c?    Z}1?"``  Counter-gradient heat transport!! ! hh88  T ?"`\G 2 $  `331?"`@  ,$D 0 7One-equation models attempts to balance red and blue N8*3e 8 hh88B  s *޽h ? a(rj___PPT10J+j܏D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-g6B fade*<3<*$ +8+0+$  +k W v n P \  (  \  \ s *p   @  \ Z PUPU ?\ r A second-order closure (cf. Mellor-Yamada 1974, Bougeault 1981, Bechtold et al. 1995, and many others) that treats  shallow convection and  turbulence together (both are sub-grid scale motions) Carries prognostic equations for <ui2> (kinetic energy of SGS motions) and for <q2>, <q2> and <qq> (potential energy of SGS motions), convection=TPETKE Uses algebraic relations for <uiuj>, <uiq> and <uiq> (computationally cheap) Uses grid-size dependent algebraic relation for the turbulence length scale (no need for re-tuning as the resolution is changed) Uses skewness-dependent formulations for the third-order moments (non-local transport properties of convection) Uses statistical SGS cloud scheme with <q 2>, <q 2> and <q q > as the most important input (coupling with microphysics and radiation schemes) Precipitation is a difficult issue! (therefore, only shallow convection first)}$         ,+  0     4        B @ @`" \ s *3@`@B 0B 0 \ s *3`@B 0B 0B \ s *޽h ? f___PPT10u..r-+D=' = @B + X p d H(  d  d s *p   @ d 0 c 0e0eA ? ?p?"?m   d 0 c 0e0eA ? ?p?"?o7   < d ZPUPU ? P  A combination of the down-gradient formulation and a skewness-dependent non-gradient formulation which is nothing but a mass-flux relation reformulated in terms of second-order moments. Accounts for anisotropic coherent motions and non-local transport typical of convection. Sq closed through itself (mass-flux formalism!). I 3e+\X &5    @ @`" d s *3@`@B 0B 0 d s *3`@B 0B 0  d 0 c 0e0eA ? ?p?"?     d Th1?`X yOld formulation(23e  hh88  d T#1?p(  yNew formulation(2  hh88vB d NDԔ?h PvB d @ ND3eԔ?P x d T$&1? X  $Down-gradient formulation that corresponds to random Gaussian turbulence. No account for strong isotropy and non-locality of convective motions. D 23e3F  hh88vB d @ ND3eԔ?xHh vB d @ NDԔ?h  d Tff1?"`88 `B d s *޽h ? f___PPT10u..r-+D=' = @B ++& Y 6%.% ""| $(  |  | TG3e1?  &hUTCS  Coupling With Other Parameterization Schemes 5(25bhh88 | TTI1?~R &Red  missing components, blue  existing components that require further development and/or adjustment. Fj 23eL    hh88v | N1?(0, | Z<\1?S"`?X | TKE-Equation    hh88, | ZTl(L1?S"`?X `P | TPE-Equation    hh88R | Z|p(L1?(   Energy Conversions (  hh88 | Tdx1? 8  lUTCS(2  hh88v  | N1?` ,  | T1? SGS Statistical Cloud Scheme(20  hh88"  | Zp1?C"? @  /EEstimates fractional cloud cover and the amount of cloud condensateFF   hh88v  | N1? Xpv  | N1?(  | T1?0   q Radiation (2   hh88v | N1?  | T1?P h@$  t Microphysics (2   hh88 | T1? P  zCumulus Convection(2  hh88R | Z1?H H |R | T(L1? 0  | Z̧1?S"`? X  ?Shallow convection should be treated in the framework of UTCS@@~   hh88` | Z1?S"`?   + Saturation adjustment(0   hh88|R | T1? 0X |R | TQ(L1?N ~  |  fGH4`1?"0 NNN?NX   LJAt present saturation adjustment does not account for the SGS processes KK    hh88|R | T.1?N J  | s *3`@B 0B 0" | s *3p@B 0B 0 | Z1?S"`?x (  &Should avoid its own cloud diagnostics''p  hh88 |  ftG[WHNc1?"0 NNN?N`H n Inconsistent at present since various parameterisation schemes use their own diagniostics of cloud cover oo    hh88 | @ N1?"0@NNN?N~  | N1?"0@NNN?N   |  f GoHbp1?"0 NNN?N KEWithout TPE-equation the SGS cloud scheme input is of poor quality FF   hh88 !| N1?"0@NNN?N J "| N1?"0@NNN?NxJP | s *޽h ?"`| | | | | | |  | | !| | | "| |  |  f___PPT10u..r-+D=' = @B +9 [ (( (( '(   )  T3e1?  UTCS for High-Resolution Models (2 ,hh88  T 1?~R &Red  missing components, blue  existing components that require further development and/or adjustment. Fj 23eL    hh88v  N1?(0,  Z11?S"`?X | TKE-Equation    hh88,  ZA(L1?S"`?X `P | TPE-Equation    hh88R  ZL(L1?(   Energy Conversions (  hh88  TP1? 8  lUTCS(2  hh88v  N1?` ,  TTX1? SGS Statistical Cloud Scheme(20  hh88"  ZZ1?C"? @  /EEstimates fractional cloud cover and the amount of cloud condensateFF   hh88v  N1? Xpv  N1?(   T#1?0   q Radiation (2   hh88v  N1?   Tx1?P h@$  t Microphysics (2   hh88  TN1? P >  Shallow Cumulus Convection(2  hh88R  Z1?H H |R  T(L1? 0   Z1?S"`? X  (A separate scheme is no longer needeed ))P hh88`  Z1?S"`?   + Saturation adjustment(0   hh88|R  T1? 0X |R  TQ(L1?N ~    f0GH4`1?"0 NNN?NX   LJAt present saturation adjustment does not account for the SGS processes KK    hh88|R  T.1?N J   s *3`@B 0B 0"  s *3p@B 0B 0  Z`1?S"`?x (  &Should avoid its own cloud diagnostics''p  hh88   fG[WHNc1?"0 NNN?N`H n Inconsistent at present since various parameterisation schemes use their own diagniostics of cloud cover oo    hh88  @ N1?"0@NNN?N~   N1?"0@NNN?N    f4GoHbp1?"0 NNN?N KEWithout TPE-equation the SGS cloud scheme input is of poor quality FF   hh88 ! N1?"0@NNN?N J " N1?"0@NNN?NxJB # TD)? & ,$@ 0B $ TD)? ,$@ 0B % TD)? d0,$@ 0B & TD)? 4$,$@ 0B ' TD)? | ,$@ 0B ( TD)? | ,$D 0P  s *޽h ?"`         !  "    fh`___PPT10@..r-+;D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*# %(D' =-g6B fade*<3<*# D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-g6B fade*<3<*$ D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*% %(D' =-g6B fade*<3<*% D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*& %(D' =-g6B fade*<3<*& D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*' %(D' =-g6B fade*<3<*' D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*( %(D' =-g6B fade*<3<*( +  I D<P  (     s *<ps   @  s * p(<$D  0  ,@ @`"  s *3@`@B 0B 0  s *3`@B 0B 0B  s *޽h ? f { ___PPT10[ ..r-+D# ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* w%(D' =-s6Bwipe(left)*<3<* wD&' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +3 K-K0  .&  (   ~  s *#p1   ~  s *$p'*  B  6"`8@ B 0 ^  hh88"  s *"`3r@)B 0B 0  s *"`3`@*B 0B 0h  BA޽h ?5%"` a(y___PPT10Y+D=' = @B +R  L LD  (   "  s *"`3(@+B 0B 0R"   ` q} ?"`@ ,$D 0 Thanks for your attention!$  hh88  # 0e0eApcosmologo1nVs   # 0e0eApdwd_logo_bluemg  P  s *޽h ?"` f___PPT10..r-+ŻOD' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* +8+0+  +1 T <4 < (  < " < s *3@`@B 0B 0B < s *޽h ? f___PPT10u..r-+D=' = @B + `   !(     s *0Ap   @"  s *3@`@B 0B 0  s *3`@B 0B 0b  T|?"`(   N8c?"`  +   TE1?p X  j4 cm(2  hh88  ZN1?L j3 cm(2  hh88  T\1? ( M ix(2   hh88   T _1?pH Find x. 4 (2     hh88B  s *޽h ? f___PPT10u..r-+D=' = @B + a   4(     s *qp   @"  s *3@`@B 0B 0  s *3`@B 0B 0b  T|?"`(   N8c?"`  +   T41?p X  j4 cm(2  hh88  Z01?L j3 cm(2  hh88  T$1? ( M ix(2   hh88   TL1?pH Find x. 4 (2     hh88   ~BCDEFB38c?(((+s+Y0H3)@)@}(4!p 0Nt>apv0V{PJ?8/( )( @             `"` r    BCDEFTA38c?77m7*Z8=dhM b8[?YJRPD]"p"p#Xqsj[50xA`j RX?LR'_*#!'(@                  "`` Z     B(CDEFA38c?((@@ "``      BCPDEFA38c?X(P@ "``h     T̝1?@ Hh  Here it is . (2  3 3  hh88B  s *޽h ? f___PPT10u..r-+D=' = @B +1 ] <4P  (   "  s *3@`@B 0B 0B  s *޽h ? f___PPT10u..r-+D=' = @B +* \ $$0 .. g$(     s *p}{<$ 0   @"  s *"`3@`@B 0B 0  s *"`3`@B 0B 0" }b  # #"."}b<$D 0      `T1?o~ tEasy    (7    `\1?=o~ y Difficult       (7-    `l1?=~ +Separation of resolved and sub-grid scales , ,+   (7    ` 1?o b Easy (straightforward)    (7    `(1?= ob y Difficult       (7)    `1? =b 'Determination of fractional cloud cover( ('   (7    `(1?o   y Difficult       (7     `1?= o  tEasy    (7    ` 1? =  !Parameterization of precipitation" " "  (7    `1?o7   z Manageable   3e    (7     `!1?=7 o  tEasy    (7*    ` +1?7 =  (Parameterization of non-local transport ) )(   (7    `41?o~7   Manageable *   3e    (7    `L>1?=~o7  y Difficult       (7    `@1?~=7  $Parameterization of pressure terms % % %  (7!    `Q1?o   Not required *      (7    `P\1?= o  Difficult *       (7(    `f1? = 2Separation of scales of convection and turbulence 3 3 3  (7    `o1?o}  xUnified Closure Scheme    (7     `p1?=}o  rMass-Flux Scheme    (7    `r1?}=  T    (7xB   Ho ?}}rB   B1 ?~~rB   B1 ?7 7 rB   B1 ?  rB   B1 ?  xB   Ho ?bbrB !  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S0@y2!44`fm608M:m#sOh+'0( 4D h t  Aktionsprogramm 2003PMuster fr VortragsfolieniDr. Volker Kurzr. 07.02.2003 Erste Version 7.0 .01750.20Microsoft PowerPoint 4.0 @@Д@8\@Pϰz9՜.+,D՜.+,   (08 @ EOn-screen Show1Dr. Volker KurzDeutscher WetterdienstTF{ ArialTimes New RomanSymbol WingdingsGeorgiaComic Sans MSSystemAP2003-Muster-030207.pptCustom DesignMicrosoft Equation 3.0Microsoft Formel-Editor 3.0JThe UTCS Project Towards Unified Turbulence - Shallow Convection SchemeOutlineSlide 3Slide 4,A Unified Treatment Possible Alternatives.Turbulence Schemes Based on the TKE Equation 5 A Missing Component Turbulence Potential Energy Slide 8The UTCS An Outline 7A Key Issue Parameterization of Non-Local Transport Slide 11 Slide 12 The Tuning Conclusions Slide 15 Slide 16+Posing the turbulence-convection problem  Slide 19%The Two Alternatives - Pros and Cons  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles 8@ _PID_HLINKSA6 -1,-1,NEXT -1,-1,PREV -1,-1,NEXT -1,-1,PREV363,15,Conclusions -1,-1,PREV -1,-1,NEXT -1,-1,PREV -1,-1,NEXT_Gt    !"#$%&'()*+,-./012456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmopqrstuwxyz{|}Root EntrydO)PicturesdCurrent User~SummaryInformation(nPowerPoint Document(3ktDocumentSummaryInformation8v