Data-Driven Ocean ModelingRaffaele Ferrari

Earth, Atmospheric and Planetary Sciences, MITCaltech, March 29 2018

Allen Center Allen

Ocean Modeling ChallengeOcean circulation is very turbulent: parametrization problem

Sub-Grid-Scale Physics

Neutral density (kg m3) section in the Pacific Ocean (WOCE, P16)

boundary layer turbulence

geostrophic turbulence

wave turbulence

Du

Dt+

1

⇢0rp� bz�r · (⌫ru) = �r · u0u0

| {z }Reynolds stresses

Db

Dt�r · (rb) = �r · u0b0| {z }

Reynolds fluxes<latexit sha1_base64="ZP1J9GAvi6sFSdiNaC4LEpA4xaA=">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</latexit><latexit sha1_base64="ZP1J9GAvi6sFSdiNaC4LEpA4xaA=">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</latexit><latexit sha1_base64="ZP1J9GAvi6sFSdiNaC4LEpA4xaA=">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</latexit><latexit sha1_base64="ZP1J9GAvi6sFSdiNaC4LEpA4xaA=">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</latexit>

Boundary Layer BiasesAssessment of Southern Ocean mixed-layer depths in CMIP5 models

Sallée et al. 2013

Boundary Layer Biases

Richter 2015

Model bias is largest in regions where turbulence is strongest

Present day approach to reducing model biases

state estimation

parameterization

Process studies + LES = parameterizations

Geostrophic turbulenceDiapycnal and Isopycnal Mixing Experiment in the Southern Ocean

Observations

“LES” modelNew SGS parameterization

Tulloch, Ferrari et al. 2014; Bates, Marshall and Ferrari 2016

S = S(KH , f, slope)<latexit sha1_base64="Do7aFTNBP6rP8BLAPLhLhDQritY=">AAACDnicbZDLSsNAFIYnXmu9RV26GSyFCqUkIuhGKLopuKloL9CEMJlO2qGTTJiZiCXkCdz4Km5cKOLWtTvfxmmbhbb+MPDxn3M4c34/ZlQqy/o2lpZXVtfWCxvFza3tnV1zb78teSIwaWHOuOj6SBJGI9JSVDHSjQVBoc9Ixx9dTeqdeyIk5dGdGsfEDdEgogHFSGnLM8up4wfwNoMXMKfKtdeoBlVn6POHVDIek+zYM0tWzZoKLoKdQwnkanrml9PnOAlJpDBDUvZsK1ZuioSimJGs6CSSxAiP0ID0NEYoJNJNp+dksKydPgy40C9ScOr+nkhRKOU49HVniNRQztcm5n+1XqKCczelUZwoEuHZoiBhUHE4yQb2qSBYsbEGhAXVf4V4iATCSidY1CHY8ycvQvukZls1++a0VL/M4yiAQ3AEKsAGZ6AOGqAJWgCDR/AMXsGb8WS8GO/Gx6x1ychnDsAfGZ8/Fgya4Q==</latexit><latexit sha1_base64="Do7aFTNBP6rP8BLAPLhLhDQritY=">AAACDnicbZDLSsNAFIYnXmu9RV26GSyFCqUkIuhGKLopuKloL9CEMJlO2qGTTJiZiCXkCdz4Km5cKOLWtTvfxmmbhbb+MPDxn3M4c34/ZlQqy/o2lpZXVtfWCxvFza3tnV1zb78teSIwaWHOuOj6SBJGI9JSVDHSjQVBoc9Ixx9dTeqdeyIk5dGdGsfEDdEgogHFSGnLM8up4wfwNoMXMKfKtdeoBlVn6POHVDIek+zYM0tWzZoKLoKdQwnkanrml9PnOAlJpDBDUvZsK1ZuioSimJGs6CSSxAiP0ID0NEYoJNJNp+dksKydPgy40C9ScOr+nkhRKOU49HVniNRQztcm5n+1XqKCczelUZwoEuHZoiBhUHE4yQb2qSBYsbEGhAXVf4V4iATCSidY1CHY8ycvQvukZls1++a0VL/M4yiAQ3AEKsAGZ6AOGqAJWgCDR/AMXsGb8WS8GO/Gx6x1ychnDsAfGZ8/Fgya4Q==</latexit><latexit sha1_base64="Do7aFTNBP6rP8BLAPLhLhDQritY=">AAACDnicbZDLSsNAFIYnXmu9RV26GSyFCqUkIuhGKLopuKloL9CEMJlO2qGTTJiZiCXkCdz4Km5cKOLWtTvfxmmbhbb+MPDxn3M4c34/ZlQqy/o2lpZXVtfWCxvFza3tnV1zb78teSIwaWHOuOj6SBJGI9JSVDHSjQVBoc9Ixx9dTeqdeyIk5dGdGsfEDdEgogHFSGnLM8up4wfwNoMXMKfKtdeoBlVn6POHVDIek+zYM0tWzZoKLoKdQwnkanrml9PnOAlJpDBDUvZsK1ZuioSimJGs6CSSxAiP0ID0NEYoJNJNp+dksKydPgy40C9ScOr+nkhRKOU49HVniNRQztcm5n+1XqKCczelUZwoEuHZoiBhUHE4yQb2qSBYsbEGhAXVf4V4iATCSidY1CHY8ycvQvukZls1++a0VL/M4yiAQ3AEKsAGZ6AOGqAJWgCDR/AMXsGb8WS8GO/Gx6x1ychnDsAfGZ8/Fgya4Q==</latexit><latexit sha1_base64="Do7aFTNBP6rP8BLAPLhLhDQritY=">AAACDnicbZDLSsNAFIYnXmu9RV26GSyFCqUkIuhGKLopuKloL9CEMJlO2qGTTJiZiCXkCdz4Km5cKOLWtTvfxmmbhbb+MPDxn3M4c34/ZlQqy/o2lpZXVtfWCxvFza3tnV1zb78teSIwaWHOuOj6SBJGI9JSVDHSjQVBoc9Ixx9dTeqdeyIk5dGdGsfEDdEgogHFSGnLM8up4wfwNoMXMKfKtdeoBlVn6POHVDIek+zYM0tWzZoKLoKdQwnkanrml9PnOAlJpDBDUvZsK1ZuioSimJGs6CSSxAiP0ID0NEYoJNJNp+dksKydPgy40C9ScOr+nkhRKOU49HVniNRQztcm5n+1XqKCczelUZwoEuHZoiBhUHE4yQb2qSBYsbEGhAXVf4V4iATCSidY1CHY8ycvQvukZls1++a0VL/M4yiAQ3AEKsAGZ6AOGqAJWgCDR/AMXsGb8WS8GO/Gx6x1ychnDsAfGZ8/Fgya4Q==</latexit>

Wave turbulenceDIMES = Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean

Observations

“LES” model

Mashayek, Ferrari et al., 2017

Wave turbulenceDIMES = Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean

Observations

New SGS parameterization

N2 [1/s2] #10-61 2 3

Heightabov

ebott

om

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0 [W/kg]10-10 10-9 10-8

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5; [m2/s3]10-5 10-4 10-3

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N2 [1/s2] #10-61 2 3

Heightabov

ebott

om

[m]

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1000

1500

2000

0 [W/kg]10-10 10-9 10-8

500

1000

1500

2000

5; [m2/s3]10-5 10-4 10-3

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1000

1500

2000

F = u0b0 = �rb<latexit sha1_base64="VqHkXDu1UI3mPXM1RMkfW0M9sMY=">AAACIHicbVDLSgMxFM34rPU16tJNsEjdWGZEqJtCURCXFewDOqXcpBkNzWSGJCOUYT7Fjb/ixoUiutOvMX0stHog5HDOvTe5hySCa+N5n87C4tLyymphrbi+sbm17e7stnScKsqaNBax6hDQTHDJmoYbwTqJYhARwdpkeDH22/dMaR7LGzNKWC+CW8lDTsFYqe9Ws4CE+DLHNRzEtnA8J5toaTkn5byGj3EwhCQBHEggwl4EFCZ9t+RVvAnwX+LPSAnN0Oi7H8EgpmnEpKECtO76XmJ6GSjDqWB5MUg1S4AO4ZZ1LZUQMd3LJgvm+NAqAxzGyh5p8ET92ZFBpPUoIrYyAnOn572x+J/XTU141su4TFLDJJ0+FKYCmxiP08IDrhg1YmQJUMXtXzG9AwXU2EyLNgR/fuW/pHVS8b2Kf31aqp/P4iigfXSAjpCPqqiOrlADNRFFD+gJvaBX59F5dt6c92npgjPr2UO/4Hx9AxRUoak=</latexit><latexit sha1_base64="VqHkXDu1UI3mPXM1RMkfW0M9sMY=">AAACIHicbVDLSgMxFM34rPU16tJNsEjdWGZEqJtCURCXFewDOqXcpBkNzWSGJCOUYT7Fjb/ixoUiutOvMX0stHog5HDOvTe5hySCa+N5n87C4tLyymphrbi+sbm17e7stnScKsqaNBax6hDQTHDJmoYbwTqJYhARwdpkeDH22/dMaR7LGzNKWC+CW8lDTsFYqe9Ws4CE+DLHNRzEtnA8J5toaTkn5byGj3EwhCQBHEggwl4EFCZ9t+RVvAnwX+LPSAnN0Oi7H8EgpmnEpKECtO76XmJ6GSjDqWB5MUg1S4AO4ZZ1LZUQMd3LJgvm+NAqAxzGyh5p8ET92ZFBpPUoIrYyAnOn572x+J/XTU141su4TFLDJJ0+FKYCmxiP08IDrhg1YmQJUMXtXzG9AwXU2EyLNgR/fuW/pHVS8b2Kf31aqp/P4iigfXSAjpCPqqiOrlADNRFFD+gJvaBX59F5dt6c92npgjPr2UO/4Hx9AxRUoak=</latexit><latexit sha1_base64="VqHkXDu1UI3mPXM1RMkfW0M9sMY=">AAACIHicbVDLSgMxFM34rPU16tJNsEjdWGZEqJtCURCXFewDOqXcpBkNzWSGJCOUYT7Fjb/ixoUiutOvMX0stHog5HDOvTe5hySCa+N5n87C4tLyymphrbi+sbm17e7stnScKsqaNBax6hDQTHDJmoYbwTqJYhARwdpkeDH22/dMaR7LGzNKWC+CW8lDTsFYqe9Ws4CE+DLHNRzEtnA8J5toaTkn5byGj3EwhCQBHEggwl4EFCZ9t+RVvAnwX+LPSAnN0Oi7H8EgpmnEpKECtO76XmJ6GSjDqWB5MUg1S4AO4ZZ1LZUQMd3LJgvm+NAqAxzGyh5p8ET92ZFBpPUoIrYyAnOn572x+J/XTU141su4TFLDJJ0+FKYCmxiP08IDrhg1YmQJUMXtXzG9AwXU2EyLNgR/fuW/pHVS8b2Kf31aqp/P4iigfXSAjpCPqqiOrlADNRFFD+gJvaBX59F5dt6c92npgjPr2UO/4Hx9AxRUoak=</latexit><latexit sha1_base64="VqHkXDu1UI3mPXM1RMkfW0M9sMY=">AAACIHicbVDLSgMxFM34rPU16tJNsEjdWGZEqJtCURCXFewDOqXcpBkNzWSGJCOUYT7Fjb/ixoUiutOvMX0stHog5HDOvTe5hySCa+N5n87C4tLyymphrbi+sbm17e7stnScKsqaNBax6hDQTHDJmoYbwTqJYhARwdpkeDH22/dMaR7LGzNKWC+CW8lDTsFYqe9Ws4CE+DLHNRzEtnA8J5toaTkn5byGj3EwhCQBHEggwl4EFCZ9t+RVvAnwX+LPSAnN0Oi7H8EgpmnEpKECtO76XmJ6GSjDqWB5MUg1S4AO4ZZ1LZUQMd3LJgvm+NAqAxzGyh5p8ET92ZFBpPUoIrYyAnOn572x+J/XTU141su4TFLDJJ0+FKYCmxiP08IDrhg1YmQJUMXtXzG9AwXU2EyLNgR/fuW/pHVS8b2Kf31aqp/P4iigfXSAjpCPqqiOrlADNRFFD+gJvaBX59F5dt6c92npgjPr2UO/4Hx9AxRUoak=</latexit>

Mashayek, Ferrari et al., 2017

Boundary layer turbulenceClimate Process team on Eddy Mixed Layer Interactions

“LES” model with no frontu (m/s)

u (m/s)

“LES” model with lateral front

New SGS parameterization

S = µ(z)h2

|f | z⇥rb<latexit sha1_base64="3zh1xG3NKZuIu65D5iMa8JYgncM=">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</latexit><latexit sha1_base64="3zh1xG3NKZuIu65D5iMa8JYgncM=">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</latexit><latexit sha1_base64="3zh1xG3NKZuIu65D5iMa8JYgncM=">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</latexit><latexit sha1_base64="3zh1xG3NKZuIu65D5iMa8JYgncM=">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</latexit>

Fox-Kemper, Ferrari and Hallberg 2008, Taylor and Ferrari 2010

Boundary layer turbulenceCLIMODE Experiment

Observations

“LES” model

Tomas, Joyce, Taylor and Ferrari et al., 2013

Observations + global model = state estimation

Ocean state estimation

FloatsShip profiles

Altimeters

Gravity

MIT Ocean Model and Its

Constrain global ocean circulation by assimilating in situ and remote data in global ocean solutions

A new approach to reducing model biases

Schneider et al., 2017

Moving forward

1. Develop unified SGS process models of boundary layer turbulence in the atmosphere and ocean

2. Develop global atmosphere and ocean model with horizontal resolution of a few kilometers and with SGS models that learn from the fly from nested LES and global observations through scalable algorithms for DA/ML

3. Couple the atmosphere and ocean models

Improve the representation of SGS physics in climate models