Ocean Modeling. Brian K. Arbic AGU Student Conference Talk December 11, 2016

Transcription

1 Ocean Modeling Brian K. Arbic AGU Student Conference Talk December 11, 2016

2 Why model the ocean? OperaHonal oceanography Fisheries Oil spills AcousHcs Climate Coastal erosion Other applicahons

3 Types of models AnalyHcal models Shallow-water equahons Advantages: useful for gaining insight, can somehmes get exact soluhons Disadvantages: usually not possible to solve for realishc condihons (complex geometries, nonlinear flows, and others )

4 Types of models Idealized models Advantages: Can include more complexihes (e.g. rough topography, nonlinearihes) than analyhcal models, but shll have some control Good for process studies SomeHmes relahvely simple to interpret Disadvantages: SomeHmes not so simple to interpret! OZen not useful to directly simulate the actual ocean Arbic and Flierl 2004

5 Types of models Realistic ocean general circulation models Advantages: Useful for simulating actual ocean Disadvantages: Can be difficult to interpret due to great complexity Journal of Geophysical Research: Oceans Volume 117, Issue C10, C10024, 27 OCT 2012 DOI: /2012JC Shriver et al. 2012

6 What goes into a realishc ocean general circulahon model? Bathymetry and coastal geometry Atmospheric forcing fields Wind stress Pressure (somehmes) Fields needed to compute air/sea buoyancy fluxes PrecipitaHon Atmospheric temperature, humidity Others Tidal forcing (somehmes) River inputs (somehmes)

7 How does one construct a realishc ocean general circulahon model? Decide on set of equahons to use Momentum Mass conversahon EquaHon of state Temperature evoluhon equahon Salinity evoluhon equahon Decide on discrehzahon issues Horizontal grid Finite difference grid Finite element grid à Number of grid points (how large is your computer?) VerHcal grid Density coordinate (isopycnal) z-coordinate (depth) Terrain-following coordinate ALE (Arbitrary Lagrangian-Eulerian) coordinate Number of grid points (how large is your computer?)

8 IllustraHon of different verhcal coordinates for ocean models Griffies et al ALE (Arbitrary Lagrangian-Eulerian) coordinate: Fusion of different coordinates so that one uses the strongest coordinate in different regions

9 Some animahons of realishc ocean models Model of 2004 Indian Ocean Boxing Day tsunami Models of barotropic and internal Hdes Models of wind-driven oceanic general circulahon

10 Data assimilahon Data assimilahon is the art of blending observahons and models Used in ocean forecashng and state eshmahon

11 Data assimilahon example Data assimilahon is the art of blending observahons and models Used in ocean forecashng and state eshmahon

12 Example of student work: Savage et al., to be resubmiged soon

13 Example of student work: Savage et al., to be resubmiged soon

14 Going with the flow: Lagrangian simulations in the geosciences Somewhat biased toward hydrology Nick Engdahl Assistant Professor Civil and Environmental Engineering Washington State University

15 2 Where do models fit in? Testing our understanding of physical processes Upscaling: Laboratories are small, geophysical systems are big Prediction: Can t wait and see to plan use of resources My own use of models: Virtual hypothesis testing laboratories Accounting for uncertainty Management/decision making support

16 3 I do water so let s think on some common hydrologic models Floodplain inundation Watershed modeling These (and most other) geophysical models are Eulerian Definition: Fixed spatial reference frame Just think: Sitting on the platform watching a train go by The box around the problem doesn t move From Sommer et al., 2009 Fig. 2 Engdahl and Maxwell, 2015

17 4 Get on the train, now you re Lagrangian Maps on your phone: Track up = Eulerian Track direction = Lagrangian The dot moves through the map The map moves around the dot Self-centered way of modeling?

18 5 Lagrangian models in the geosciences: random walk Discretize the mass on to particles (mesh-free) Very common for transport of solutes, microbes etc (air or water) New position of particle Old position Drift Diffusion/di spersion Standard normal R.V. The drift is just the fluid velocity most of the time Limit case as Δt 0 makes a partial differential equation

19 6 Let s look at some examples For Advection each particle: in groundwater - flows Where am I in the velocity field? Start on the vertical line - How fast am I moving and in what Each direction? distorted line is a later time - How long do I have to move? No diffusion or dispersion - (no The spreading) just do it Modified from Fig. 8/9 Benson et al., 2017

20 Source zone identification 7 A backward in time approach Send mass back to where it came from Risk assessment/litigati on Engdahl et al., 2012 Another angle on that same simulation

21 Models can be as simple as asking yes or no Matlab, define a bunch Remember: of particles, say This Time is ONLY step of asking dt=0.125, each particle dx=0.5 to flip a coin to decide go left or right Each particle can only move left or right Incredibly simple yet it s a great Blue model dots are of diffusion particles, height is proportionate to # at that site

22 Things besides motion can be simulated this way too Chemical reactions stuff mixes then it can react 9 A reaction is the intersection of two probabilities Chemistry says yes Close enough to find each other If red (A) and blue (B) meet, they can react

23 10 My thing right now: Simulating reactions with particles The basics of it: Put some particles in a simulation Bottom line: All Pick that a search is how order, we translated to visit this physical every A processes into an algorithm for a computer Find it s nearby B particles - Crucial Evaluate part colocation of any model probability is good process level understanding of the physics involved Pick a random number, to decide if they react 2 Distance s 3σ density contour A B Colocation region

24 11 Example: Acid mine drainage Nasty stuff in streams/lakes Chemical stability of ore changes when at surface vs at depth Gold King Mine, CO Animas river incident of 2015

25 Let s try to model that complicated system 12 Acid-mine drainage + snowmelt =??? Complex geochemistry on particles Start with a conceptual model and DRAW a picture!

26 Complex systems are really difficult to predict without a model Take home message: Snapshot in time - This system has a lot going on Flow to the left V=0.5 [L/T] 13 - Lagrangian lets us follow the water through the system Lots of sharp interfaces Complementary - Moving reactants and reacting Competitive processes flows (i.e. it s a tricky problem)

27 14 Let s ponder that last acid-mine drainage example Key points: 1. A lot is going on: 41 aqueous species are all moving and reacting in different ways (I only showed you 6 of them) 2. You can make that system as an experiment but you can t monitor all 41 species everywhere at all times Could grab samples now and then at some points, at best 3. That model could help design a better experiment Gives an idea what to look for, where, when, and how much

28 15 Models let us go inside an experiment in unique ways 1. We have complete control over every aspect of the model (um, assuming it was build right in the first place) 2. We can probe anywhere for any quantity and can simply save the output files for later re-analysis 3. Sensitivity and uncertainty analysis show the importance of each knob - Quantifies how being a little wrong with a value affects the results

29 16 But keep in mind, a model is not: Tons of these disclaimers, but here are my big two: 1. A substitute for observations/experiments How do you know your model is correct without those? Models can form a bridge back to reality 1. Reality By definition a scaled representation of reality Let s you test ideas with the same governing equations perhaps, but it will never be real

30 17 Punchline: Models are tremendously helpful for understanding the world around us, but they re only as good as you make them Please don t hesitate to ask me any question(s) you may have throughout the week when you see me! 3-D pore-scale reactive transport model

31 Look a blank slide! That means I ll shut up now 18