Laboratory in Oceanography: Data and Methods Observations vs. Models

1. Laboratory in Oceanography: Data and Methods Observations vs. Models MAR550, Spring 2013 Miles A. Sundermeyer

2. Observations vs. Models • Observational data • Numerous steps involved in making and interpreting observations: • turn environmental signal to something we can measure (e.g., resistance or voltage in case of thermister) • signal conditioning – e.g., operational amplifier, low pass filter • discrete sampling – e.g., A/D converter, determines sampling rate/frequency, resolution/precision • internal processing - e.g., conditional sampling, averaging, etc. • data storage • calibration • processing/analysis

3. Observations vs. Models • Observational data • The ocean is a fundamentally a continuous environment • When we sample it, we make a finite number of discrete measurements • When we make discrete measurements, we also: • subsample • average

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11. Observations vs. Models • Measured vs. computed variables • Some of the quantities we observe are properties of the water, others are environmental variables, • e.g., salinity is a property of water, velocity is an environmental variable • Some quantities we wish to observe are directly measured, some are computed from measured quantities; • e.g., temperature is measured (sort of), salinity is computed • Measurement noise / uncertainty • Observations can contain noise from either: • Instrument noise / sampling error • Environmental variability at unresolved / unknown scales

12. Observations vs. Models • Instrument calibration • Once observations are made, sensor output converted / interpreted to yield physical units of variable being measured • e.g., CTD returns voltages, which are converted to conductivity and temperature, which are used to compute salinity

13. Observations vs. Models Other considerations for observational data accuracy - how well the sensor measures the environment in an absolute sense resolution / precision - the ability of a sensor to see small differences in readings e.g. a temperature sensor may have a resolution of 0.000,01º C, but only be accurate to 0.001º C range - the maximum and minimum value range over which a sensor works well. repeatability - ability of a sensor to repeat a measurement when put back in the same environment - often directly related to accuracy drift/stability - low frequency change in a sensor with time - often associated with electronic aging of components or reference standards in the sensor hysteresis - present state depends on previous state; e.g., a linear up and down input to a sensor, results in output that lags the input, i.e., one curve on increasing pressure, and another on decreasing response time - typically estimated as the frequency response of a sensor assuming exponential behavior self heating - to measure the resistance in the thermistor to measure temperature, we need to put current through it settling time - the time for the sensor to reach a stable output once it is turned on

14. Observations vs. Models • How do we define a “model?” • Theoretical model - an abstraction or conceptual object used in the creation of a predictive formula • Computer model - a computer program which attempts to simulate an abstract model of a particular system • Laboratory model - a laboratory apparatus that reproduces a particular observed dynamic / characteristic • Mathematical model - an abstract model that uses mathematical language • Statistical model - in applied statistics, a parameterized set of probability distributions

15. Observations vs. Models Example: Analytical model Equations of motion – e.g., Boussinesq equations and advection / diffusion equation for passive tracer

16. Observations vs. Models Example: Numerical model

17. Observations vs. Models • Numerical model data • For numerical models, effectively replace first two steps with: • continuous equations representing problem to be solved, e.g, Navier-Stokes equations. • reduce the equations to simplified form appropriate to problem of interest • discretized version of these in form of numerical model (finite difference, volume, Fourier modes, etc.) • ... • signal conditioning – e.g., operational amplifier, low pass filter • discrete sampling – e.g., A/D converter, determines sampling rate/frequency, resolution/precision • internal processing - e.g., conditional sampling, averaging, etc. • data storage • calibration • processing/analysis

18. Observations vs. Models Example: Statistical model

19. Observations vs. Models Example: Laboratory model Vertically oscillated grid mixers Top View

20. Observations vs. Models Example: Regression / curve fitting to data yi = mxi + b y = Xb

21. Observations vs. Models • Purpose of Models • Wish to be able to predict/describe the state of the ocean environment based on some form of model • Need to be able to go from one type of model to another to better understand each – sometimes models seem as complicated as real world • Ultimately seek to understand the ocean environment • Interpret observations with the context of models • Formulate new models based on observations

22. Total Flowrate 300 Salinity Concentration Neap 32.0 250 Spring Neap Spring 30.0 200 150 28.0 SAL (ppt) /sec) Flowrate (ft 100 26.0 3 50 24.0 0 -50 22.0 -100 20.0 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 -150 Time (minutes since High Tide) -200 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 Time (minutes since High Tide) Observations vs. Models Example: Allens Pond, Westport, MA Data and figures courtesy of Case Studies in Estuarine Dynamics (MAR620) project team, Spring 2008

23. Observations vs. Models Example: Allens Pond, Westport, MA (cont’d) • Conceptual Model of Allens Pond: • Estuary connected to ocean via frictional sill • Tidal range in open water extends below sill. High water mark Outer Stage

24. Observations vs. Models Example: Allens Pond, Westport, MA (cont’d) • Theoretical Model of Allens Pond: • Frictional flow, i.e., pressure gradient balanced by friction • Assume hydrostatic balance: • Assume quadratic drag law: • Volume conservation:

25. Observations vs. Models Example: Allens Pond, Westport, MA (cont’d) Total Flowrate 300 Neap 250 Spring 200 150 /sec) Flowrate (ft 100 3 50 0 -50 -100 -150 -200 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 Time (minutes since High Tide)