1. Laboratory in Oceanography: Data and Methods
Observations vs. Models
MAR599, Spring 2009
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

4. Observations vs. Models

5. Observations vs. Models

6. Observations vs. Models

7. Observations vs. Models

8. Observations vs. Models

9. Observations vs. Models

10. Observations vs. Models

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 = X b

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. Observations vs. Models Example: Allens Pond, Westport, MA
Total Flowrate
-200
-150
-100
-50 50
100
150
200
250
300
-500
-400
-300
400
500
600
Time (minutes since High Tide)
Flowrate (ft 3
/sec)
Neap
Spring
Salinity Concentration
20.0
22.0
24.0
26.0
28.0
30.0
32.0
-500
-400
-300
-200
-100
100
200
300
400
500
600
Time (minutes since High Tide)
SAL (ppt)
Neap
Spring
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
-200
-150
-100
-50 50
100
150
200
250
300
-500
-400
-300
400
500
600
Time (minutes since High Tide)
Flowrate (ft 3
/sec)
Neap
Spring