Laboratory in Oceanography:
Data and Methods
Observations vs. Models
MAR550, Spring 2013
Miles A. Sundermeyer
Sundermeyer
MAR 550
Spring 2013
1
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
Sundermeyer
MAR 550
Spring 2013
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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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MAR 550
Spring 2013
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Observations vs. Models
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Observations vs. Models
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Observations vs. Models
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Observations vs. Models
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Observations vs. Models
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Observations vs. Models
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Observations vs. Models
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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
Sundermeyer
MAR 550
Spring 2013
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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
Sundermeyer
MAR 550
Spring 2013
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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
Sundermeyer
MAR 550
Spring 2013
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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
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MAR 550
Spring 2013
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Observations vs. Models
Example: Analytical model
Equations of motion – e.g., Boussinesq equations and advection / diffusion
equation for passive tracer

Du
1
g



 fi3  u   p  i3
   2 2u   6 6u
Dt
0
0
D
  2 2    6 6 
Dt
DC
  2  2 C   6 6C
Dt

u  0
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Observations vs. Models
Example: Numerical model
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Observations vs. Models
Numerical model data
• For numerical models, effectively replace first two steps with:
• continuous equations representing problem to be solved, e.g, NavierStokes 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
Sundermeyer
MAR 550
Spring 2013
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Observations vs. Models
Example: Statistical model
C   C 
 

t x  x 
1
2
  S 2
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Observations vs. Models
Example: Laboratory model
Vertically oscillated
grid mixers
Top View
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Observations vs. Models
Example: Regression / curve fitting to data
yi = mxi + b
y=Xb
 y1 
y 
 2
 y2  
 

 y n 
[n  1] 
Sundermeyer
MAR 550
Spring 2013
 x1 1
 x 1
 2  m
 x3 1  

 b 
  
 xn 1
[n  2] [2  1]
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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
Sundermeyer
MAR 550
Spring 2013
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Observations vs. Models
Example: Allens Pond, Westport, MA
Total Flowrate
300
Neap
Spring
250
3
/sec) (ft
Flowrate
200
150
100
50
0
-50
-100
-150
-200
-500
-400
-300
-200
-100
0
100
200
300
400
500
600
Time (minutes since High Tide)
Salinity Concentration
32.0
Neap
Spring
SAL (ppt)
30.0
28.0
26.0
24.0
Data and figures courtesy of Case Studies in Estuarine
Dynamics (MAR620) project team, Spring 2008
22.0
20.0
-500
-400
-300
Sundermeyer
MAR 550
Spring 2013
-200
-100
0
100
200
300
Time (minutes since High Tide)
400
500
600
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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
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MAR 550
Spring 2013
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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:
0
•
•
1 P
 g  P  gh
 z
Assume quadratic drag law:
u
u
1 P
 u  fv  
 C d | u |2
t
x
 x
1 P
0
 C d | u |2
 x
1 P
| u |2 
Cd  x
Volume conservation:
dV
 u  Achannel
dt
Sundermeyer
MAR 550
Spring 2013
24
Observations vs. Models
Example: Allens Pond, Westport, MA (cont’d)
Total Flowrate
300
Neap
Spring
250
3
/sec) (ft
Flowrate
200
150
100
50
0
-50
-100
-150
-200
-500
-400
-300
-200
-100
0
100
200
300
400
500
600
Time (minutes since High Tide)
Sundermeyer
MAR 550
Spring 2013
25