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= Description of the course = == Description of the course ==
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= Deliverable: Report (15 August 2011) =
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 * Description of conducted experiments
 * Assumptions
 * Governing equations
 * Model variables
 * Forcing data
 * Model results (graph and descriptions)
 * Source code
 * Discussion and conclusions
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= Acknowledgments =

This lecture is derived from content taken from a lecture ''Sea ice modeling'' by Aike Beckmann (Univ. Hamburg, Summer 2009) and a short course on ''Ice-Ocean Modeling and Data Assimilation'' which was conducted by Frank Kauker and Michael Karcher (Univ. Bremen, 6-7 December 2006).

= Project work: source code, results =
[[/Gruppe1]] [[/Gruppe2]] [[/Gruppe3]] [[/Gruppe4]] [[/Gruppe5]]
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= Lesson 3+4: Incoming shortwave radiation =

== Top of the atmosphere ==

A rough approximation for the flux of solar irradiance at the top of the atmosphere (TOA) can be derived from geometric considerations, e.g. Parkinson and Washington (1979)

{{{#!latex
$Q_{SW}^{\downarrow}=S \cos(Z)$
}}}
with the solar constant ''S''=1360 W/m^2^, the solar zenith angle ''Z''. The cosine of the zenith angle is given by

{{{#!latex
$\cos Z=\sin \phi \sin \delta + \cos \phi \cos \delta \cos HA$
}}}
where

{{{#!latex
 $\phi, \delta, HA, $
}}}
are [[http://en.wikipedia.org/wiki/Equatorial_coordinate_system|latitude, declination, and hour angle]], respectively. The declination and hour angle are calculated as

{{{#!latex
$$ \delta=23.44^\circ \times \cos (( 172- \textrm{day of year}) \times \pi/180) $$
$$ HA= (12 \textrm{hours - solar time}) \times \pi/12 $$
}}}

=== A long term numerical solution for the insolation quantities of the Earth ===

For paleoclimate applications it is interesting to know how to calculate the insolation from astronomical parameters: [[http://www.aanda.org/index.php?option=com_article&access=doi&doi=10.1051/0004-6361:20041335&Itemid=129|La2004]], [[http://www.imcce.fr/Equipes/ASD/insola/earth/La2004/index.html|source code]]


== Research questions ==
 * Calculate and plot the diurnal cycle of solar irradiance for the latitude of Hamburg on May 1st.
 * Calculate and plot the daily averaged solar irradiance for three latitudes (0, 50, 90) as a function of time
 * Calculate and plot the zonal averaged solar irradiance for different months (e.g. January and July)
 * Compare with the calculated irradiance with CERES measurements
 * Calculate and plot the oceanic mixed layer temperature (''h_ml=10''m, ''T(0)=10''^°^ C) forced with the solar irradiance (lat=30^°^). Integration time shall be 3000 days. Explain the relation of temperature and irradiance.
 * Change the time step to one hour and calculate the diurnal cycle of the oceanic mixed layer temperature. Vary the mixed layer depth and latitude.

== Validation ==
Radiative flux measurements are available from the [[http://science.larc.nasa.gov/ceres/index.html|Clouds and the Earth s Radiant Energy System (CERES) sensor]]. Climatology products from the NASA Langley Research Center Atmospheric Science Data Center can be used to validate flux parameterizations. The [[http://lposun.larc.nasa.gov/cgi-bin/cgiwrap/ceresdm/browse/browse.pl|CERES-Terra 5-year TOA global product]] has an easy to use browse interface. Select Terra based CERES EBAF (Net Adjusted) Browse Products (Monthly Means) Shortwave Incoming for a comparison to your results.



= Results =

Source code and results of project work

[[/Gruppe1]] [[/Gruppe2]] [[/Gruppe3]] [[/Gruppe4]] [[/Gruppe5]]


= Deliverable: Report (15 August 2011) =

 * Description of conducted experiments
 * Assumptions
 * Governing equations
 * Model variables
 * Forcing data
 * Model results (graph and descriptions)
 * Source code
 * Discussion and conclusions

= Acknowledgments =

This lecture is derived from content of a lecture ''Sea ice modeling'' by Aike Beckmann (Univ. Hamburg, Summer 2009) and a short course on ''Ice-Ocean Modeling and Data Assimilation'' which was conducted by Frank Kauker and Michael Karcher (Univ. Bremen, 6-7 December 2006).
Line 63: Line 115:
[[/Refs|References for download]] [[/References|References for download]]

Sea ice 2

Lecture, exercises and practical by Jun.-Prof. Dr. Lars Kaleschke

  • Monday 13:30-15:00
  • Room ZMAW 022

Description of the course

The lecture will cover the thermodynamic coupling between the sea ice, the ocean, and the atmosphere. It is designed for master-level students with moderate knowledge in numerical methods, scientific programming, and sea ice physics. A conceptual model of the Arctic will be derived and simulation results will be analyzed. For didactical reasons the model will be developed from scratch and kept as simple as possible, but complex enough to learn about the basic principles of the thermodynamic interaction between the ocean, the ice and the atmosphere for climatic, oceanographic and meteorological studies.

Table of Contents

Contents

  1. Sea ice 2
    1. Description of the course
  2. Table of Contents
  3. Lesson 1+2 - Ocean mixed layer and radiative forcing without sea ice and atmosphere
    1. Scenario 1
    2. Research questions
  4. Lesson 3+4: Incoming shortwave radiation
    1. Top of the atmosphere
    2. Research questions
    3. Validation
  5. Results
  6. Deliverable: Report (15 August 2011)
  7. Acknowledgments
  8. Literature

Lesson 1+2 - Ocean mixed layer and radiative forcing without sea ice and atmosphere

Scenario 1

  • Ocean mixed layer forced by shortwave radiation only
  • No atmosphere
  • No exchange with deeper ocean layers, immediate mixing
  • Heat balance at the sea surface: Short wave incoming radiation + long wave outgoing radiation 
    latex error! exitcode was 2 (signal 0), transscript follows:
  • Numerics: forward-in-time integration, finite differences 
  • latex error! exitcode was 2 (signal 0), transscript follows:

Research questions

Compute the time evolution of the ocean mixed layer temperature T_ml(t) for different h_ml, initial temperatures T_ml(t=0), and short wave insolation Q_SW.

Estimate the typical time scale for stationarity and select appropriate time step delta_t for model integration.

Change insolation after the model has reached stationarity.

Lesson 3+4: Incoming shortwave radiation

Top of the atmosphere

A rough approximation for the flux of solar irradiance at the top of the atmosphere (TOA) can be derived from geometric considerations, e.g. Parkinson and Washington (1979) 

latex error! exitcode was 2 (signal 0), transscript follows:

with the solar constant S=1360 W/m2, the solar zenith angle Z. The cosine of the zenith angle is given by 

latex error! exitcode was 2 (signal 0), transscript follows:

where 

latex error! exitcode was 2 (signal 0), transscript follows:

are latitude, declination, and hour angle, respectively. The declination and hour angle are calculated as 

latex error! exitcode was 2 (signal 0), transscript follows:

A long term numerical solution for the insolation quantities of the Earth

For paleoclimate applications it is interesting to know how to calculate the insolation from astronomical parameters: La2004, source code

Research questions

  • Calculate and plot the diurnal cycle of solar irradiance for the latitude of Hamburg on May 1st.
  • Calculate and plot the daily averaged solar irradiance for three latitudes (0, 50, 90) as a function of time
  • Calculate and plot the zonal averaged solar irradiance for different months (e.g. January and July)
  • Compare with the calculated irradiance with CERES measurements

  • Calculate and plot the oceanic mixed layer temperature (h_ml=10m, T(0)=10° C) forced with the solar irradiance (lat=30°). Integration time shall be 3000 days. Explain the relation of temperature and irradiance.

  • Change the time step to one hour and calculate the diurnal cycle of the oceanic mixed layer temperature. Vary the mixed layer depth and latitude.

Validation

Radiative flux measurements are available from the Clouds and the Earth s Radiant Energy System (CERES) sensor. Climatology products from the NASA Langley Research Center Atmospheric Science Data Center can be used to validate flux parameterizations. The CERES-Terra 5-year TOA global product has an easy to use browse interface. Select Terra based CERES EBAF (Net Adjusted) Browse Products (Monthly Means) Shortwave Incoming for a comparison to your results.

Results

Source code and results of project work

/Gruppe1 /Gruppe2 /Gruppe3 /Gruppe4 /Gruppe5

Deliverable: Report (15 August 2011)

  • Description of conducted experiments
  • Assumptions
  • Governing equations
  • Model variables
  • Forcing data
  • Model results (graph and descriptions)
  • Source code
  • Discussion and conclusions

Acknowledgments

This lecture is derived from content of a lecture Sea ice modeling by Aike Beckmann (Univ. Hamburg, Summer 2009) and a short course on Ice-Ocean Modeling and Data Assimilation which was conducted by Frank Kauker and Michael Karcher (Univ. Bremen, 6-7 December 2006).

Literature

References for download

Maykut, G.A. & N. Untersteiner, 1971: Some results from a time-dependent thermodynamic model of sea ice. J. Geophys. Res.,76, 1550-1575.

Semtner, A., 1976: A model for the thermodynamic growth of sea ice in numerical investigations of climate, J. Phys. Oceanogr, 6, 379-389.

Hibler III, W.D., 1979: A dynamic-thermodynamic sea ice model. J. Phys. Oceanogr., 9, 815-846.

Parkinson, C.L. & W.M. Washington, 1979: A large-scale numerical model of sea ice., J. Geophys. Res., 84, 311-337.

Sellers, W.D., 1969: A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System, J. Appl. Met., 8(3), 392-400.

LehreWiki: 63-936_2015 (last edited 2015-07-22 12:07:20 by anonymous)