Sea ice 2

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

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.

Deliverable: Report (15 August 2010)

Acknowledgments

This lecture is based on 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

Table of Contents

Contents

  1. Sea ice 2
  2. Description of the course
  3. Deliverable: Report (15 August 2010)
  4. Acknowledgments
  5. Project work: source code, results
  6. Table of Contents
  7. Lesson 1+2 - Ocean mixed layer and radiative forcing without sea ice and atmosphere
    1. Scenario 1
    2. Research questions
  8. Lesson 3+4+5: Incoming shortwave radiation
    1. Top of the atmosphere
    2. Research questions
    3. Validation
  9. Lesson 5+6: Energy fluxes at the ocean surface
    1. Scenario
    2. Research questions
    3. Observed fluxes from SHEBA experiment
  10. Lesson 7: Sea ice model
    1. Scenario
    2. Research questions
  11. Literature

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

Scenario 1

mixed_layer.png

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+5: 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

$Q_{SW}^{\downarrow}=S \cos(Z)$

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

$\cos Z=\sin \phi \sin \delta + \cos \phi \cos \delta \cos HA$

where

$\phi, \delta, HA, $

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

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

Research questions

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.

Lesson 5+6: Energy fluxes at the ocean surface

In this lesson we look at the energy fluxes at the ocean surface in polar latitudes. We will analyse the importance (magnitudes) of the different fluxes.

Scenario

Research questions

Observed fluxes from SHEBA experiment

The Surface Heat Budget of the Arctic Ocean Project provides a unique data set for sea ice studies.

Huwald et al. 2005 Table 2 Table with numbers only and columns ordered Jan. to Dec. 

Table 2. Monthly and Yearly Means of the Energy Budget Componentsa                                                                                                      

Var     Nov.    Dec.    Jan.    Feb.    March   April   May     June    July    Aug.    Sept.   Oct.    Year Mean
Fswd    0.1     0.0     0.0     5.1     46.3    142.3   248.7   280.4   211.4   110.8   39.9    20.0    92.1
Fswu    -0.1    0.0     0.0     -4.3    -39.4   -120.5  -204.4  -200.2  -135.9  -77.6   -25.9   -13.0   -68.5
Fsw     0.0     0.0     0.0     0.8     7.0     21.9    44.4    80.1    75.5    33.2    13.9    7.0     23.6
Fswp    0.0     0.0     0.0     0.1     0.6     1.8     3.6     9.6     12.8    5.5     0.5     0.2     2.9
Flwd    209.6   152.0   170.5   163.8   201.2   220.0   245.7   282.5   299.7   299.3   282.2   245.9   231.0
Flwu    -227.1  -185.2  -197.6  -190.2  -222.1  -242.4  -273.7  -308.2  -314.5  -310.7  -293.0  -260.1  -252.1
Flw     -17.6   -33.2   -27.1   -26.4   -20.8   -22.4   -28.0   -25.7   -14.8   -11.4   -10.7   -14.2   -21.0
Fsh     3.4     6.4     4.7     7.5     3.0     0.6     -1.1    1.5     1.6     -2.3    -0.4    1.5     2.4
Flh     0.3     0.3     0.1     0.0     -0.6    -0.5    -2.1    -2.2    -0.3    -1.5    -0.9    -0.3    -0.6
Fnet    -13.8   -26.5   -22.4   -18.2   -12.0   -2.1    11.9    44.2    49.1    12.5    3.8     -5.0    1.7
Fcs     14.8    19.7    13.1    13.1    8.3     7.0     2.2     -2.0    -3.7    -0.5    4.6     9.7     7.2
Fms     0.0     0.0     0.0     0.0     0.0     0.0     -3.2    -30.4   -48.0   -6.0    -4.0    -2.0    -7.8
Frs     1.0     -6.8    -9.3    -5.2    -3.7    4.8     10.9    12.4    -2.7    7.6     5.4     3.2     1.5
Fcb     -9.4    -13.0   -14.6   -13.3   -11.9   -8.2    -5.5    -2.6    -0.4    1.3     -2.3    -5.9    -7.1
Fmb     6.4     9.6     10.7    8.3     4.5     4.2     0.9     -7.3    -13.5   -15.2   -8.0    -0.8    0.0
Focn    3.0     3.4     3.9     5.0     7.4     4.0     4.6     9.9     13.9    13.9    10.3    6.7     7.1
Abbreviations are as follows: Fswd, Fswu, Fsw, Fswp, downward, upward, net, and penetrating shortwave radiation, respectively; Flwd, Flwu, Flw, downward, upward, and net longwave radiation, respectively; Fsh, Flh, sensible and latent heat flux, respectively; Fnet, net atmospheric heat fluxes; Fcs, conductive heat flux at the surface; Fms, energy of melt at the surface; Frs, net residual heat flux at the surface. The last three lines show the monthly and yearly means of the basal conductive heat flux (Fcb), energy of melt (Fmb), and the net residual heat flux, i.e., the ocean heat flux (Focn). All values are given in Wm-2.

Lesson 7: Sea ice model

The 0-layer model of Semtner (1976) shall be implemented and tested.

0-layer.png

Standard parameters of Semtner (1976) in SI units:

\begin{tabular}{llll} $k_i$ & thermal conductivity of sea ice & 2.0334 & W m$^{−1}$ K$^{−1}$ \\ $k_s$ & thermal conductivity of snow & 0.3096 & W m$^{−1}$ K$^{−1}$\\ $(\rho c)_i$ & volumetric heat capacity of sea ice & 1882.8 & kJ m$^{−3}$ K$^{−1}$\\ $(\rho c)_s$ & volumetric heat capacity of snow & 690.36 & kJ m$^{−3}$ K$^{−1}$\\ $(\rho c)_w$ & volumetric heat capacity of water & 4284 & kJ m$^{−3}$ K$^{−1}$\\ $L_B$ & volumetric heat of fusion of ice at lower surface & 2.67776 10$^5$ & kJ m$^{−3}$\\ $L_i$ & volumetric heat of fusion of ice at upper surface & 3.01248 10$^5$ & kJ m$^{−3}$\\ $L_s$ & volumetric heat of fusion of snow & 1.09621 10$^5$ & kJ m$^{−3}$\\ $\alpha_i$ & bare ice albedo & 0.64 & \\ $\alpha_s$ & snow albedo & 0.64-0.85 & \\ $I_0$ & fraction of penetrating shortwave radiation & 17 & \% \\ $\sigma$ & Stefan-Boltzmann constant (not correct!) & 5.7948 ·10$^{−8}$ & W m$^{−2}$ K$^{−4}$\\ $T_{f}$ & freezing temperature of sea water & -2 & $^\circ$C\\ \end{tabular}

Scenario

Research questions

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: SeaIce2 (last edited 2010-06-21 15:10:36 by anonymous)