Thermal Stratification

I. Properties of Water

    A. Bonding -- dipole moment
          high dipole moment; electrons associate with O with a higher probability than with H

covalent bonds in water molecules

hydrogen bonds in water molecules

            H-O-H angle is 104.5 degrees
            hydrogen bonds

            good solvent for salts and polar organic molecules

    B. Characteristics of water

        1. specific heat
            - capacity to absorb thermal energy per unit change in temperature
            - water takes 1 cal/g to raise the temperature 1 degree C

        2. latent heat of vaporization
            - amount of thermal energy needed to change from water to gas
            - for water this is 540 cal/g
            - for heat of sublimation (ice to gas) is 679 cal/g

        3. latent heat of fusion
            - amount of thermal energy needed to be removed to change 1 g. of material from liquid (water) to solid (ice)
            - for water this is79.7 cal/g

        So these attributes make water a good thermal buffer

        4. density – See Figure 2-3 in Wetzel

        - Density = rho = r = g x cm-3
        - Temperature of maximum density is 3.98 degrees C
        - Ice lattice has more space and so ice less dense
        - Density vs. temperature - nonlinear

          Density-temperature relationship is affected by:

                a) dissolved salts -- increased density with increasing salts

                b) particulates

                c) dissolved gases

                d) pressure -- increase of pressure decreases the temperature of maximum density.                    

        5. Viscosity – water is 775 times density of air and more viscous; [viscosity decreases as temperature increases]

        6. Surface tension high

II. Thermal Stratification

    A. Layering

thermal layers in a lake: epilimnion, metalimnion and hypolimnion

        1. epilimnion -- upper mixed layer -- warmer water (less dense)

        2. metalimnion -- middle layer -- where temperature changes
            - thermocline is the plane where dT/dz is maximum

        3. hypolimnion -- lower layer -- cooler water (more dense)


    B. Seasonal cycles for a temperate lake
        1. winter

temperate stratification -- winter pattern

                  reverse stratification or inverse stratification  cold water is on top of warmer water

2. early spring
   spring turnover or overturn

temperate stratification -- early spring

        3. late spring –
           incipient stratification

temperate stratification -- late spring

              Resistance to mixing proportional to d(r)/dz

        4. early to mid-summer
             summer stratification

temperate stratification -- summer

            Why is hypolimnion temperature in summer often more than 4 degrees C?

        5. early fall

temperate stratification -- fall

        6. fall overturn

        7. return to winter and inverse stratification

        8. complex summer temperature profiles

stratification -- complex summer profiles

    C. Factors affecting the mixing cycle
        1. morphology

        thermal bars -- in a large lake with shallow water nearshore, the shallow area will warm faster

thermal bar formation

heat exchange in shallow portions of the lake

        2. geography

        3. water clarity

        4. weather

III. Patterns of stratification

        holomictic -- 

        depth-time diagram of isotherms

    A. Dimictic -- 

depth-time stratification figure for a temperate lake
    B. Monomictic
monomictic lake stratification patterns
        1. cold monomictic  

        2. warm monomictic

    C. Special considerations in tropical lakes

    D. Polymictic

polymictic lake mixing patterns
        1. cold polymictic

        2. warm polymictic

    E. Oligomictic

    F.  Amictic

    G. Meromictic  (mero=partial)

           mixolimnion -- shallow layer that mixes
           monimolimnion -- deep layer that doesn't mix
           pycnocline -- region of maximum density change
           chemocline -- region of change in density due to change in salinity; dissolved salts or organics

        1. ectogenic -- external event brings salt water into a freshwater lake or freshwater into a saline lake

        2. crenogenic -- submerged saline springs release dense water to deep portions of lake basins

        3. biogenic -- accumulation of salts due to decomposition in the sediments, sinking organic matter,
                                and photosynthetic precipitation of carbonate

    H. Patterns of lake mixing types

Distribution of lake mixing types based on adjusted latitude and depth

            - Updated version of figure 6-7 in Wetzel from Hutchinson and Loffler, 1956

IV. Resistance to mixing and stability
    A. Resistance to mixing proportional to dr /dz

    B. Stability – the resistance to mixing; the amount of work that would be required to mix an entire lake to uniform density without adding
            or subtracting heat in the process.

        1. Whole lake stability – determines if the whole lake will mix; is the amount of energy required to mix the entire lake to uniform density (KJ/cm3)

            a.  S =  1/A S  (rzraverage) (z - z raverage) (Az) dz

              where S is actually an integral symbol (apparently non-existent on my html font file for now!)
              where    Ao = the surface area in cm
                           Az = the area at some depth z (in cm)
                         raverage = the final or mean density that would result if the lake were completely  mixed
                         rz = the density at depth z
                           zraverage = the depth (cm) where the final (mixed) mean density exists prior to mixing
                           zmax = maximum depth in cm
                           z0 = surface or zero depth

        2. Richardson’s stability – determines whether or not two fluids will mix
            a. Ri = (g x dr/dz) / raverage (du/dz)2
                  Where g = acceleration of gravity
                         r = density
                           u = horizontal velocity
            b. Ri > 0.25 then no mixing -- numerator dominates
            c. Ri < 0.25 then will mix -- denominator dominates (energy of mixing)

    C. Heat in lakes
        1. Annual heat budget (Birgean heat budget) – record of the heat content of the lake
            - Winter heat income – amount of heat required to warm a dimictic lake from winter stratification to isothermal mixing in spring
            - Summer heat income – amount of heat required to heat the lake from spring mixing to its maximum summer heat content

                A = Area at depth z
                Ts = maximum summer temperature at depth z
                Tw = minimum winter temperature at depth z

heat budget

        2. Analytical heat budget – budget based on identification of all the sources and sinks for heat to or from a lake

   D. Streams and Heat

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