I. Properties of Water

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

            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

        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)

HOW ARE THESE LAYERS FORMED?

    B. Seasonal cycles for a temperate lake
        1. winter
 
 

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

2. early spring
   spring turnover or overturn

            Isothermal
        3. late spring –
           incipient stratification

              Resistance to mixing proportional to d(r)/dz

        4. early to mid-summer
             summer stratification

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

        5. early fall

        6. fall overturn

        7. return to winter and inverse stratification

        8. complex summer temperature profiles

    C. Factors affecting the mixing cycle
        1. morphology
             fetch

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

        2. geography

        3. water clarity

        4. weather

III. Patterns of stratification

        holomictic -- 

        depth-time diagram of isotherms

    A. Dimictic -- 

        2. warm monomictic

    C. Special considerations in tropical lakes

    D. 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

            - 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)
 

                                z_max
            a.  S =  1/A₀  S  (r_z – r_average) (z - z _raverage) (A_z) dz
                                  Z₀

              where S is actually an integral symbol (apparently non-existent on my html font file for now!)
              where    A_o = the surface area in cm
                           A_z = the area at some depth z (in cm)
                         r_average = the final or mean density that would result if the lake were completely  mixed
                         r_z = the density at depth z
                           z_raverage = the depth (cm) where the final (mixed) mean density exists prior to mixing
                           z_max = 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) / r_average (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
                T_s = maximum summer temperature at depth z
                T_w = minimum winter temperature at depth z

        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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