Heat budgets Significant impacts on water quality - Physical processes (thermal stratification), chemical and biological transformations of matters in water - Diurnal temperature variations: ammonia toxicity - Effects on biota Relationship btw. Temp and Heat  Water has a very high value of specific heat T = temperature ( o C or K)  = density (kg/m 3 or g/cm 3 ) H = heat (J or cal) C p = specific heat (J kg -1 o C -1 or cal g -1 o C -1 ) substanceDensity (kg/m 3 ) at 20 o CSpecific heat (J kg -1 o C -1 ) Dry air Water Common brick Cast iron

Heat balance Governing equation Accumulation = inflow – outflow  surface heat exchange  heat exchange with sediment Accumulation: Inflow: Outflow: Surface heat exchange: Heat exchange with sediment: Total balance Surface heat exchange InflowOutflow Heat exchange with sediment

Surface heat exchange The components of surface heat exchange Radiation – energy that transmitted in the form of electromagnetic waves and does not depend on matter for its transmission Non-radiation – depends on the motion of molecules of matter (conduction, evaporation) Net absorbed radiation – independent of water temperature Water-dependent components – affected by water temperature

Surface heat exchange The total surface heat flux J sn = net solar shortwave radiation J an = net atmospheric longwave radiation J br = longwave back radiation from the water J c = conduction J e = evaporation Net absorbed radiation Solar shortwave radiation = f (solar altitude, scattering, absorption, reflection, shading) J 0 = extraterrestrial radiation a t = atmospheric attenuation (Bras’ method = f (turbidity) or Ryan/Stolzenbach’s method = f (elevation, solar altitude) a c = cloud attenuation 1-R s = reflection, R s = albedo (fraction reflected) 1-S f = shading, S f = effective shade (fraction blocked by vegetation and topography) Atmospheric longwave radiation – longwave radiation emitted by the atmosphere itself  = the Stefan-Boltzmann constant T air = air temp. ( o C)  sky = effective emissivity of the atmosphere 1-R L = reflection, R L = longwave reflection coeff. (  0.03)  sky can be determined by one of three methods: Brutsaert’s, Brunt’s, and Koberg’s (QUAL2K manual – Brutsaert’s method-physically-based, good for intermediate latitude- is broadly used)

Surface heat exchange Water-dependent components Water longwave radiation – back radiation from the water surface  = emissivity of water (  0.97) T s = water surface temp. Conduction (transfer of heat from molecule to molecule when matter of different temperatures come into contact) and convection (heat transfer that occurs due to mass movement of fluids) c 1 = Bowen’s coeff. (  0.47 mmHg/ o C) f(Uw) = wind velocity term, determined by one of three methods: Brady-Graves-Geyer’s, Adams 1’s, and Adams 2’s (QUAL2K manual) Evaporation and condensation – heat loss represented by Dalton’s law e s = saturation vapor pressure at the water surface (mmHg) e air = vapor pressure in the overlying air (mmHg) Wind speed conversion – to enter the equivalent wind velocity value in QUAL 2K (wind speed at 7 meters above the water surface) U wz = wind speed measured at a height z w (m/s) z = 7 m, z w = height at wind speeds measured (m)

Sediment-water heat exchange Heat flux btw. bottom sediment and overlying water  s = sediment density (g/cm 3 ) C ps = specific heat for the sediment (0.7 cal g -1 o C -1 in QUAL 2K)  s = sediment thermal diffusivity (0.005 cm 2 /s in QUAL 2K) H sedi = effective thickness of the sediment layer (cm) T sedi = temp. of the bottom sediment Total heat flux Net solar radiation Atmospheric longwave radiation Water longwave radiation Conduction/ convection Evaporation/ condensation Sediment-water heat exchange

Atmospheric moisture Relative humidity e air = vapor pressure of the air (mmHg) e sat = saturation vapor pressure (mmHg) T d = dew-point temperature Ex 30.3 calculation of relative humidity, dew point and air temp. Air temp = 25 o C, relative humidity = 60%, and water temp. = 35 o C (a) Air vapor pressure and dew-point temp. (b) Evaporation takes place?

Temperature simulation in QUAL 2K Heat balance for a reach I, Bulk dispersion coefficient, Net heat loads from point/nonpoint sources,