This section summarizes the basic features of the water temperature model used in the current study. Full documentation of the model is available elsewhere (Nath, 1996).
Briefly, the model assumes ponds to be fully mixed, conducts an energy balance for the entire pond volume, and integrates the rate of temperature change (dT/dt; °C d-1) to arrive at daily water temperature profiles over the simulation period. For the current study, ponds were also assumed to have steady-state volumes. The differential equation for temperature change in such ponds is:
where φnet = interfacial heat transfer due to various processes that occur at the pond surface (kJ m-2d-1); ρw = density of water (kg m-3); cpw = heat capacity of water (kJ kg-1°C-1); and d = pond depth.
Heat transfer processes that are typically considered in the calculation of φnet for ponds include the net short-wave solar radiation penetrating the water surface (φsn), net atmospheric long-wave radiation (φan), long-wave water-surface radiation (φws), evaporative heat transfer (φe), and conductive heat transfer (φc) (Ryan et al., 1974; Fritz et al., 1980; Henderson-Sellers, 1984). Energy gained or lost via precipitation is usually considered to be negligible (Henderson-Sellers, 1984). The general expression for φnet is given by:
φnet = φsn + φan - φws - φe ± φc
When short-wave solar radiation (φs) strikes the water surface, part of the energy is reflected and the remainder (i.e., φsn) penetrates the water surface. Because pond water temperatures are closely related to variations in short-wave solar radiation (Fritz et al., 1980), measured values of φs (e.g., from a local weather station) should be used whenever available. In such cases, φsn is given by:
φsn = φs (1 - As)
where As = short-wave reflectivity, which has a typical value of 0.06 (Henderson-Sellers, 1984). If measured values of φs are unavailable, the methods employed by Fritz et al. (1980) can be used to estimate this variable.
Any material with a temperature above absolute zero emits radiation according to the Stefan-Boltzmann fourth-power law (Henderson-Sellers, 1984). This law is used to calculate the net long-wave atmospheric radiation into the pond (φan) and the water-surface- or back-radiation losses (φws; see below) from the pond. φan is the difference between the incident and reflected components of long-wave radiation, and can be approximated by (Henderson-Sellers, 1984):
φan = (1 - r)εa σΤak4
where: r = water surface reflectance to long-wave radiation (decimal fraction);
εa = atmospheric emissivity (dimensionless);
σ = Stefan-Boltzmann constant (4.896 × 10-6 kJ m-2 d-1 K-4); and
Τak = absolute air temperature (°K).
Water surface reflectance is typically assumed to be 0.03 (e.g., Henderson-Sellers, 1984; Losordo and Piedrahita, 1991). εa can be calculated as follows (Wunderlich, 1972):
εa = 0.937 × 10-5 × Τak2 × (1 + 0.17 Cc2)
Water surface radiation (φws) is the result of heat emission from pond water, and can be estimated as follows (Henderson-Sellers, 1984):
φws = εw σΤwk4
where: εw = emissivity of water (≈0.97); and
Τwk = absolute water temperature (°K).
Energy loss (φe) associated with the process of evaporation is given by (Ryan et al., 1974):
φe = (es - ea) [λ(Τwv - Τav)⅓ + b0u2]
where: es = saturated vapour pressure at the current water temperature (mm Hg);
ea = water vapour pressure immediately above the pond surface (mm Hg);
Τwv and Τav are the virtual water and air temperatures respectively (°K);
λ and bo are constants with values of 311.02 kJ m-2d-1 mm Hg-1K-⅓ and 368.61
kJ m-2d-1 mm Hg-1(m s-1)-1 respectively; and
u2 = wind velocity (m s-1) at a reference height of 2 m.
Vapour pressure data (es and ea in the evaporative heat loss equation) can be approximated as follows (Troxler and Thrackston, 1977):
where: Rh = relative humidity (decimal fraction).
The virtual water and air temperatures are given by (Ryan et al., 1974):
where: P = barometric pressure (mm Hg), which was assumed to be equivalent to one atmosphere (760 mm Hg) for the current study.
Heat may be removed or added to pond water because of conduction between air and the water surface; this flux can be estimated as follows (Ryan et al., 1974):
The references cited are included in the list of references, at the end of the main text
