List of symbols

TrEnCh project, Buckley Lab, Department of Biology, University of Washington


The tables below compile the symbols which are used by TrenchR functions:


Symbol Description
\(A\) surface or cross-sectional area (\(m^2\))
\(a\) altitude angle of the sun (degrees) (subscripts: s, for normal to a slope; c ,for the axis of a cylinder); solar absorptivity (proportion) (subscripts: \(l\), lizard thermal absorptivity; \(s\), lizard solar absorptivity)
\(Acondfact\) proportion of the animal surface area that is in contact with the ground
\(Agradfact\) proportion of the animal projected area exposed to radiation from the ground
\(air_{pressure}\) air pressure (kPa)
\(aran\) scale performance value for performance curve? if aran = 0, no scaling; if aran = 1, includes a thermodynamic effect on mean performance
\(breadth\) breadth of the thermal performance curve
\(c\) specific heat capacity (subscripts: \(a\), air; \(p\), air at constant pressure; \(so\), soil) (\(J kg^{-1}K^{-1}\) or \(J kg^{-1}{°C}^{-1}\))
\(CT\) critical thermal limit (\(°C\)) (subscripts: min, minima; max, maxima), the lower and upper temperature limit for performance
\(D\) characteristic dimension (\(m\)); thoracic diameter (\(cm\))
\(d\) thickness of material (\(m\)); diameter of a cylinder (\(m\))
\(day\) or \(doy\) day of year
\(deg\) angle (degrees)
\(depth\) depth (\(cm\))
\(e\) water vapor pressure (\(N m^{-2}, mbar\)) (subscripts: \(a\), of the air; \(s\), at saturation)
\(ef\) enhancement factor, used to adjust convective heat transfer coefficient to field conditions
\(elev\) elevation above mean sea level (\(m\)).
\(F\) view factor between the animal and radiation stream (dimensionless) (subscripts: \(a\), atmospheric radiation; \(d\), diffuse solar radiation; \(g\), ground thermal radiation; \(r\), reflected solar radiation)
\(g_{a}\) a shape factor for soil particles |
\(H_L\) or \(H\) convective heat transfer coefficient (\(W m^{-2}{°C}^{-1}\) or \(W m^{-2}K^{-1}\)) |
\(h\) height (\(m\)); length of a cylinder (\(m\)); relative humidity (decimal fraction); Planck’s constant (\(J s\)); hour angle (rad) |
\(hp\) mean month relative humidity (percentage)
\(hour\) hour (0-24)
\(K\) thermal conductance (\(W m^{-2}{°C}^{-1}\)) (subscripts f, fur; g, substrate; s, skin; sf, skin and fur; o, overall heat conductance for an animal; c, surface boundary layer for convection; so, soil).
\(k\) von Karman’s constant (dimensionless), k~0.41
\(k_{so}\) soil thermal conductivity (\(W m^{-1}K^{-1}\) or \(W m^{-1}C^{-1}\))
\(K_t\) or \(kt\) clearness index, the ratio of the global solar radiation measured at the surface to the total solar radiation at the top of the atmosphere (dimensionless)
\(L\) Monin-Obukhov length (\(m\)), a measure of the instability of heat flow
\(l\) or \(L\) length (\(m\))
\(lon\) longitude (degrees)
\(lat\) latitude (degrees)
\(LDT\) lower developmental threshold (\(°C\))
\(lw\) downward flux of near-infrared radiation (\(Wm^{-2}\))
\(m\) mass (\(kg\) or \(g\)); air mass (dimensionless)
\(P\) monthly precipitation (\(mm\))
\(psa\) proportion surface exposed (dimensionless) (subscripts: \(air\), for exposure to air; \(ref\), for exposure to ground; \(dir\), for exposure to sky or enclosure; \(g\), for exposure to substrate)
\(Q_{abs}\) solar and thermal radiation absorbed (\(W\))
\(Q_{emit}\) thermal radiation emitted (\(W\))
\(Q_{conv}\) energy exchange between an animal and the surrounding substance due to convection (\(W\))
\(Q_{cond}\) energy exchange between an animal and the surface due to conduction (\(W\))
\(Q_{met}\) energy emitted due to metabolism (\(W\))
\(Q_{evap}\) energy emitted due to evaporative water loss (\(W\))
\(r\) reflectance (decimal fraction) (subscripts: \(g\), of ground; \(S\), to direct sunlight; \(s\), to skylight); diffusion resistance to water vapor (\(s m^{-1}\)) (subscripts: \(b\), boundary layer; \(i\), internal or intercellular); resistance to heat flow (\(s m^{-1}\)) (subscripts: \(h\), \(ha\), boundary layer; \(j\), diffusion resistance to molecular species j; radius (\(m\)) (subscripts: \(b\), of inside body wall of animal; \(r\), of outer surface of animal)
\(rad\) angle (radians)
\(raz\) solar azimuth angle (degrees)
\(S\) amount of sunlight incident upon the earth’s surface (\(W m^{-2}\)) (subscripts: \(dir\), direct solar radiation; \(dif\), diffuse solar radiation; \(h\), on a horizontal surface; \(ref\), reflected solar radiation)
\(shade\) whether soil temperature is calculated in the shade or not
\(shift\) mode of the thermal performance curve
\(skew\) skewness of the thermal performance curve
\(sol.elev\) solar elevation angles (degrees)
\(SSA\) solar absorptivity of soil surface (proportion)
\(svl\) lizard snout vent length (\(mm\))
\(t\) time (\(hr\) or \(s\)) (subscripts: \(as\), after sunset; \(n\), time of minimum temperature; \(r\), sunrise; \(s\), sunset; \(p\), rise the following day; \(x\), time of maximum temperature)
\(T\) temperature (\(°C\) or \(K\) or \(°F\)) (subscripts: \(a\), air; \(g\), ground; \(s\), surface; \(sh\), shade; \(sky\), effective radiant temperature of the sky)
\(T_{dewpoint}\) dewpoint temperature (\(°C\))
\(T_{e}\) Operative environmental temperature (\(°C\))
\(T_{max}\) maximum temperature of the day (\(°C\))
\(T_{min}\) minimum temperature of the day (\(°C\))
\(Tg_{max}\) maximum soil surface temperature of the day (\(°C\))
\(Tg_{min}\) minimum soil surface temperature of the day (\(°C\))
\(T_{opt}\) thermal optima, the temperature at which peak performance occurs (\(°C\))
\(T_{soil0}\) initial soil temperature (\(°C\))
\(tolerance\) maximal breath (\(°C\)) of the thermal performance curve
\(u\) wind speed (\(m s^{-1}\)) (subscripts: \(r\), reference height or heights)
\(UDT\) upper developmental threshold (\(°C\))
\(V\) volume (\(m^{3}\)) |
\(water_{content}\) water content (percent)
\(x\) vector of volume fractions of soil constituents (e.g., clay, quartz, minerals other than quartz, organic matter, water, air)
\(z\) distance, or height above a surface (\(m\)) |
\(zr\) reference height (\(m\))
\(z0\) roughness height (\(m\))

Greek Symbols

Symbol Description
\(\alpha\) angle (rad or degrees); azimuth angle of the sun (degrees); time difference between time of maximum temperature and noon (\(hr\)) |
\(\beta\) slope angle, direction of normal from horizontal (degrees); time difference between time of maximum temperature and sunrise (\(hr\))
\(\delta\) thoracic fur thickness (\(mm\))
\(\epsilon\) emissivity (decimal fraction) (subscripts: \(a\), of atmosphere; \(s\), surface emissivity); angle (radian or degree); angle between axis of a cylinder and direction of the sun’s rays; equivalent temperature (\(°C\)); thermal absorptivity as a fraction (subscript: \(so\), soil)
\(\gamma\) decay parameter for rate of time change from sunset to time of minimum temperature
\(\lambda\) vector of the thermal conductivities (\(W m^{-1} K^{-1}\)) of the soil constituents
\(\mu\) dynamic viscosity (\(mol\:s^{-1}m^{-1}\))
\(\nu\) kinematic viscosity coefficient (\(m^2 s^{-1}\))
\(\psi\) solar zenith angle (degrees)
\(\rho\) density (\(kg m^{-3}\)) (subscripts: \(a\), of dry air; \(j\), of molecular species; \(o\), of standard air; \(w\), of water vapor; \(so\), of soil); radius of a cylinder (\(m\)); reflectivity (decimal fraction) (subscript: \(S\), surface albedo)
\(\tau\) atmospheric transmissivity (proportion) (subscripts: \(d\), to diffuse radiation; \(t\), to total radiation); thermal time constant (\(s\) or \(hr\)) (superscript: \(a\), apparent)
\(\theta\) angle between the solar beam and the longitudinal axis (degrees)

Dimensionless Groups

Symbol Description
\(Gr\) Grashof number
\(Nu\) Nusselt number
\(Re\) Reynolds number