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); albedo (subscript: s, surface) | |

\(Acondfact\) | 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 | |

\(abs\) | absorptivity to solar radiation (proportion) | |

\(air_{pressure}\) | 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 | |

\(H\) | solar radiation (\(W m^{-2}\)) (subscripts: \(sdir\), for direct flux; \(sdif\), for diffuse flux; \(sref\), for reflected flux) | |

\(H_L\) or \(H\) | convective heat transfer coefficient (\(W m^{-2}{°C}^{-1}\) or \(W m^{-2}K^{-1}\)) | |

\(Hr\) | mean month relative humidity (percentage) | |

\(h\) | height (\(m\)); length of a cylinder (\(m\)); relative humidity (decimal fraction); Planck’s constant (\(J s\)); hour angle (rad) | |

\(hour\) | 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 (\(W m^{-1}K^{-1}\)) | |

\(K_t\) 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) | |

\(solrad\) | solar radiation (\(W m^{-2}\) per day) | |

\(SSA\) | 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 (\(°C\)) | |

\(V\) | velocity (\(m s^{-1}\)); 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 (\(m\)); zenith angle (°) | |

\(zr\) | reference height (\(m\)) | |

\(z0\) | roughness height (\(m\)) |

Symbol | Description | |
---|---|---|

\(\alpha\) | angle (rad or degrees); azimuth angle of the sun (degrees); solar absorptivity (proportion) (subscripts: \(L\), lizard thermal absorptivity; \(S\), lizard solar absorptivity); 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) |

Symbol | Description | |
---|---|---|

\(Gr\) | Grashof number | |

\(Nu\) | Nusselt number | |

\(Re\) | Reynolds number |