Author: TrEnCh project, Buckley Lab, Department of Biology, University of Washington
Date: 2026-04-28

# List of symbols

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

#### 2026-04-28

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

### Parameters

# Symbol \(A\) | # Description 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 |