List of symbols

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

2026-04-29

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