List of symbols

Parameters

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)

Symbol	Description
$Gr$	Grashof number
$Nu$	Nusselt number
$Re$	Reynolds number

List of symbols

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

2023-09-13

Parameters

Greek Symbols

Dimensionless Groups