# List of symbols

#### 2022-09-20

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

### 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); 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 ($$m$$)

### Greek Symbols

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)

### Dimensionless Groups

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