In trenchproject/TrenchR: Tools for Microclimate and Biophysical Ecology
knitr::opts_chunk$set(echo = TRUE)
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); 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 | |
trenchproject/TrenchR documentation built on Oct. 10, 2023, 10:12 p.m.
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knitr::opts_chunk$set(echo = TRUE)
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); 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 | |
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