Symbols

Latin symbols

Greek symbols

Subscripts

Operators

empirical constants in [Best 1950] drop spectrum (eq. 2.24)

[m $^{2}$ ] area

$A_{\text{catch}}$ [m $^{2}$ ] catchment area

empirical constant in [Best 1950] drop spectrum (eq. 2.24)

slope of the fit function , in correlation plots

[-] mean pressure coefficient

empirical constant in [Best 1950] drop spectrum (eq. 2.24)

, , , parameters in a general formula for raindrop spectra (eq. 2.25)

[-] drag coefficient

$C_\mu$ [-] - $\epsilon$ model constant

$C_{1\epsilon}$ [-] - $\epsilon$ model constant

$C_{2\epsilon}$ [-] - $\epsilon$ model constant

[m] displacement height

[m] raindrop diameter

$D_{50}$ [m] median median drop size (eq. 2.20)

[-] roughness parameter (eq. 6.5)

[-] fraction of liquid water in the air comprised by drops with diameters less than (eq. 2.19)

[m s $^{-2}$ ] gravitational acceleration

$h_{\text{i.b.l.}}$ [m] internal boundary layer height

$\mathcal{H}$ [m] building height; obstacle height

[-] turbulence intensities

[-] driving rain ratio (eq. 2.28)

$\text{\fontfamily{computermodern}\selectfont\itshape k}$ [-] von Kármán constant (0.4)

[m $^{2}$ s $^{-2}$ ] turbulent kinetic energy per unit of mass

$\ell_{\text{stop}}$ [m] stopping distance

$\mathcal{L}$ [m] characteristic eddy dimension (section 2.2.3)

$\mathcal{L}_g$ [m] smaller of $2\mathcal{H}$ (two times building height) and $\mathcal{W}$ (building width), section 2.1.4

[m] integral length scale

[kg] mass

[kg m $^{-3}$ m $^{-1}$ ] raindrop mass concentration spectrum

[m $^{-3}$ m $^{-1}$ ] raindrop number concentration spectrum

[m $^{-3}$ m $^{-1}$ ] parameter in [Marshall and Palmer 1948] drop spectrum (eq. 2.21)

[-] number

empirical constant in [Best 1950] drop spectrum (eq. 2.24)

correlation coefficient; the coefficient of determination is (eq. 3.4)

[mm h $^{-1}$ ] rain intensity, also expressed in [kg m $^{-2}$ s $^{-1}$ ] = [mm s $^{-1}$ ]

$R_{\text {f}}$ [mm h $^{-1}$ ] driving rain intensity

$R\!e$ [-] Reynolds number

[s] time

$t_{\text{cl}}$ [s] averaging and summation period, the periods are synchronised to clock and calendar; the first period of a day starts at 00h00.

$t_{\text{dry}}$ [s] pause between rain spells

$t_{\text{s}}$ [s] sample time

$t_{\text{prec}}$ [s] precipitation time

[s] integral time (eq. 6.7)

$u_\ast$ [m s $^{-1}$ ] friction shear velocity

$\vec{u}$ [m s $^{-1}$ ] wind velocity vector

[m s $^{-1}$ ] longitudinal, lateral and vertical wind velocity

$\vec{u}_{\text{D}}$ [m s $^{-1}$ ] raindrop velocity vector

$u_{\text{D}}, v_{\text{D}}, w_{\text{D}}$ [m s $^{-1}$ ] raindrop velocity in , and direction

[m s $^{-1}$ ] wind speed $= \sqrt{U_x^2+U_y^2+U_z^2}$

$U_{\text {h}}$ [m s $^{-1}$ ] horizontal wind speed $= \sqrt{U_x^2+U_y^2}$

$U_{\text{10}}$ [m s $^{-1}$ ] horizontal wind speed at 10 m height on open terrain with = 0.03 m and = 0 m

[m s $^{-1}$ ] wind velocity components ( is due north, west, upwards)

[m s $^{-1}$ ] wind velocity vectors according to the anemometer axis system

$V_{\text{tip}}$ [ml] effective volume of a rain gauge bucket

$w_{\text{term}}$ [m s $^{-1}$ ] terminal drop speed

[kg m $^{3}$ ] liquid water content (i.e. amount of liquid water per unit of air)

$\mathcal{W}$ [m] building width

[m] position coordinates ( is upwards)

-axis quantity and -axis quantity of the fit function , in correlation plots

[m] roughness length

$\alpha$ coefficient in Lacy's formula 2.29

$\alpha$ coefficient in model 2 (eq. 5.4)

$\beta$ exponent in Lacy's formula 2.29

$\beta$ exponent in model 2 (eq. 5.4)

$\beta$ constant in eq. 6.8

$\gamma$ exponent in model 2 (eq. 5.4)

$\epsilon$ [m $^{2}$ s $^{-3}$ ] dissipation rate of

$\eta (D)$ [-] catch ratio (eq. 2.26)

$\theta$ [ $^\circ$ ] constant in function $\text {\textit {L}}$ (fig. 5.23) for model 2 (eq. 5.4)

$\theta$ [ $^\circ$ ] angle (in chapter 6)

$\kappa$ [-] obstruction factor, eq. 2.35

$\Lambda$ [m $^{-1}$ ] parameter in [Marshall and Palmer 1948] drop spectrum (eq. 2.21)

$\mu$ parameter in [Ulbrich 1983] drop spectrum (eq. 2.23)

$\mu$ [kg m $^{-1}$ s $^{-1}$ ] dynamic viscosity (1.6-1.8 10 $^{-5}$ kg m $^{-1}$ s $^{-1}$ for air), $\mu = \rho \nu$

$\nu$ [m $^{2}$ s $^{-1}$ ] kinematic viscosity (1.3-1.5 10 $^{-5}$ m $^{2}$ s $^{-1}$ for air), $\nu = \mu /\rho$

$\nu_t$ [m $^{2}$ s $^{-1}$ ] turbulent or eddy viscosity

$\xi$ [-] constant in function $\text {\textit {L}}$ (fig. 5.23) for model 2 (eq. 5.4)

$\rho$ [kg m $^{-3}$ ] density

$\sigma_K$ [-] - $\epsilon$ model constant

$\sigma_\epsilon$ [-] - $\epsilon$ model constant

$\tau$ [N m $^{-2}$ ] turbulent shear stress $\rho u' w'$

$\tau_0$ [N m $^{-2}$ ] surface shear stress (eq. 2.2)

$\varphi(D)$ [kg m $^{-2}$ s $^{-1}$ m $^{-1}$ ] raindrop mass flux spectrum (definition of $\varphi _{\text {h}}(D)$ in eq. 2.16)

$\Phi$ [ $^\circ$ ] horizontal wind direction, angle from which the wind blows, clock wise from north (e.g. 270 $^\circ$ is wind from west)

5, 10, 60 clock period $t_{\text{cl}}=$ 5, 10 and 60 min respectively

$\text{a}$ air

$\text{c}$ corrected, esp. for rain intensity: rain intensity is obtained by combining data of a tipping-bucket rain gauge and a rain indicator (see section 3.4.3)

$\text{D}$ raindrop

$\text{e}$ estimate (eq. 3.4)

$\text{f}$ at façade

$\text{h}$ horizontal (at reference unless otherwise indicated)

$\text{m}$ measurement (eq. 3.4)

P1, P2, ... measurement positions

$\text{r}$ reference

$\text{u}$ uncorrected, esp. for rain intensity: rain intensity is obtained by simply counting the tippings of a tipping-bucket rain gauge (see section 3.4.3)

$\text{v}$ vertical (at reference unless otherwise indicated)

fluctuating component of ( $x = \bar{x} + x'$ )

$\sigma_{x}$

standard deviation of

$\text {\textit {L}}(\Phi ,\theta ,\xi )$

$\cos((\Phi-\theta)/\xi)$ for $-90\text{$^\circ$}\xi \le \Phi-\theta \le 90\text{$^\circ$}\xi$ , and by for the other values of $\Phi$ , where $\xi$ is limited to the interval 0-1 (fig. 5.23)

$\bar{x}$ mean of

fluctuating component of ( $x = \bar{x} + x'$ )

$\sigma_{x}$ standard deviation of

$\text {\textit {L}}(\Phi ,\theta ,\xi )$ $\cos((\Phi-\theta)/\xi)$ for $-90\text{$^\circ$}\xi \le \Phi-\theta \le 90\text{$^\circ$}\xi$ , and by for the other values of $\Phi$ , where $\xi$ is limited to the interval 0-1 (fig. 5.23)

Subsections

© 2002 Fabien J.R. van Mook
ISBN 90-6814-569-X
Published as issue 69 in the Bouwstenen series of the Faculty of Architecture, Planning and Building of the Eindhoven University of Technology.

		empirical constants in [Best 1950] drop spectrum (eq. 2.24)
	[m $^{2}$ ]	area
$A_{\text{catch}}$	[m $^{2}$ ]	catchment area
		empirical constant in [Best 1950] drop spectrum (eq. 2.24)
		slope of the fit function , in correlation plots
	[-]	mean pressure coefficient
		empirical constant in [Best 1950] drop spectrum (eq. 2.24)
, , ,		parameters in a general formula for raindrop spectra (eq. 2.25)
	[-]	drag coefficient
$C_\mu$	[-]	- $\epsilon$ model constant
$C_{1\epsilon}$	[-]	- $\epsilon$ model constant
$C_{2\epsilon}$	[-]	- $\epsilon$ model constant
	[m]	displacement height
	[m]	raindrop diameter
$D_{50}$	[m]	median median drop size (eq. 2.20)
	[-]	roughness parameter (eq. 6.5)
	[-]	fraction of liquid water in the air comprised by drops with diameters less than (eq. 2.19)
	[m s $^{-2}$ ]	gravitational acceleration
$h_{\text{i.b.l.}}$	[m]	internal boundary layer height
$\mathcal{H}$	[m]	building height; obstacle height
	[-]	turbulence intensities
	[-]	driving rain ratio (eq. 2.28)
$\text{\fontfamily{computermodern}\selectfont\itshape k}$	[-]	von Kármán constant (0.4)
	[m $^{2}$ s $^{-2}$ ]	turbulent kinetic energy per unit of mass
$\ell_{\text{stop}}$	[m]	stopping distance
$\mathcal{L}$	[m]	characteristic eddy dimension (section 2.2.3)
$\mathcal{L}_g$	[m]	smaller of $2\mathcal{H}$ (two times building height) and $\mathcal{W}$ (building width), section 2.1.4
	[m]	integral length scale
	[kg]	mass
	[kg m $^{-3}$ m $^{-1}$ ]	raindrop mass concentration spectrum
	[m $^{-3}$ m $^{-1}$ ]	raindrop number concentration spectrum
	[m $^{-3}$ m $^{-1}$ ]	parameter in [Marshall and Palmer 1948] drop spectrum (eq. 2.21)
	[-]	number
		empirical constant in [Best 1950] drop spectrum (eq. 2.24)
		correlation coefficient; the coefficient of determination is (eq. 3.4)
	[mm h $^{-1}$ ]	rain intensity, also expressed in [kg m $^{-2}$ s $^{-1}$ ] = [mm s $^{-1}$ ]
$R_{\text {f}}$	[mm h $^{-1}$ ]	driving rain intensity
$R\!e$	[-]	Reynolds number
	[s]	time
$t_{\text{cl}}$	[s]	averaging and summation period, the periods are synchronised to clock and calendar; the first period of a day starts at 00h00.
$t_{\text{dry}}$	[s]	pause between rain spells
$t_{\text{s}}$	[s]	sample time
$t_{\text{prec}}$	[s]	precipitation time
	[s]	integral time (eq. 6.7)
$u_\ast$	[m s $^{-1}$ ]	friction shear velocity
$\vec{u}$	[m s $^{-1}$ ]	wind velocity vector
	[m s $^{-1}$ ]	longitudinal, lateral and vertical wind velocity
$\vec{u}_{\text{D}}$	[m s $^{-1}$ ]	raindrop velocity vector
$u_{\text{D}}, v_{\text{D}}, w_{\text{D}}$	[m s $^{-1}$ ]	raindrop velocity in , and direction
	[m s $^{-1}$ ]	wind speed $= \sqrt{U_x^2+U_y^2+U_z^2}$
$U_{\text {h}}$	[m s $^{-1}$ ]	horizontal wind speed $= \sqrt{U_x^2+U_y^2}$
$U_{\text{10}}$	[m s $^{-1}$ ]	horizontal wind speed at 10 m height on open terrain with = 0.03 m and = 0 m
	[m s $^{-1}$ ]	wind velocity components ( is due north, west, upwards)
	[m s $^{-1}$ ]	wind velocity vectors according to the anemometer axis system
$V_{\text{tip}}$	[ml]	effective volume of a rain gauge bucket
$w_{\text{term}}$	[m s $^{-1}$ ]	terminal drop speed
	[kg m $^{3}$ ]	liquid water content (i.e. amount of liquid water per unit of air)
$\mathcal{W}$	[m]	building width
	[m]	position coordinates ( is upwards)
		-axis quantity and -axis quantity of the fit function , in correlation plots
	[m]	roughness length

$\alpha$		coefficient in Lacy's formula 2.29
$\alpha$		coefficient in model 2 (eq. 5.4)
$\beta$		exponent in Lacy's formula 2.29
$\beta$		exponent in model 2 (eq. 5.4)
$\beta$		constant in eq. 6.8
$\gamma$		exponent in model 2 (eq. 5.4)
$\epsilon$	[m $^{2}$ s $^{-3}$ ]	dissipation rate of
$\eta (D)$	[-]	catch ratio (eq. 2.26)
$\theta$	[ $^\circ$ ]	constant in function $\text {\textit {L}}$ (fig. 5.23) for model 2 (eq. 5.4)
$\theta$	[ $^\circ$ ]	angle (in chapter 6)
$\kappa$	[-]	obstruction factor, eq. 2.35
$\Lambda$	[m $^{-1}$ ]	parameter in [Marshall and Palmer 1948] drop spectrum (eq. 2.21)
$\mu$		parameter in [Ulbrich 1983] drop spectrum (eq. 2.23)
$\mu$	[kg m $^{-1}$ s $^{-1}$ ]	dynamic viscosity (1.6-1.8 10 $^{-5}$ kg m $^{-1}$ s $^{-1}$ for air), $\mu = \rho \nu$
$\nu$	[m $^{2}$ s $^{-1}$ ]	kinematic viscosity (1.3-1.5 10 $^{-5}$ m $^{2}$ s $^{-1}$ for air), $\nu = \mu /\rho$
$\nu_t$	[m $^{2}$ s $^{-1}$ ]	turbulent or eddy viscosity
$\xi$	[-]	constant in function $\text {\textit {L}}$ (fig. 5.23) for model 2 (eq. 5.4)
$\rho$	[kg m $^{-3}$ ]	density
$\sigma_K$	[-]	- $\epsilon$ model constant
$\sigma_\epsilon$	[-]	- $\epsilon$ model constant
$\tau$	[N m $^{-2}$ ]	turbulent shear stress $\rho u' w'$
$\tau_0$	[N m $^{-2}$ ]	surface shear stress (eq. 2.2)
$\varphi(D)$	[kg m $^{-2}$ s $^{-1}$ m $^{-1}$ ]	raindrop mass flux spectrum (definition of $\varphi _{\text {h}}(D)$ in eq. 2.16)
$\Phi$	[ $^\circ$ ]	horizontal wind direction, angle from which the wind blows, clock wise from north (e.g. 270 $^\circ$ is wind from west)

	5, 10, 60				clock period $t_{\text{cl}}=$ 5, 10 and 60 min respectively
	$\text{a}$				air
	$\text{c}$				corrected, esp. for rain intensity: rain intensity is obtained by combining data of a tipping-bucket rain gauge and a rain indicator (see section 3.4.3)
	$\text{D}$				raindrop
	$\text{e}$				estimate (eq. 3.4)
	$\text{f}$				at façade
	$\text{h}$				horizontal (at reference unless otherwise indicated)
	$\text{m}$				measurement (eq. 3.4)
	`P1, P2, ...`				measurement positions
	$\text{r}$				reference
	$\text{u}$				uncorrected, esp. for rain intensity: rain intensity is obtained by simply counting the tippings of a tipping-bucket rain gauge (see section 3.4.3)
	$\text{v}$				vertical (at reference unless otherwise indicated)