Hydrologie II, part II

Rsw = I₀/4 = 342 W/m2 (due to shape and night)

surface = 188 W/m2

R1/a1=R2/a2 or R1/e1=R2/e2

a: absorptivity, e: emissivity

"a good reflector is a bad emitter"

a=1 -> black body

R= R(lambda, T),

Rtot = integral from 0 to infinity over R(lambda)d_lambda

lambda_max = b/T

b: wiens konstant = 2898 um/K

describs the displacement of the wavelength with max radiation depending on the Temperature

Rtot = sigma * T⁴

radiation as a function of Temperature

alpha = Rr/Ri

alpha = alpha(lambda)

Rn = Rsw(1-alpha) + R_LW_in - _{R_LW_out}

Rn = reflected + atmos - surface

R_{LW_in} = e_cs*K*sigma*T_A⁴

R_{LW_out} = e_s*K*sigma*T_s⁴

K is funct of cloud cover

e is frunct of vapour presure and temp

Rn - lambda*E - H - G -Lp*Fp + A_H = dU/dt

net radiation - latent heat - sensible heat - ground heat flux - energy from carbon fluxes (photosynthesis) + energy advection = energy stored in the system

Rn - lambda*E -H -G =0

lambda*E >> H: over the ocean

lambda*E << H: in the city

equal: on human body

momentum

energy

mass

heat: diffusion, conduction -> H = -KdT/dz [J/m2s]

momentum: laminar conduction -> tau = mu*du/dz [Ns/m2s]

mass: diffusion -> Q = -D* dC/dz or E=-D*dq/dz [kg/m2s]

K: thermal conductivity

D: molecular diffusivity

mu: dynamic viscosity

ABL

SBL-> dynamic sublayer + interface sublayer

mass: E=rho*Δq/r_av

energy: H=rho*Cp*ΔT/r_ah

momentum: tau=rho*u/r_am

with simplified turbulent flux + log wind profile ->

E=f(Δq, Δe, u, T)

u=0, free convection -> f(Ta-Ts)

u>0, forced convection -> f(u)

e_sat(0)= 610 Pa

e_sat(100) = 101325 Pa

water budget

energy budget

mass transfer -> aerodynamic method

combined mass and energy transfer -> perman approach

ET =Pr +Qi -Qo

assumption: dS/dt = 0

Rn- lambda*E - H - G = 0

further simplified:

Rn - lambda *E - H = 0

-> E = Rn/(lambda* (1+Bo))

problem: qs=?? and Ts=??

-> assumption: Bo = const or 0

-> E=Rn/lambda [kg m-2 s-1]

-> E = Rn/(roh_w* lambda) [m s-1]

Bo = H/(lambda*E) = sensible heat/ latent heat

= (Cp*ΔT)/(lambda*Δq)

problems: usually qs and Ts are unknown

E = (rho*Δq)/r_a

empirical observations: E = f(u)(e_s-e_a) -> f(u) = (0.622/P)*(rho/r_a) -> Problem: e_s still unknown

assumption: e_s = e_sat(T_s) = e_sat(T_a) -> E = ~f(u)(e_s(T_a)-e_a)

~f(u): empirical function, but often is the theoretical f used

combination of mass and energy transfer

Δ = de_sat/dT=[e_sat(T_s)-e_sat(T_a)]/(T_s-T_a) ≈ f(T_a)

  timescale: (hourly to) daily

E=Δ/(Δ+gamma)*E_ene + gamma/(Δ+gamma)*E_aer

approximation:

E≈1.26*Δ/(Δ+gamma)*E_ene

typically ea and Ta are not in potential condition

generally: potential = not limited by the supply

-> reduction factor: E = E_pot*ß_R, ß_R=f(θ), θ: water content

Δq, Δe, u, T_a + Plant physiology

vary LAI

open/close stomata

r_c = r_s/LAI = somata resistance/ leaf area index

replace ra with ra+rc

A_n, Δe,CO₂, θ, N

eddy covariance: direct measurement of turbulent fluctuations ov vert. wind vel. and specific humidity

pan evaporation: usually needs to be corrected by 0.7 due to eddy turbulences at edges.

Lysimeter: weight loss of a soil control volume

.

≈ vadose zone

source of moisture for vegetation

E+T and recharge into deeper auquifers occur

constrols separation bewteen runoff and infiltration -> dominant for hydr processes

highly non-linear