Surface Water Balance
Review of last lecture: Surface energy balance
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
SWdn
=Scos
SWup
=SWdn 
LWdn
LWup
=Tair4 =Ts4
LH=CdLV(qsurface- qair)
SH=CdCpV(TsurfaceTair)

dT/dt
• What is sensible heat flux? What is latent heat flux?
Fc = -  dT/dz
• Bowen ratio B= SH/LH = Cp(Tsurface - Tair) / L(qsurface - qair) provides a simple
way for estimating SH and LH when the net radiative flux Fr is available
LH=Fr/(B+1), SH=Fr B/(B+1)
• Factors affecting soil thermal conductivity
• Other heat sources: precipitation, biochemical, anthropogenic
The global water cycle
Video: Weather Wet
Components of global water cycle
•
•
•
•
•
Atmosphere (water vapor, clouds, precipitation)
Land (soil moisture, rivers, snow, ice sheet and glaciers)
Sea ice
Ocean
Biosphere (including human beings)
Atmosphere: water vapor
Atmosphere: Precipitation
Inter-tropical convergence
zone (ITCZ)
Strong rainfall
(heating)
Weak rainfall
GPCP Annual Mean Precipitation for 1979-2005 (mm/day)
Land snow/Ice cover provide a reservoir
Flow of >1000 rivers on the seven continents
Mississippi river
Amazon river
Yangtze river
Land: Soil moisture
Flow of ocean currents
A significant fraction of the human body is
water (~75%)
About every 16 days
nearly 100% of the
water in a human
body is exchanged.
The remaining: fat, protein,
carbonhydrate, other solids
So the water we drink may come from …
Therefore we need to protect the environment because any pollution we put
into the environment may someday come back into our bodies
Surface water balance
The changing rate of soil moisture S
dS/dt = P - E - Rs - Rg + I
Precipitation
(P)
Evaportranspiration
(E)
Irrigation
(I)
Runoff
(Rs)
dS/dt
Infiltration
(Rg)
Evaportranspiration
• Is equivalent to latent heat flux
• Has four components: E = Eb + Ei + Es + TR
Evaporation from
inception storage
(Ei)
Evaporation from
bare soil (Eb)
Transpiration (TR)
Snow sublimation
(Es)
Evaportranpiration: Penman-Monteith equation
where λ is latent heat of evaporation, Rn is the net radiation,
G is the soil heat flux, (es - ea) represents the vapour
pressure deficit of the air,  a is the mean air density at
constant pressure, cp is the specific heat of the air, D
represents the slope of the saturation vapour pressure
temperature relationship, g is the psychrometric constant
(=66 Pa/K), and rs and ra are the (bulk) surface and
aerodynamic resistances.
Soil moisture
• Typically expressed as ‘volumetric soil water content’
S = Vwater / Vsoil
• Increases with depth
• Complicated to measure
Root zone
Intermediate
zone
Ground
water
Soil moisure regimes
US Soil moisture map
Palmer drought severity index (PDSI)
• was developed by Wayne Palmer in the 1960s
and uses temperature and rainfall information in
a model to determine dryness of soil moisture.
• is most effective in determining long term
drought (a matter of several months) and is not
as good with short-term forecasts (a matter of
weeks).
• It uses a 0 as normal, and drought is shown in
terms of minus numbers; for example, minus 2 is
moderate drought, minus 3 is severe drought,
and minus 4 is extreme drought.
Change of PDSI in the last 100 years
PSDI for US in January 2015
A different index: U.S. Drought Monitor
Video: Crippling Drought in the
Golden State: California Soul
• https://www.youtube.com/watch?v=lmUwjk
4S3gw
Glacier mass balance
Structure of a glacier
• A glacier forms when the
accumulation of snow and
ice exceeds its overall
loss of mass by ablation
(sublimation and melting).
• A glacier can be divided
into two zones; the
zone of accumulation
and the zone of
ablation. They are
separated by the
“equilibrium line”.
Accumulation zone
• Surface accumulation
processes include
snow and ice from
direct precipitation,
avalanches and
windblown snow.
• There may be minor
inputs from hoar frost
(radiation frost).
• The snow and ice is
then transferred
downslope as the
glacier flows.
Ablation zone
• Surface ablation processes
include surface melt, surface
meltwater runoff, sublimation,
avalanching and windblown
snow.
• Glaciers on steep slopes may
also dry calve, dropping large
chunks of ice onto unwary
tourists below.
• Other processes of ablation
include subaqueous melting, and
melting within the ice and at the
ice bed
Glacier mass balance for the globe
Glacier mass balance for different regions
Summary:
Components of global water cycle
•
•
•
•
•
Atmosphere (water vapor, clouds, precipitation)
Land (soil moisture, rivers, snow, ice sheet and glaciers)
Sea ice
Ocean
Biosphere (including human beings)
Surface water balance
The changing rate of soil moisture S
dS/dt = P - E - Rs - Rg + I
Precipitation
(P)
Evaportranspiration
(E=Eb+Ei+Es+TR)
Penman-Monteith eq
Irrigation
(I)
Runoff
(Rs)
dS/dt
(PDSI, desertification)
Infiltration (Rg
Darcy’s law)
Works cited
• http://ffden2.phys.uaf.edu/212_spring2011.web.dir/Jocelyn_Simpso
n/Slide3.htm
• http://www.antarcticglaciers.org/modernglaciers/introduction-glacier-mass-balance/