Surface Water Balance (2)
Review of last lecture
Components of global water cycle
• Ocean water
• Land soil moisture, rivers, snow cover, ice sheet and
glaciers
• Sea ice
• Atmosphere water vapor, clouds, precipitation
• Water in 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)
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)
Reference evaportranspiration
• A large number of more or less empirical methods have
been developed over the last 50 years by numerous
scientists and specialists worldwide to estimate
evapotranspiration from different climatic variables.
Relationships were often subject to rigorous local
calibrations and proved to have limited global validity.
Testing the accuracy of the methods under a new set of
conditions is laborious, time-consuming and costly, and
yet evapotranspiration data are frequently needed at
short notice for project planning or irrigation scheduling
design.
• To meet this need, the Food and Agriculture Organization
(FAO) of the United Nations developed and published
four methods for calculating a reference
evaportranspiration: the Blaney-Criddle, radiation,
modified Penman and pan evaporation methods.
Evaluation of the four methods
• The Penman methods may require local
calibration of the wind function to achieve
satisfactory results.
• The radiation methods show good results in
humid climates where the aerodynamic term is
relatively small, but performance in arid
conditions is erratic and tends to underestimate
evapotranspiration.
• Temperature methods remain empirical and
require local calibration in order to achieve
satisfactory results. A possible exception is the
1985 Hargreaves' method which has shown
reasonable ETo results with a global validity.
Evaluation of the four methods (cont)
• Pan evapotranspiration methods clearly reflect the
shortcomings of predicting crop
evapotranspiration from open water evaporation.
The methods are susceptible to the microclimatic
conditions under which the pans are operating
and the rigour of station maintenance. Their
performance proves erratic.
• The relatively accurate and consistent
performance of the Penman-Monteith approach in
both arid and humid climates has been indicated
in many studies.
Penman-Monteith equation
where Rn is the net radiation, G is the soil heat flux, (es - ea)
represents the vapour pressure deficit of the air, r 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, 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.
PSDI for US in August 2012
Change of PDSI in the last 100 years
Desertification
• Caused mainly be
human activities and
climate change
• Is one of the most
significant global
environmental problems
• About a billion people
are under threat
Global desertification vulnerability
Infiltration - Darcy’s law
• The infiltration flux
Rg
where
• Y is wetting front soil suction head
• h0 is the depth of ponded water above the ground surface
• K is the hydraulic conductivity
• L is the total depth of subsurface ground in question.
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)