John Dalton established quantitative hydrology in 1799 by creating a water balance for England and Wales using rainfall and river flow data. He attributed the origin of springs to rainfall, rejecting long-held myths and laying the foundation for the modern understanding of the hydrological cycle. Recent work has focused on understanding soil evaporation dynamics at the pore scale, finding that as the soil surface dries, the spacing between pores increases, leading to higher evaporative flux per pore that can maintain an overall constant evaporation rate despite a decreasing surface area. This pore-scale model provides insights into evaporation rates, surface resistance, and energy partitioning during drying.

1. On Dalton, Evaporation and the hydrologic cycle
– a brief journey to scientific discovery
Dani Or - Dept. Environmental Systems Science - Swiss Federal Institute of Technology, ETH Zurich
EGU – April 2017

2. ETH 2016
ETH 2009
The people behind the science
ETH 2011
UConn 2004

3. Special thanks to my mentors and colleagues
Eshel Bresler (1930-1991) John Hanks (1927-2014)
Hannes Flühler
Rainer Schulin
Shmuel Assouline
Peter
Lehmann
Experimental Farm
Upper Galilee 1979

4. Outline - a brief journey to scientific discovery
• A bit about our research group and activities (1 slide only…)
• The magic of the hydrological cycle – myths and milestones
• Dalton’s view of the hydrological cycle and quantitative hydrology
• A timeline of evaporation history and modern context
• New insights into soil evaporation (our recent work):
o Soil determines evaporation dynamics and stage transition
o Evaporation from pores – why is this important?
• Reflections and lessons on scientific discovery…

5. A snapshot of research activities @ETH-STEP (2017)
www.eyeofscience.com
Evaporation from porous surfaces
Biophysics of soil microbial life
Landslide triggering
Pore & grain scale acoustic emissions
Spatial statistics and inventories
Soil structure restoration

6. The magic of the hydrological cycle – early views
• The existence of a natural water cycle
has been known to the ancient Greeks,
Egyptians, and appears in the bible
• Key concepts related to conservation
of mass, evaporation (sun and wind)
have been formulated by the Greeks
• The myth (“magic”): two competing
theories regarding the origins of
springs and rivers date back to
Aristoteles: (1) water flowing back
from the sea into the ground leaving
salts behind (”sea filtration”) ;
(2) the existence of large subterranean
reservoirs that supply springs
(Mundus subterraneus)
Athanasius Kircher
Mundus subterraneus (1665)

7. The hydrological cycle in ancient Greece (Google…)

8. Great thinkers…
• “Facts are meaningless, you could use them
to prove anything that's even remotely true!”
• “Words empty as the wind are best left unsaid”
Homer (800–701 BC)
Homer Simpson (1987 – present)
• “The same, spread out before the sun, will dry;
Yet no one saw how sank the moisture in,
Nor how by heat off-driven. Thus we know,
That moisture is dispersed about in bits
Too small for eyes to see”
Lucretius Caro (99-55 BC)
De Rerum Natura
Aristotle (384-322)
Meteorology (c.350 B.C.)
On evaporation:

9. Early views of the hydrological cycle – Lucretius (99-55 BC)
• The work of Lucretius Caro (a roman philosopher) was
influenced by the scientific school of Epicurus – no magic,
everything is governed by laws of nature
• His book “On the Nature of Things” (De Rerum Natura)
describes some of the fundamental modern physics (atomistic
theory) to the roles of sun and wind in the hydrological cycle
Whence may the water-springs, beneath the sea,
Or inland rivers, far and wide away,
Keep the unfathomable ocean full?
And now, since I have taught that things cannot
Be born from nothing, nor the same, when born,
To nothing be recalled, doubt not my words,
Because our eyes no primal germs perceive;
A Florentine bibliophile named Poggio Braccionlini,
who, in 1417, stumbled upon a 500-year-old copy
of De Rerum Natura in a German monastery

10. The origins of quantitative hydrology
Mariotte
Halley
• Edmond Halley (1656-1742) was active in a
generation immediately following Pierre Perrault
(1608-1680) and Edmé Mariotte (1620-1684) –
the founders of quantitative hydrology
James C. Dooge
(1998 John Dalton medalist – EGS)

11. John Dalton (1766-1844) – background and contributions
• John Dalton was born in Cumberland in 1766 – the son of a
weaver and smallholder
• At age 15 he became assistant teacher at a Quaker boarding
school in Kendal; at age 19 joint principle with his brother
• He summarized some of his early interest in hydro-meteorological
observations in “Meteorological Observations and Essays” in 1793
as he left Kendal to Manchester
• Dalton kept a life long interest in meteorological observations until
his death in 1844
• Dalton’s scientific legacy is often associated with
modern atomic theory, gas laws, color blindness
• Dalton’s contributions to hydrology and
chemistry are linked by his keen interest in
gases, temperature and water vapor:
“from a background of interest in the atmosphere (and
hence the gases which compose it) and in deductive,
predictive mathematical science that Dalton went on to
think about atomic theory in chemistry” Knight 2012

12. The birth of quantitative hydrological cycle (1)
• In 1799 Dalton established a water balance for England and Wales using rain gauges, defined
catchments for river flow estimates (scaled to the Thames), and evaporation experiments
from a lysimeter – to establish whether rainfall was sufficient to explain runoff & evaporation

13. 'The origin of springs may still therefore be attributed to rain… and it becomes
unnecessary to controvert the other two opinions respecting this subject.'
• Dalton thus closed a 2300 years old debate regarding the origins of springs by rejecting the
myths of “Mundus subterraneus” and “sea water filtration” theories, and attributing these to
rainfall, hence laying the foundation for modern hydrological cycle we now take for granted
The birth of quantitative hydrological cycle (2)

14. Evaporation - scientific timeline
Halley 1687 Schmidt 1915
Slatyer and McIlroy (1961)
Lucretius 99 BC
Sea water is rendered potable by
evaporation; wine and other liquids
can be submitted to the same
process, for, after having been
converted into vapours, they can be
condensed back into liquids
Aristotle
Meteorology (c. 350 B.C.)
"Essay on Evaporation” Dalton’s equation: E = f(u)*(e0-ea)
where f(u) a function of wind speed, e0 is saturation
vapor pressure, and ea is the vapor pressure of the air

15. Global evaporation – modern context and numbers…
• Globally, evaporation consumes
~ 25% of solar energy input (40K TW);
50% of solar radiation goes to heating
surfaces/oceans
• About 60% of global terrestrial
precipitation (111x103 km3/ yr) return
to the atmosphere via transpiration
(40%) or direct soil evaporation (20%)
• The atmosphere represents an
“unlimited” sink for vapor exerting
large driving forces for evaporation
Fluxes in:
1000 km3/year

16. Our recent work – evaporation from terrestrial surfaces
• Evaporation is often described from atmospheric
point of view - we seek to understand the role of
soil (& terrestrial surfaces) in evaporation dynamics
• Soil evaporation rates exhibit abrupt changes linked
with soil internal transport mechanisms – the
characteristics are not fully understood
• Evaporation from terrestrial surfaces is significantly
different than from free water surfaces (drying,
capillarity, opacity)
• Interactions between surface drying and mass
exchange rates from discrete pores across air BL
introduce nonlinearities that affect drying dynamics
and surface energy partitioning

17. (1) What controls the transition in evaporation
rates from stage 1 (high) to stage 2 (low)?
To quantify effects of capillary and porous media
properties on evaporation characteristics
(2) What keeps evaporation rate during stage-1
constant even as the surface gradually dries?
We seek a pore scale model for vapor exchange
across a boundary layer that considers evaporative
(diffusive) fluxes from discrete pores while the
porous surface gradually dries
Research questions - Evaporation dynamics
• Assumption - energy input is constant
• Stage 1 is defined by vaporization plane at the surface
(1)
(2)

18. Modeling concepts: evaporation from discrete pores
• Vapor transfer from an evaporating porous surface
to flowing air above occurs across a viscous
sublayer (BL) of thickness δ (varies with air velocity)
• Unlike the drying of uniformly moist surfaces (or
free water surfaces) – soil evaporation takes place
from discrete pores of different sizes
• Theory shows that air BL thickness δ affects: (i)
average vapor gradient (higher air velocity →
thinner δ→ higher rate), and (ii) the space for
diffusive vapor shells forming above active pores
• Surface pores empty at a particular sequence due
to capillary forces (largest empty first) resulting in
increased spacing between surviving pores
δ
Shahraeeni et al. WRR 2012
Gradual drying of a porous surface
(red – smallest pores)

19. Modeling evaporation from discrete pores
2r
δ
Schlünder (1988)Suzuki and Maeda (1968)
Key ingredients – previous models
1. Suzuki and Maeda (1968) and Schlünder
(1988) ADE-based models were extended to
consider a wide range of pore sizes that are
sequentially invaded during drying
2. In addition to capillary pore invasion we solve
for force balance at the menisci and capillary
flow to supply surface evaporation
Shahraeeni et al. WRR 2012
Haghighi et al. WRR 2013

20. (E/E0)
Evaporation from pores: pore size and spacing effects
• As the surface gradually dries, the evaporative flux per pore increases (diffusion field 1D→3D)
and may compensate for reduced evaporating area (i.e., lower surface water content)
• The boundary layer (BL) thickness (δ) defines: mean vapor gradients and the space for 3-D
diffusion vapor shells forming over individual pores
Shahraeeni et al. WRR 2012
• For a surface with regularly
spaced pores of equal size
(drying = larger spacing); three
critical lengths: pore size and
pore spacing relative to BL
thickness δ jointly determine
flux compensation efficiency
and drying curve shape (E/E0
vs. surface saturation)

21. Pore size & spacing affect per-pore evaporative flux
• Evaporation rate per pore increases with increased pore spacing as the
diffusion field becomes 3-D. The increased flux may compensate for loss
in evaporating area (drying surface)
1.0
Increased flux
per pore
Relative(per-pore)evaporationrate
Surface relative saturation
1

22. increased
flux per
pore
Pore scale model – so how a “constant rate” is maintained?
• Evaporative flux per pore increases with increased
spacing between active pores as soil surface dries
(during stage-1 = vaporization plane at surface)
• Increased “per pore” flux could compensate for
reduced evaporating area resulting in constant
evaporation rate (while energy input remains constant)
Surface drying (larger spacing)
Increased evaporative flux per pore
Epore/E0[-]
Relative surface saturation
Shahraeeni et al. WRR 2012

23. Applications of pore-based evaporation model: surface resistance
• The pore-scale evaporation model was used to estimate surface evaporative
resistance as a function of water content (θsurf) and mean pore size <Rp>
• The physically-based representation of the nonlinear surface resistance is
critical for remote sensing of soil evaporation (reducing empiricism)
van de Griend and Owe (1994 WRR) Haghighi et al. WRR 2013
D
fR
r
surfPm
BLS
)(θδ ><+
=+
( ) 







−= 1
44
2
θ
π
θ
π
π
θf

24. Injecting surface energy balance into the pore-based
(“atomistic”) view of evaporation enables:
1. Analytical links between evaporation rates and surface
temperature - pore scale coupled energy balance (PCEB)
and surface drying feedback
2. The model permits prediction of energy partitioning during
surface drying (i.e., Bowen Ratio β or Priestley-Taylor α in
predictive mode for various climatic conditions) to improve
remote sensing of surface fluxes
Energy partitioning on evaporating surfaces
Aminzadeh and Or (2013, WRR)
Aminzadeh and Or (2014, J. Hydrol.)
Aminzadeh, Roderick and Or (2016, WRR)
3. New insights into energy, evaporation
and temperatures of surfaces enabling
generalization of the complementary
relationship (CR) for estimating actual
evaporation from large areas
Aminzadeh & Or (2017, Int. J. Heat Mass Trans.)

25. Lessons and reflections: (1) on data and models
• The statement above should not be interpreted as
superiority of data over theory – both are essential
ingredients of the scientific method
• In defense of a good theory - clearly experiment
serve as the sole judge, yet, don’t rush to
judgment and allow for a deliberate appeal
process
• Big data is becoming extremely useful (machine
learning, etc.), yet without a paradigm or a theory
no generalization is possible (& nothing to “judge”)
Dalton’s mass (im)balance
Big
data
models

26. Lessons and reflections: (2) scientific history and cultural bias
• The Chinese, Mayan, Egyptian, Russian accounts of the origins and scientific history of
the hydrological cycle are likely different than the Euro-centric tales we’ve just heard
• It is interesting and rewarding to look at scientific developments from different cultural
angles to gain appreciation of their impacts in different societies and at different times
Yu the Great
2205 to 2197 BC
The hydrological cycle - Olmec
culture, Mesoamerica, 800 BC
Hapi – source of the Nile
Dujiangyan irrigation
system 256 BC

27. Nima Stan Ebrahim
Uri
Erfan
Shmuel
Dani Hans Peter
Mike
Milad
KlausRainer Mina
Martina

28. • Evaporative losses from reservoirs and other water
bodies may exceed 20% of water used in irrigated
agriculture (in some regions >40%)
• A useful option for reducing evaporative losses from
reservoirs is based on self-assembling floating covers –
do we want large or small “pores” for floating covers?
Water losses from partially covered reservoirs
Assouline, Narkis & Or (WRR 2010; 2011)
Evaporating surface area (m2 m-2)
Relativeevaporationrate
Larger “pores” more efficient cover!
δ=2 mm
91% of area covered
R=20 mm

29. The origins of the CR asymmetry
Aminzadeh, Roderick & Or (2016, WRR)
• The surface temperature range on the horizontal axis is defined by surface
properties and climatic variables determine the origins of the CR asymmetry
(thus different values of the parameter b) where surface properties define the
temperature range and the energy input the location (position) of hatched area
Input energy
Surface properties

30. Pore size and spacing affect per-pore evaporative flux
“thick” boundary layer

31. Global evaporation – some numbers…
• Globally, evaporation consumes
~ 25% of solar energy input (40K
TW); 50% of solar radiation goes to
heating surfaces/oceans
• About 60% of global terrestrial
precipitation (111x103 km3/ yr)
returns to the atmosphere via
transpiration (40%) or direct soil
evaporation (20%)
• The atmosphere represents an
“unlimited” sink for vapor exerting
large driving forces for evaporation
Fluxes in:
1000 km3/year
Horton (1931) – defending the creation of hydrology
section of the AGU (previously rejected as “active
scientific interest in the U.S. did not justify a separate
section of scientific hydrology within the AGU”
(National Research Council 1991, 40)