Lecture Packet 13. Stages of Desaturation

  1.72, Groundwat er Hydrology Prof. Charles Harvey

  

Le ct u r e Pa ck e t # 1 3 : St a ge s of D e sa t u r a t ion

St a ge s of D e sa t u r a t ion

  1. Com plet e sat urat ion

  2. Air ent ry

  3. Funicular sat urat ion

  a. Pores dewat er from large t o sm all

  b. Air and wat er phases are cont inuous

  c. Average suct ion ( over REV) dom inat ed by direct suct ion t ransm ission t hrough t he cont inuous phase, alt hough film s of sorbed wat er exist at very large negat ive pot ent ials.

  4. Pendular sat urat ion

  a. Wat er phase discont inuous – no direct pressure t ransm ission b. Air phase is cont inuous.

  5. Hydroscopic wat er

  a. Sorbed wat er

  b. Large suct ions

  c. May or m ay not be cont inuous

  1

  2

  3

  2

  4

  3 Sand Grain

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  ψ _{ae 1} Air- ent ry t ension

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  0.0 0 0.1 0.2 0.3 0.4 0.5 θ Wat er cont ent ,

  Exfilt rat ion n o ti ra lt fi

  Ground surface In n o ti u

  Plant upt ake ib tr is d e

  I nt erflow R

  Capillary rise Wat er

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  65 .05 .10 .15 .20 .25 .30 0.18 0.22 0.26 0.30 0.34 0.38

Wat er cont ent , θ Moist ur e cont ent , θ

  

I nfilt rom et er ring

Wat er surface

Ground surface t

¹

t

²

t

₃

t

⁴

Figure: I nfilt rom et er diagram show ing wet t ing- front

  m ovem ent from t im e t ^{1 t o t 4 .}

  D a r cy’s La w for ve r t ica l u n sa t ur a t e d flow

  z is elevat ion ( posit ive up)

  ∂ [z − ψ (θ )] q = K( − _z θ )

  ∂ z ( θ ) ∂ ψ (θ ) = K( − = K( −

  θ ) ∂ z + K(θ ) ∂ψ θ ) + K(θ ) ∂ z ∂ z ∂ z ∂ q ∂ θ _z

  Mass balance

  − = ∂ z ∂ t Richa r d’s Equa t ion ( ve r t ica l unsa t u r a t e d por ou s- m e dia flow )

  Different iat e Darcy’s Law :

  ( ∂ q ∂ K( θ ) ∂ θ ) ⎤ _z ⎡ = + − K ( θ ) ∂ψ

  ⎢ ∂ z ∂ z ∂ z ⎣ ∂ z ⎦⎥

  Use Mass Balance equat ion:

  ( ∂ ∂ θ ∂ K(θ ) ⎡ θ ) ⎤ = − K ( θ ) ∂ψ

  ⎢ ∂ t ∂ z' ∂ z ⎣ ∂ z ⎦⎥

  ψ form :

  ( ∂ θ ∂ θ ∂ψ (θ ) θ )

  Not ing t hat : = = C(

  ψ ) ∂ψ ∂ t ∂ ψ (θ ) ∂ t ∂ t

  Richard’s Equat ion becom es:

  K ( ∂ ψ ) ∂ ⎡ ψ ⎤

  C( ψ ) ∂ψ ∂ = − ∂ t ∂ z' ∂ z ⎣

  

⎢ K(ψ ) ∂ z ⎦⎥

  θ form :

  1 ∂ ψ (θ ) ∂ψ (θ ) ∂θ ∂ θ

  Not ing t hat : = =

  ∂ z ∂ θ ∂ z C(ψ ) ∂ z

  Richard’s Equat ion becom es:

  ∂ θ ∂ K(θ ) ∂ ⎡ ∂ θ ⎤ = − ∂ t ∂ z ∂ z ⎣ ⎢ D(θ ) ∂ z ⎦⎥

  K ( θ )

  Where

  D( θ ) = Unsat urat ed Diffusivit y C( θ ) Advant ages

  1. D does not vary over as m any orders of m agnit ude as K

  2. D is not as hyst eret ic as K

  3. I f gravit y can be neglect ed ( horizont al flow ) equat ion is nonlinear diffusion equat ion Disadvant age

  

∂

θ

  Does not w ork for ψ < ψ _{ae C( θ) = = 0}

  

∂ θ ψ )

(

  I n filt r a t ion ( “pe r cola t ion ”) - The process by which wat er arriving at t he soil surface ent ers t he soil.

  The rat e of infilt rat ion changes in a syst em at ic w ay during rainfall, even t hough t he rainfall rat e m ay be const ant . Consider t hree different condit ions:

  1. No ponding. I nfilt rat ion rat e is less t han or equal t o t he infilt rat ion capacit y, t he m axim um possible rat e.

  2. Sat urat ion from above. Wat er input rat e exceeds t he infilt rat ion rat e, so ponding develops. The infilt rat ion rat e is equal t o t he infilt rat ion capacit y.

  3. Sat urat ion from below. The wat er t able has risen t o or above t he surface so t he soil is sat urat ed. Ponding occurs and t he infilt rat ion rat e m ay be zero. Fact ors affect ing infilt rat ion rat e: 1. Rat e at which wat er arrives.

  2. Conduct ivit y at t he surface

  a. Plant s i. Large pores ii. Shingling ( leaves spread on t he ground) b. Frost i. “ concret e” effect ii. Polygonal cracks c. Sw elling- Drying

  d. I nw ashing of fines

  e. Modificat ion of soils

  3. Wat er Cont ent

  a. Sat urat ion

  b. Ant ecedent wat er cont ent ( how wet is t he soil before t he rainfall?)

  4. Surface slope and “ roughness” cont rols ponding

  5. Chem ist ry of soils

  θ θ

  φ t ² t ¹ t = t _{3 p} t ⁴ w t ⁵ z f ( t ^{5 )} t ⁶ K hsat t p t w t

  Wat er cont ent , θ t ^{2 t 1 t t t} ₃ ^{2 t 1 t}

  ’ z , th p e D Profiles show a t ypical w at er dist ribut ion aft er deep soil infilt rat ion in t he absence of evaporat ion. t is defined as t he t im e w hen redist ribut ion begins.

  a) Redist ribut ion w it h dom inant capillary force over gravit at ional force

  b) Redist ribut ion w hen grav it at ional force dom inat es capillary force

  Ra in fa ll- Ru n off M e ch a n ism s S tr e a m fl o w

  2/ 3- 3/ 4 groundwat er rem ainder is rainfall. Unclear w hy but w e know t his based on chem ical st udies

  T Surface Processes Channel I nt ercept ion

• Rainfall right into the channel
• Channels usually represent a sm all area of the watershed. But this m echanism has been found t o represent up t o 40% of t he event response

  Hort onian Overland Flow

• Water input rate exceeds the saturation hydraulic conductivity, so the top becom es sat urat ed and ponding and runoff occurs
• Widely accepted as the prim ary m echanism for event response from 1930’s t o 1960’s
• Now we believe that it’s rare – only very intense rains on very im perm eable soils

  Sat urat ion Overland Flow • Saturation from below. The water table rises to the surface.

• Occurs near stream s because the depth to the water table is low and flow is t oward st ream s. Flow on t he surface dum ps direct ly int o t he st ream .
• Most of the flow is rainfall runoff, but if the storm continues groundwater discharge can becom e im port ant .
• Variable source area. During a storm the saturated area m ay grow increasing t he am ount of runoff. This effect am plifies t he event response.

  Su bsu r fa ce Pr oce sse s

• Large scale groundwater flow
• Groundwater m ounds near stream s

  I nfilt rat ion quick

• Pressurization of capillary fringe

  st rong suct ion Hydrost at ic pressure

• Perched water table _o

  Com m on t o have a less perm eable layer below t he surface _o Sat urat ion layer develops t hat is not connect ed t o regional wat er t able _o “ Sloping slab” flow down hill _o Response t im e t oo slow t o explain event response - days

• Flow in the unsaturated zone – interflow or throughflow _o

  Moist ure dependent anisot ropy – wat er want s t o flow lat erally because of higher conduct ivit ies due t o higher m oist ure cont ent _o Response m ight be quick because wat er does not have t o penet rat e very far downward.

• Saturation from below can also occur when: _o

  Groundw at er flow lines converge in surface concavit ies _o Slope breaks _o Thin spot s in t he m ost t ransm issive m at erial _o

  40 m 50 m 60 m Surface zone

  Decreasing conduct ivit y

  sat urat ed Subsurface flow pat hs

  Ch e m ica l a n d I sot opic I n dica t or s

  Mass balance for dissolved const it uent s: CQ = C r Q r + C o Q o + C s Q s + C g Q g

  Groundw at er St ream w at er Dir ect Overland Subsurface Rain flow st or m flow

  Mass Balance for wat er: Q = Q r + Q o + Q s + Q g

  Approxim at e: Q r = 0 Q d = Q o + Q s

  Dir ect runoff

  CQ = C d Q d + C g Q g Q = Q d + Q g ₁₈

  δ Solut es such as Na, Ca, Mg, Cl, et c. I sot opes such as O ( Oxygen- 18) _{18 18}

  ⎛ ⎞ ⎛ ⎞ C − C δ O − O δ _{d d}

  ⎜ ⎟ ⎜ ⎟ Q = Q Q = Q _{g g 18 18}

  ⎜ ⎟ ⎜ ⎟

C − C O − O

_{g d δ g δ d}

  ⎝ ⎠ ⎝ ⎠ C ,

  C g n o ti a

  C tr n e c n o

  C d C

  St ream flow hy drograph ) _{3 /} s

  Dir ect runoff com ponent (m Q , w o fl m a e tr S

  Groundw at er Com ponent Tim e