Land atmosphere interaction –
introduction and a conceptual
model
Bart van den Hurk
(KNMI/IMAU)
Land atmosphere interaction and conceptual model
Last time assignment
• Identify a new topic that involves land use-climate
feedback, and describe the feedback processes
using the diagram qualitatively, e.g.
– green roofs in cities
– irrigation
– crop disease
– ...
Land atmosphere interaction and conceptual model
Definition of feedback
• According to Oxford Dictionary
– 1 information given in response to a product,
performance etc., used as a basis for
improvement.
– 2 the modification or control of a process or
system by its results or effects.
– 3 the return of a fraction of the output of an
amplifier, microphone, or other device to the
input, causing distortion or a whistling sound.
• Negative/positive feedback
– output damps/amplifies the process generating
the output
Land atmosphere interaction and conceptual model
Thermal land-atmosphere coupling
•
Typical nighttime surface energy balance:
Q*
Q*  H  G
H
G
Q*  L   Ts4
H  c p C H U (Ts  Ta )
G   (Ts  Tsoil )
•
The surface temperature takes value closing the energy balance.
Determined by:
– radiative input
– radiative & turbulent cooling to atmosphere
– diffusion of heat into soil
Land atmosphere interaction and conceptual model
Feedback of surface energy balance
• In most occasions:
– Ts is strongly coupled to atmosphere (high wind
speed) and/or soil (efficient conduction of heat)
• Special conditions: ‘runaway’ surface temperature
– weak winds
– low turbulence due to stable stratification
– strong radiative cooling (clear sky)
• Feedback loop:
– low L and H  low Ts  large Ta – Ts  stable
stratification  poor turbulent coupling (low H)
 low near surface air temperature
Land atmosphere interaction and conceptual model
A simple surface energy balance
• See spreadsheet
•
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Q*
Ta(t) = aTa(t-t) + (1-a)Ts
Q* = L - Ts4 = H + G
L = a Ta4
H = cpUCH(z/L) (Ts – Ta)
z/L = f(Ts-Ta, u) (stability)
G = (Ts – Tsoil)
Tsoil(t) = sTsoil(t-t) + (1-soil)Ts
H
G
Land atmosphere interaction and conceptual model
Hydrological land-atmosphere coupling
• In typical mid-latitude climate: soil moisture is
resulting from P – E balance, E is mainly energy
limited
• In dry warm summers, E can become moisture
limited
• Feedback loop:
– low precipitation  low soil moisture  low
evaporation  low precipitation
• Requires
– sensitivity of evaporation to soil moisture
– sensitivity of precipitation to evaporation
Land atmosphere interaction and conceptual model
When strong positive hydrological
feedback likely?
ET→P
W→ET
sensitivity
climate transition
zones
Arid
Humid
dry
wet
Land atmosphere interaction and conceptual model
Areas with strong feedback
Koster et al, Science, 2004
Land atmosphere interaction and conceptual model
Precipitation efficiency and recycling ratio
• Precipitation efficiency
– How much of the water passing an area is
actually raining out?
– Multiple definitions:
p
P
0.5(Qin  Qout )
p
P
Qin
Land atmosphere interaction and conceptual model
Precipitation efficiency and recycling ratio
• Recycling ratio
– How much of the total precipitation originates
from local evaporation?
– Budget equation:
P  Pa  Pl
Qout  Qin  ( E  P) L
Q  0.5(Qin  Qout )
Pa Qa Qin  0.5 Pa L


Pl Ql 0.5( E  Pl ) L

Pl
EL

P EL  2Qin
Land atmosphere interaction and conceptual model
Some examples
p = 83%
 = 17%
p = 22%
 = 8%
p = 28%
 = 11%
Land atmosphere interaction and conceptual model
Global distribution
Trenberth, J.Climate, 1999
Land atmosphere interaction and conceptual model
A Lagrangian approach
P = Pa + Pl
E = Ea + El
El = Pl
 = Pl/P
 = El/E
Pa = advected P
Pl = originating from local E
Ea = E leaving domain
El = E staying within domain
• Subdivide into continental and ocean source/sink,
P = Pc + Po
E = Ec + Eo
• and trace water via Lagrangian (trajectory
following) buget equation:


 L E(x )

R  1  exp 
dx

x
 0
q(x ) 


t
R = recycling ratio
E = evaporation
L = integration length scale
x = grid box length
t = model time step
q = column water content
(Dominguez et al, 2006)
Land atmosphere interaction and conceptual model
Continental sources/sinks
mean moisture flux
Van der Ent et al, 2010
Land atmosphere interaction and conceptual model
Layout of a conceptual land-atmosphere
hydrology model
Fin
P
Fout
R
E
ds/dt
L
Land atmosphere interaction and conceptual model
Layout of a conceptual land-atmosphere
hydrology model
P = 0.5 g(s) (uw/L + E)
uw / L + 
residual
Stochastic
forcing
E = Epot sc
 = evaporative fraction
Q* = net radiation
g = precip.efficiency
 = runoff efficiency
D = soil depth
L = horizontal length scale
uw = wind speed  atm.moisture
r, c = coefficients
R = Psr
ds/dt = (P-E-R)/D
Land atmosphere interaction and conceptual model
Stochastic Differential Eq (SDE)
s
D  PER
t
P  0.5g ( s)uw / L     E ( s) 
stochastic (forcing) term
Discretization and rewriting leads to
s
D  Gt  gr t
t
G = drift term (gains and losses by P, E, R)
gr = random term
r = Gaussian number with variance 1 and mean 0
Land atmosphere interaction and conceptual model
Column structure
Fin + 
Fout = Fin
P
E
Fout = Fin
Fout = Fin
P
E
P
…
E
R
R
R
ds/dt
ds/dt
ds/dt
i=1
i=2
i=n
Land atmosphere interaction and conceptual model
Parameterization of g, E, R
• Precipitation efficiency
g(s) = a s + b
• Evaporation
E(s) = Epot sc
Epot(i) = linear interpolation between Epot(1) and Epot(n)
i = column number, n = nr of columns
• Runoff
R = P sr
Land atmosphere interaction and conceptual model
Code list
weak / strong
REAL
REAL
REAL
REAL
REAL
RAEFF
RBEFF
RUW
RLEN
RSDEV
0.0 / 0.2
0.3 / 0.2
200.
1000000
0.1
REAL
REAL
REAL
REAL
REAL
RAEPOT
RBEPOT
RECOF
RR
REPSIL
1.
2.
0.5
0.1
0.1
REAL
REAL
REAL
RSDEP
RTIME
RZCR
0.5
0.0001
0.01
REAL
REAL
INTEGER
INTEGER
RSTMAX
RYEAR
NCOL
NPPSTEP
1
10
10
1000
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coefficient A in PrecEff = A s + B
coefficient B in PrecEff = A s + B
advection U x W (m/s kg/m2 = kg/m s)
horizontal length scale (m)
Standard deviation of stochastic term
on UW/L (fraction)
Epot at first column (m/yr)
Epot at last column (m/yr)
Coefficient c in E = Epot s^c
Coefficient r in R = e P s^r
Coefficient e in R = e P s^r (runoff
efficiency)
Storage reseroir depth (m)
Time step length (yr)
soil saturation below which red noise is
restricted to postive values
clipping value of zst
Number of years to simulate
nr of adjacent columns
output interval (nr of steps)
Land atmosphere interaction and conceptual model
Weak coupling between s and g
Land atmosphere interaction and conceptual model
Strong coupling between s and g
Land atmosphere interaction and conceptual model
Soil moisture evolution
weak
strong
Land atmosphere interaction and conceptual model
Summary
• Response (one factor affecting another) 
feedback (closed loop of responses)
• Land-atmosphere feedback at multiple time/space
scales
• Relevant domains:
– Carbon-climate feedback
– Land use – climate feedback
– Thermal coupling
– Hydrological coupling
– ...
• Conceptual model oversimplifies but allows
systematic exploration
Land atmosphere interaction and conceptual model
Next week (mandatory!)
• Prepare an experimental set-up using the
conceptual model
• Write down, hand over to me (will be commented),
add student nr
• Criteria
– Should be inspired by a “true” physical question
– Should include at least 2 experiments
– Should describe the analysis method and
conclusions expected
• Example:
– Strong/weak coupling affects the gradient of
precipitation more than the gradient of soil
moisture
Land atmosphere interaction and conceptual model
More information
• Bart van den Hurk
– hurkvd@knmi.nl
– www.knmi.nl/~hurkvd
Land atmosphere interaction and conceptual model