ABL budget method to estimate regional CO2 flux

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ABL budget method to estimate regional CO2 flux

• 1. equations
• 2. c-q, dc-dq

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• - What we are interested in is usually the fluxes
  over an area, not at a point.
• estimate area-averaged flux according to mass
  conservation

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1-D equation

• In the literature, 1-D equation is usually used

Where, cm mean CO2 concentration in the CBL,
w vertical velocity
h CBL height means
just above the CBL top
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• Real atmosphere is heterogeneous

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small
mean field
subgrid terms H is a height of CBL
top or above CBL. Turbulent flux above CBL is
small, (zero) Horizontal subgrid term can be
ignored. w c is equal to zero on the
surface. After rewritten, the equation is,
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After using Leibnitz rule of integration,
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Some terms are not easily constructed, e.g.,
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1. wc

• Usually small near the surface
• Increases with height, because w-bar fluctuation
  increases then decreases, because c-bar
  fluctuation decreases.
• Depends on flows, but small (0) at free
  atmosphere
• Evidence from IHOP

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How to calculate

• - 1-km average

leg
c1 c2 c3 c4 c5
.. w1 w2 w3 w4 w5

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CO2 turbulent flux
sub-grid flux
Entrainment zone
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Water vapor turbulent flux
sub-grid flux
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Sensible heat turbulent flux
sub-grid flux
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• wc above entrainment zone is small
• H is not CBL height, but h?h

Free atmosphere
h?h h h-?h
CBL
CO2
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2. Cq, dc/dxdq/dx

• Under fair weather/clear sky condition, water
  vapor is transported into atmosphere mostly by
  plant evapotranspiration over vegetated areas
• CO2 is negatively correlated with water vapor due
  to photosynthesis process.
• Absolute values of CO2 and q mixing ratio are
  affected by, e.g., large-scale weather. Dc and dq
  can eliminate them to some degree. So dcdq are
  correlated better than cq.
• Evidence

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• C-q , dc dq
• 1-km average

leg
c1 c2 c3 c4 c5
.. q1 q2 q3 q4
q5 dq1 dq2 dq3 dq4
dc1 dc2 dc3 dc4
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1830 UT
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Correlation is not always high

• Correlation depends on weather history (e.g.,
  rain)
• If more water vapor evaporated from soil (e.g.,
  after rain), the negative correlation is
  weakened.
• Correlation is more sensitive to weather for low
  NDVI than high NDVI

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NDVI0.1
dcdq
rainfall
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NDVI0.4
dcdq
rainfall
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NDVI0.65
dcdq
rainfall
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• Correlation coefficient NDVI,
• time

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Correlation between dc and dq
NDVI0.1
NDVI0.4
NDVI0.65
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conclusions

• Correlation between dc and dq increases with NDVI
• Correlation between dc and dq increases with time
  (afternoon)
• CO2 mixing ratio is also negatively correlated
  with water vapor mixing ratio when,
• large NDVI
• late afternoon

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WLEF region

• NDVI in the region is about 0.7
• Surface is a major source (sink) of water vapor
  and CO2 under fair weather (clear sky)
• dc/dx and dq/dx might be linearly correlated
  according to the evidence from IHOP.
• Compute dq/dx, dc/dx by budget equation
  (multi-level fluxes measurements)

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WLEF region, NDVI 0.7, 98,99 data, fair
weather, afternoon
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3. ltcgtm-ltcgt

• It is somewhat difficult to estimate the
  difference.
• No long-term measurements of ltcgt
• Measurements at other sites? E.g., CAR
• Marine BL at the same latitude? 2-3 ppm
  difference
• Nighttime 396-m values?
• Inferred from water vapor? (considering the same
  mixing process)

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Approximately, one-D CBL model is used to find
the averaged ratio of ?C and ?q
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Mean Slope-0.710.2 lt?Cgt-0.71lt?qgt, similar to
Hellikers (2002) estimate Need data to verify
this
y
x
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C(mean)- C(tower) depends on, tower height
stability CBL height
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Height-dependent influence of surface
heterogeneity on turbulent flux ??
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Motivation

• - Single-point measurements are usually used to
  represent fluxes over an area.
• - Errors depend on horizontal variations due to
  surface heterogeneity and flow characters

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• Methods
• Scaling arguments
• A simple analytical solution under idea
  conditions -- unrealistic
• (3) Numerical solutions more realistic than (2)
• (4) Aircraft data--- IHOP, Real situation

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Scaling arguments
(1)
Blending height approach describes the
influence of surface heterogeneity on a single
well-defined scale Indicate that Influence
of small-scale heterogeneity decreases faster
with height than that of larger-scale
heterogeneity
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(2) Flux conservation equation
More straightforward way shows the horizontal
variation depends on scale and height.
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Analytical solution Idealized solution shows the
mechanism of mixing and transport

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assumptions

• K and U are constant, linear equation
• the surface variations of c can be built up
  through a Fourier series
• Influence of surface variation disappear as z -?
  infinite

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For typical CBL, U10m/s, K100m2/s, damping
rate0.56 Although unrealistic, it still shows R
depends on z and L
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Numerical solution Second-order model to simulate
CBL and diffusion of a passive scalar
ß is a function of U, w, and zi (CBL height)
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ß
Uzi /w
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The spatial variability of the flux --
increases with the spatial scale of the
heterogeneity (L) --decreases with
measurement height (z), wind speed (U)
, and the convective velocity scale.
Consistent with qualitative analyses in Mahrt
(2000).
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IHOP data analyses

• Not yet finished

From the data, we propose,
Where L0 is a scale partitioning heterogeneous
(scales gtL0) and homogeneous (scales ltL0)
flows ---For heterogeneous flows, R depends on
the flows, not necessarily following the above
formula.
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Standard deviation of mean flux vs scale
63m
471m
602m
Less heterogeneous
heterogeneous
1/L0
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Relationship of Area-averaged carbon dioxide and
water vapor fluxes to atmospheric variablesL.
Mahrt and D. VivkersAgricultural and Forest
Meteorol.,112, 195-202,2002
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Motivation

• Much less effort to estimate spatially-averaged
  fluxes over a region with multiple ecosystems
• To construct area-averaged fluxes
• To examine the relationship of the area-averaged
  fluxes to Vapor pressure deficit, solar
  radiation, and others

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Method

• Increasing the representativeness of the tower
  measurements by adjusting the tower fluxes
  according to companion aircraft data,
• e.g., aircraft measured less sensible heat
  and greater latent heat compared to the tower

Where a(i) represents corrections for the tower
data for the ith surface type W(i) is the
fractional coverage for the ith surface type.
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- Highly correlated - Because solar radiation is
the principle source of energy for daytime
evaporation
Area-averaged latent flux solar radiation,
mid-day, 1100-1500 LST
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Area-averaged water vapor flux VPD
Increase with VPD, but largely scattered because
evaporation proportional to VPD, but stomata
close partially with large VPD.
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Area-averaged CO2 flux VPD Midday
- CO2 downward flux decreases with VPD greater
than 0.7kpa - Scattered, because stomata close
partially as VPD increases
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Water use efficiency VPD
Less scattered compared to fluxes VPD WUF Less
changed with VPD greater than 1.8 Scatter is due
to inclusion of evaporation from soil, standing
water, dew and intercepted water WUE is a
function of other variables, e.g., soil moisture,
plant type,.
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Diurnal variation of area-averaged WUE VPD

• - CO2 flux reaches maximum at about 1030, then
  limited by the influence of VPD.
• WUE reaches maximum at 900
• in late afternoon, rapidly changed

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Area-averaged site values
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Less scatter than that for individual tower sites