Characterization of Errors in Turbulent Heat Fluxes Caused by Different Heat and Moisture Roughness Length Parameterizations

1
Characterization of Errors in Turbulent Heat
Fluxes Caused by Different Heat and Moisture
Roughness Length Parameterizations
Josh Griffin and Mark Bourassa
1. Background and Motivation When performing
height adjustments on temperature and humidity or
calculating turbulent heat fluxes, the
parameterization of the roughness length is not
taken into great consideration as long as the
parameterization seems reasonable. However not
taking the differences of these parameterizations
into consideration could lead to unaccounted for
error in data. This unknown error has the
potential for creating false trends in the
data. The different parameterizations of the
roughness length for this research include Wall
Theory (Bourassa et al. 1999), CFC ( Clayson et
al. 1996), Zilitinkevich (2001), LKB (Liu et al,
1979), and COARE3.0 (Fairall, 2003). The first
goal of the research will be to attempt to
determine which parameterization performs best in
calculating turbulent fluxes and under what
conditions it performed better.
4. Methodology The data from the two
experiments will be used to generate modeled heat
fluxes to compare against the observed heat
fluxes. The Bourassa (2006) version of the
Bourassa, Vincent, Wood (BVW) model is used to
generate the fluxes based on the parameterization
desired. The observed winds, air temperature,
sea surface temperature, and air humidity are
passed to the model and it creates sensible and
latent heat fluxes based on those observations.
The roughness length parameterization is changed
with a simple flag in the model. Each set of
observations is run five separate times, once for
each parameterization of the roughness length.
After the modeled heat fluxes are generated,
they are first compared against the observed
covariance and inertial dissipation fluxes. This
is done to determine which method for observing
fluxes are matching best to the modeled fluxes.
The figures below show the observed vs. modeled
heat fluxes for each of the two cruises. While
simple linear regressions could be done to see
which modeled fluxes are most like the observed
fluxes, this would not give us information about
the errors in the parameterizations. It is also
not ideal because there are different errors
affecting the two values being compared and also
the errors are going to have different
characteristics for each parameterization.
Estimates of random error in each model and the
data will be estimated, as a function of
different assumed biases (starting with zero
bias). One obvious constraint is that the
estimated error in the observed fluxes should be
the same for each comparison.
3. Parameterizations Wall Theory (Bourassa et
al. 1999) Treats surface as smooth, transfer
dominated by viscous processes CFC (Clayson
et al. 1996)- Uses Surface Renewal Theory and
improvements to the LKB parameterizations
(better at higher wind speeds) Zilitinkevich et
al. 2001- Uses a different scaling for
calculating the roughness lengths LKB- (Liu et
al. 1979)- Uses surface renewal theory and
considers only molecular activity at the
interface COARE3.0- (Fairall et al. 2003)-
Improved version of LKB, with much updated
curve fit to data inferred from far more
observations.

• 2. Data
• The data used is from the Joint Air-Sea Monsoon
  Interaction Experiment (JASMINE) and the Nauru99
  experiment. The JASMINE experiment occurred over
  the Indian Ocean in May of 1999. The ship took
  measurements throughout the onset of the monsoon
  over the Indian Ocean. The Nauru experiment took
  place from June 23 July 17, 1999 in the Eastern
  Pacific.
• Hourly wind, temperature, humidity, and SST
  measurements
• Hourly averaged sensible and latent heat fluxes
• Both Covariance and Inertial Dissipation
  (hereafter ID) method

Modeled Fluxes Wm-2
Observed Fluxes Wm-2
Jasmine Cruise Data
Nauru99 Cruise Data
Wall Theory
CFC
Wall Theory
CFC
Zilitinkevich
LKB
COARE3.0
Zilitinkevich
LKB
COARE3.0
Latent Heat Flux Covariance Method
Latent Heat Flux Covariance Method
Latent Heat Flux Inertial Dissipation Method
Latent Heat Flux Inertial Dissipation Method
Sensible Heat Flux Covariance Method
Sensible Heat Flux Covariance Method
Sensible Heat Flux Inertial Dissipation Method
Sensible Heat Flux Inertial Dissipation Method
The figures above compare the modeled turbulent
fluxes vs. observed turbulent fluxes for the
NAURU99 experiment. The x-axis is the observed
heat fluxes and the y-axis is the modeled fluxes.
Each column represents the different
parameterizations while each row compares the
modeled fluxes vs. the turbulent flux listed at
the beginning of the line.
The figures above compare the modeled turbulent
fluxes vs. observed turbulent fluxes for the
Jasmine experiment. The x-axis is the observed
heat fluxes and the y-axis is the modeled fluxes.
Each column represents the different
parameterizations while each row compares the
modeled fluxes vs. the turbulent flux listed at
the beginning of the line.
7. References Bourassa, M. A., D. G. Vincent, and
W. L. Wood, 1999 A flux parameterization
including the effects of capillary waves and sea
state. J. Atmos. Sci., 56, 1123-1139. Bourassa,
M. A., 2006, Satellite-based observations of
surface turbulent stress during severe weather,
Atmosphere - Ocean Interactions, Vol. 2., ed.,
W. Perrie, Wessex Institute of Technology Press,
Southampton, UK, 35 52 pp. Clayson, C. A., C.
W. Fairall, and J. A. Curry, 1996 Evaluation of
turbulent fluxes at the ocean surface using
surface renewal theory. J. Geophys. Res., 101,
28503-28513. Fairall, C.W., E.F. Bradley, J.E.
Hare, A.A. Grachev, and J.B. Edson, 2003 Bulk
parameterization of air-sea fluxes Updates and
verification for the COARE algorithm. J.
Climate,16, 571-591. Liu, W.T., K.B. Katsaros,
and J.B. Businger, 1979 Bulk Parameterization of
air-sea exchanges of heat and water vapor
including the molecular constraints at the
interface. J. Atmos. Sci.,36, 1722-1735. Zilitinke
vich, S. S., A. A. Grachev, and C. W. Fairall,
2000 Notes and Correspondence on Scaling
Reasoning and field data on the sea surface
roughness lengths for scalars. J. Atmos. Sci.,
58, 320-325.
6. Future Plans Additional plans for the
research could include looking at other cruises
outside of the tropics. There is high signal to
noise ratio in the tropics that might not be seen
in data for other cruises.
5. Discussion The figures above show that the ID
method has a much closer clustering of the
modeled vs. observed fluxes. This is true for
both the latent and sensible heat fluxes, but it
is much easier to see on the plots of the
sensible heat fluxes. This was not the expected
result since the ID method tends to have less
confidence than the covariance method. The ID
method has been thought of as less accurate since
1996 due to the fact that it assumes little
interaction between atmospheric turbulence and
water waves (Bourassa, Fall 2007, Lecture notes).
After contacting one of the lead scientists for
both cruises, Chris Fairall, he confirmed that
the covariance method has higher noise than the
ID method and could explain our results (Sept.
2008, personal communication). However, the
covariance results are expected to have smaller
biases. The next portion of my research will
focus on this noise issue. Propagation of errors
caused by noise in input observations to each
parameterization could be a large reason why the
parameterizations seem to vary quite a bit. Once
the noise characteristics and estimated biases
are found for each parameterization, more typical
statistical techniques can be used to assess
confidence in the bias corrected
parameterizations.