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
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
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.
Modeled Fluxes
Wm-2
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.
Observed Fluxes
Wm-2
Jasmine Cruise Data
Zilitinkevich
LKB
Wall Theory
COARE3.0
CFC
Zilitinkevich
LKB
COARE3.0
Latent Heat Flux
Covariance Method
CFC
Sensible Heat Flux
Covariance Method
Sensible Heat Flux
Covariance Method
Sensible Heat Flux
Inertial Dissipation Method
Sensible Heat Flux
Inertial Dissipation Method
Latent Heat Flux
Inertial Dissipation Method
Latent Heat Flux
Inertial Dissipation Method
Latent Heat Flux
Covariance Method
Wall Theory
Nauru99 Cruise Data
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.
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.
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.
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.
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.
Zilitinkevich, 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.