6. Heat flux and Ustar comparisons

I originally thought that ustar should be corrected proportional to wind speed. But when I did this, it made the comparisons with the hazer worse. In hindsight thinking we could correct ustar this way was foolish. I now realize that correcting ustar is more complicated than simply changing ustar proportional to the wind speed correction. Bias errors would affect the rotation of the axes but not the u' prime values thereafter. And slope errors would not be proportional to wind speed but rather u'. And since ustar is the square root of mean u'w' the correction should be only proportional to the square root of the wind correction. I think the ustars need to be recalculated using the corrected sonic components. I don't think a correction can be applied after the fact. Can anybody think of a way? I have removed the part of the read_prof_all2.m MATLAB prgram which changed ustar to the corrected value. The program now leaves ustar as it was. The following figures show comparisons of heat flux and ustar during the calibration periods. I did not attempt calibrations based on the results.

These plots included all wind directions when fluxes were available.

Here are the median and standard deviations of heatflux(level 1) - heatflux(level 2,3,4,5) for all the calibration periods combined. The following tables include only data whe RWD1 > 300 deg or RWD1 < 100 deg. In parentheses are the same comparisons, for the entire experiments (levels at different elevations). Only periods with WS1 > 2 m/s were included in the latter.

Heat Flux Comparisons (W/m2)

Median BiasStandard Dev
hs1-hs20.2 (-0.4)1.42 (3.72)
hs1-hs30.1 (-0.3)3.07 (3.82)
hs1-hs40.5 (0.0)2.18 (4.86)
hs1-hs50.8 (-0.2)1.50 (5.30)

Uncorrected Ustar Comparisons (m/s)

Median BiasStandard Dev
us1-us20.00 (-0.01)0.0158 (0.0321)
us1-us3-0.01 (-0.02) 0.0282 (0.332)
us1-us40.00 (-0.02)0.0332 (0.0365)
us1-us5-0.01 (-0.02)0.0276 (0.0427)

These tables provide a way to estimate the accuracy of our measurements. Bias errors in heat flux are very low, less than 1 W/m^2. And it looks like even random errors are generally less than 3 W/m^2. Of course as the plots show, compared to the low absolute values anyway, these are fairly large when expressed as a percentage. Ustar biases are at the resolution in Ola's file, 0.01 m/s. The mean value of ustar for all of SHEBA was about 0.18 m/s so the random errors (based on the standard deviations) above are about 8% - 18%. Wind stress percentage errors would be twice that. (I guess I could divide by sqr(2) since we are comparing two values that each have errors.) I hope the ustar errors would decrease if we re-calculated the fluxes using the corrected wind speeds...

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Last update: 5/5/99

Please send all comments and suggestions to the author, Peter Guest,