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Up Topic Special Topics / Inherent Optical Properties Workshop / Rrs(0+) -> Rrs(0-) & water coefficients (locked)
- - By bryan Date 2008-08-05 14:32
Here's a simple question for group consensus:  what is the preferred method of converting from above-water to below-water reflectance.  The competition seems to be between these options:

1) Rrs(0-) = Rrs(0+) / 0.5238

2) Rrs(0-) = Rrs(0+) / [0.52+1.7 Rrs(0+)]

-- bryan
Parent - - By jeremy Date 2008-08-06 08:43
Following, might we agree upon a standard suite of aw and bbw coefficients for use in our analyses?  I acknowledge the ongoing debate regarding bbw values, but perhaps internal consistency is best, at least to start?  Although, analyses regarding the sensitivity of these "constants" might be prudent for the Workshop.  This is a list of 11-nm average aw and bbw for SeaWiFS, MODIS, and MERIS, as recorded here (aw = Pope and Fry 1997, bbw = 0.0038 * (400. / wl)^4.32).  Thoughts? 

    412      443      490      510      555      670
aw  0.00457, 0.00706, 0.01513, 0.03253, 0.05979, 0.44054
bbw 0.003344,0.002445,0.001581,0.001330,0.000923,0.000409

    412      443      488      531      551      667      678
aw  0.00457, 0.00706, 0.01448, 0.04395, 0.05979, 0.43395, 0.46040
bbw 0.003344,0.002445,0.001610,0.001118,0.000923,0.000417,0.000389

    412.5    442.5    490      510      560      620      665      681.25
aw  0.00453, 0.00695, 0.01513, 0.03253, 0.06211, 0.27570, 0.42970, 0.47251
bbw 0.003327,0.002457,0.001581,0.001330,0.000888,0.000572,0.000423,0.000381
Parent - - By EmmanuelBoss Date 2008-08-06 10:40
Dear all,               
Shouldn't we vary the water IOPs for Salinity and Temperature? bbw is                    
strongly salinity dependent (30% between zero and 39psu) its value                       
will not change much between open ocean environment but since we know                    
it we may as well get used to do it (and thus will not forget to                         
change it when we do Great Lakes work). Similarly modulating                             
absorption with temperature is important in the red and NIR (we can                      
also salinity correct).                                                                  
Note that salinity and temperature corrections are often applied to                      
the ac-9 simply so their effect on water is not translated to the                        
signal relative to water (due to dissolved and particulate materials).                   
When water is added back to a_pg and c_pg (e.g. when total a and total                   
c are reported), most often the water added is fresh and at a specific                   
temperature (e.g. Pope and Fry's) and thus is not representative of                      
the conditions where the water was measured (e.g. arctic ocean). It is                   
important that any ac-9 data used here should be those of the                            
particulate and/or dissolved components only (w/o the added water).                      
In coastal waters this may not be an issue but in mid-ocean gyre it                      
will be. In addition this introduces a bias we can easily do without.                    
Another issue: the value you report below have probably been evaluated                   
using a 1 or 2nm bandwidth spectrophotometer. The satellite bandwidth                    
is larger (10-20nm) which means it averages over a certain band range.                   
We should do our best to perform that average on all optical                             
properties we use (validation set and water values) to insure that                       
areas where these properties may be changing non-linearly are not                        
introducing biases. in-situ ac and bb instrument have typically 10 or                    
20nm bandwidth (though some c meters have laser sources with less than                   
1nm bandwidth).                                                                          
Parent - - By bryan Date 2008-08-06 13:24

The numbers we actually use for aw and bbw in satellite processing are 11-nm averages derived from 1-nm tabulated values.  The tables can be obtained here:

We use 11-nm averages because, in standard operational processing, we report the satellite retrievals for a 10-nm square band-pass centered on the nominal wavelength (i.e., we correct the nLw retrieval from full band-pass to nominal center band as the last step in the normalization of Lw).  If this correction is not applied, the code uses full-band aw and bbw, as reported here:

These are the 11-nm averages that we currently use for aw and bbw (as computed internally):

SeaWiFS      aw          bbw
  0     412  4.641e-03  3.327e-03
  1     443  7.098e-03  2.438e-03
  2     490  1.527e-02  1.583e-03
  3     510  3.260e-02  1.334e-03
  4     555  5.965e-02  9.299e-04
  5     670  4.402e-01  4.171e-04
  6     765  2.851e+00  2.376e-04
  7     865  4.603e+00  1.413e-04

MODIS         aw          bbw
  0     412  4.641e-03  3.327e-03
  1     443  7.098e-03  2.438e-03
  2     469  1.050e-02  1.909e-03
  3     488  1.458e-02  1.611e-03
  4     531  4.394e-02  1.123e-03
  5     551  5.697e-02  9.590e-04
  6     555  5.965e-02  9.299e-04
  7     645  3.267e-01  4.903e-04
  8     667  4.339e-01  4.251e-04
  9     678  4.610e-01  3.966e-04
10     748  2.848e+00  2.614e-04
11     859  4.421e+00  1.455e-04
12     869  4.748e+00  1.385e-04
13    1240  1.152e+02  2.865e-05
14    1640  6.356e+02  8.564e-06
15    2130  2.513e+03  2.768e-06

MERIS         aw          bbw
  0     412  4.641e-03  3.327e-03
  1     443  7.098e-03  2.438e-03
  2     490  1.527e-02  1.583e-03
  3     510  3.260e-02  1.334e-03
  4     560  6.206e-02  8.950e-04
  5     620  2.756e-01  5.801e-04
  6     665  4.282e-01  4.306e-04
  7     681  4.716e-01  3.892e-04
  8     708  7.827e-01  3.300e-04
  9     754  2.865e+00  2.527e-04
10     761  2.866e+00  2.430e-04
11     779  2.700e+00  2.200e-04
12     865  4.603e+00  1.413e-04
13     885  5.564e+00  1.283e-04
14     900  6.415e+00  1.195e-04

-- Bryan
Parent - - By EmmanuelBoss Date 2008-08-06 13:39
Thanks Bryan.
I think we need to modulate them with temperature (measured) and salinity (climatology).
Parent - - By bryan Date 2008-08-06 14:50
Yes, I think that's a good suggestion. It shouldn't be too difficult to achieve.  For SeaWiFS we'd probably use Reynolds SST (weekly 1-deg or the new daily 0.25-deg product), which we already ingest.  Not sure if there is an equivalent SSS product available.  If you or others can post the dataset(s) to use and the correction method, that would solidify the recommendation.

-- bryan
Parent - - By jilly Date 2008-08-06 19:25
Hi bryan,

I agree it's worth tackling T and S adjustments now.  The best/newest/only global salinity dataset i know of is the World Ocean Atlas

But both T and S on a 1deg grid are not going to be ideal for, say, estuaries with strong, tide-driven changes in T and S over time;  we need to check the magnitude of the T/S corrections at in situ matchups where CTD data are available, and see how suitable the climatologies are.

My 2cents,
Parent - - By EmmanuelBoss Date 2008-08-07 01:23
I agree with Jill on the source for S coefficient.
Even if we may be off on the exact salinity value, we will be better, on average, than not accounting to it.
The source for T, as Bryan suggested, could be within the ocean color output.

The latest numbers on the backscattering coefficient (including S contribution) are in Twardowski et al., 2007 in Biogeoscience. For the S and T contribution to to a_sw I used to use Pegau and Zaneveld, 1997.  Newer values were published by Sullivan et al., 2006, in Applied Optics, using the ac-s.

Parent - - By jeremy Date 2008-08-07 09:52
For what it's worth, here's some (sloppy) IDL code to calculate b_sw(wl,temp,sal):

Based on Twardowski et al. 2007 and Buiteveld et al. 1994.

I'll use this for some sensitivity analyses.  Will hopefully provide a template for l2gen. 

But, someone might want to check my math ...

Will compile similar software for a_sw when back in office next week.
Parent - By jeremy Date 2008-08-12 15:52
Here's a crack at IDL software to calculate a_sw(wl,temp,sal):

Based on:
(1) aw (22 C, 0 PSU) from Pope and Fry 1997
(2) temp and sal correction factors from Table 2 of Sullivan et al. 2006
(3) the relationship [ aw_corr = aw_meas - temp_corr * (temp - 22.) - sal_corr * sal ]

Returns either (a) 11-nm average of aw centered on input wl, or (b) aw spline fit to 1-nm increments from 400-700 nm.

Again, someone should really check my implementation. 

Otherwise, enjoy.
Parent - - By dem Date 2010-03-30 09:45

Are these values still up-to-date or did you have recomputed them with the sst and salinity correction?
And please could you give me the nominal 11-nm square bandpasses values of aw, bbw and also F0 you use for the new MODISA 547 band (old 551 re-defined)?


Parent - - By bryan Date 2010-03-30 14:15

The numbers have not changed.  We haven't implemented salinity and temperature effects yet, but that would likely be done as a correction algorithm applied to these values. Here's latest numbers for MODIS with 547.

wave    aw              bbw
412 4.640990e-03 3.327229e-03
443 7.098098e-03 2.437585e-03
469 1.049904e-02 1.909299e-03
488 1.457921e-02 1.610938e-03
531 4.393521e-02 1.122943e-03
547 5.337546e-02 9.892991e-04
555 5.964877e-02 9.298773e-04
645 3.266578e-01 4.902821e-04
667 4.339156e-01 4.251321e-04
678 4.609707e-01 3.965882e-04
748 2.848320e+00 2.613615e-04
859 4.421082e+00 1.454898e-04
869 4.748336e+00 1.385429e-04
1240 1.151705e+02 2.865000e-05
1640 6.356376e+02 8.563636e-06
2130 2.512734e+03 2.768182e-06
Parent - By EmmanuelBoss Date 2010-03-30 17:44
If you are to add the salt effect on bbw (which you should) the latest values are available from X. Zhang papers from 2009 in Optics Express.
All the best,
Parent - By dem Date 2010-03-31 04:40
Thanks a lot Bryan,

Do you have also the corresponding F0 for 547?

Parent - - By Loisel Date 2008-08-07 12:57
Hi all,                                                                                  
Here are some elements concerning the conversion of Rrs(0+) to Rrs(0-).                  
These results are based on hydrolight simulations used in the IOPs                       
inversion workshop IOCCG, report 5). Only wavelength at 490 nm, and 3 sun                
angles (0, 30, 60) are considered here.                                                  
A constant values is not appropriated as i) this value change with the sun               
angle (see figure called constant-ratio), and ii) a hyperbolic fit                       
((x/(a+bx), with a and b some constants) is much more appropriated than a                
linear fit.                                                                              
For the hyperbolic fit, and based on the data set used in the IOCCG report,              
the constant a and b are different from those given in Lee et al. 1999                   
(a=0.52, and b=1.7). However, the difference between the Lee et al's fit,                
and the one presented here is quite small (not more than 5%, at this                     
wavelength). However, one may see an effect of sun angle (as expected) on                
this conversion (see figure called polyfit).                                             
I believe that we should use the hyperbolic fit instead of a constant                    
value. Moreover, I think it will be better to include the effect of sun angle            
in this hyperbolic form (through a parameterisation or tables). It is quite              
easy, and we have the simulations (perhaps two other sun angles will be                  
useful: Zhong Ping do you still have the inputs of the IOCCG-simulations ?).             
We know that it will improve the conversion, so ....       
Parent - By zplee Date 2008-08-07 14:56
Hubert and all:

The (0.52 & 1.7) coefficients were developed for nadir view, as an overall average for various Sun angles. As Hubert showes here, apparently not that bad (within 5%). The 0.52 will change a little for view angle away from nadir, but to what extent will depend on angles and VSF, etc. We have an ongoing project looking into that, and would be happy to report our findings later this year or next year.

On the other hand, these coefficients affect more to derived bb or bbp, less to atot. If all measurements are made within a 30 deg view angle and Sun are within 70 deg from zenith, the angle-introduced error to retrieved IOPs will be small (<10%).

As to Hubert's question of IOCCG data set, yes, it is there, but only nadir-viewed Rrs(0+) and Rrs(0-).

Parent - By sokoletsky Date 2011-11-23 16:02 Edited 2011-11-23 16:59
Hi Hubert,

Thank you for interesting information! I am also interested by this issue for my ocean color modeling. I did my own attempts to find Rrs(0+)/Rrs(0-) ratio. Actually, a form of this ratio was established by Saunderson in 1942 (so called "Saunderson's correction"), and it is just in the form (hyperbolic) that use you or Lee at al. I also used this form, attracting some theoretical (Fresnel & Snell's laws; Quan and Fry, 1995; Morel and Gentili, 1996; Molenaar et al., 1999), observational (Aas and HØjerslev, 1999; Toole et al., 2000) and radiative transfer modeling (Mobley, 1999; Aas, 2010; Kokhanovsky & my own, unpubl.) stuff. I have results now for any wavelength and solar zenith and viewing angles, but for the better comparing with your results, I may give "a" & "b" for your lambda (490 nm),  3 sun angles (0, 30, 60) and nadir viewing:

0 deg: a = 0.515, b = 1.642    
30 deg: a = 0.515, b = 1.744   
60 deg: a = 0.515, b = 2.057

Thus, my results are extremely close to Zhongping's results, and, of course, close to yours.

Interestingly to analyze an impact of temperature and salinity. My model allows to do this. As an example, I can show coefficients for the normal temperature (25 deg), extremal high salinity (280 per mil) and previous wavelength and angles:

0 deg: a = 0.479, b = 1.768    
30 deg: a = 0.479, b = 1.877   
60 deg: a = 0.479, b = 2.214

Best wishes,

Up Topic Special Topics / Inherent Optical Properties Workshop / Rrs(0+) -> Rrs(0-) & water coefficients (locked)

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