Global distribution of Case-1 water
ZhongPing Lee, ChuanMin Hu
Abstract
In recent decades, Case-1 bio-optical models and numerous remote-sensing algorithms
for chlorophyll concentration have been developed. To reliably apply these models and
algorithms for oceanography studies, it is necessary to know the distribution of Case-1
water in global scale. To map Case-1 water by remotely measured water-leaving radiance,
a quantitative Case-1 criterion is developed based on Case-1 bio-optical models. Apply
the criterion to water-color data obtained by SeaWiFS, global distribution of Case-1
water is obtained for the first time. Depending on the width of the quantitative boundary,
the range of Case-1 water can be from ~40 to 70% for the world surface waters.
Regionally, lesser waters belong to Case-1 in the northern hemisphere, while more
belong to Case-1 in the southern hemisphere.
Introduction
Studies in the past decades have found that mainly there are three active constituents
affect optical water properties: phytoplankton, colored dissolved organic matter (CDOM),
and re-suspended sediments. Phytoplankton and sediments contribute to both absorption
and scattering coefficients, while CDOM contributes to absorption coefficients
(especially to the blue wavelengths). In the modeling of optical water properties and
ocean color remote sensing for phytoplankton (represented by concentration of
chlorophyll: Chl), a scheme to simplify the dependence between optical properties and
water constituents was proposed: i.e. the Case-1 and Case-2 separation of global waters.
In short, Case-1 waters are those whose optical properties can be adequately described by
Chl, whereas Case-2 waters are otherwise.
In the recent decades, with extensive measurements of optical water properties and
chlorophyll concentration, bio-optical models and numerous remote-sensing algorithms
for Chl have been developed for Case-1 waters. To reliably apply these models and
algorithms for oceanography studies, it is necessary to know the global distribution of
Case-1 water and its temporal variation. However, there is no geographic map of Case-1
water yet, except in common practice oceanic waters are assumed as Case-1 without
rigorous scrutinizing.
Case-1 is a concept to separate out optical simple waters from optically complex
waters. Optically, if a water belongs to the Case-1 category, its optical properties can then
be predicted solely from Chl. Apparently, classification of Case-1 is not based on the
geographic location, nor based on the values of Chl. Water in the coastal region could be
Case-1, where as water in the open ocean could be Case-2. Similarly, water with Chl as
low as 0.05 mg/m3 could be Case-2, while water with Chl as high as 50 mg/m3 could
really be Case-1. Clearly, the key to judge if a water belongs to Case-1 or not relies on
the dependence between optical water properties (such as absorption, scattering, and
backscattering coefficients) and Chl.
Ideally, it requires concurrent measurements of both optical water properties and Chl
to map the global distribution of Case-1 waters. Unfortunately, restricted by insufficient
spatial and temporal coverage associated with traditional ship survey, such kind of
approach is unrealistic to obtain high-resolution results for global coverage. A practical
means to meet the desire of mapping the global distribution of Case-1 is to use ocean
color data obtained from satellite sensors.
In this study, based on the bio-optical models for Case-1 waters developed from
recent and historical measurements, we devised a relaxed remote-sensing criterion for
Case-1 waters. Further, we applied this criterion to the lately updated global ocean color
measurements obtained by the SeaWiFS to analyze for the first time the global
distribution of Case-1 waters and its seasonal variations. The results of this study provide
a general guidance where Case-1 remote-sensing algorithms and bio-optical models could
be applied.
2. Remote-sensing criterion for Case-1 water
In ocean color remote sensing, the only available information is the water-leaving
radiance (a quantitative measure of water color) measured by a remote sensor, along with
some auxiliary information such as observation geometry, sea state, etc. Optical
properties and Chl could be derived from water-leaving radiance with a remote-sensing
algorithm. The derived optical properties and Chl values by such an approach, however,
are associated with uncertainties (especially Chl), and many times different Chl could be
obtained with different remote-sensing algorithms. These characteristics make it difficult
to use remotely derived optical properties and Chl to map Case-1 waters. Also, for
application of Case-1 remote-sensing algorithms and bio-optical models, a method to
map Case-1 waters by water-leaving radiance is useful and desirable.
Fundamentally, Case-1 waters are those whose optical properties can be determined
by Chl. These optical properties include water’s inherent optical properties (such as
absorption and scattering coefficients, etc) and apparent optical properties (such as
remote-sensing reflectance, Rrs). Therefore, for case-1 waters, there is certain dependence
among the Rrs values at different spectral bands. Note that Rrs is the ratio of water-leaving
radiance to downwelling irradiance just above the surface (Ed). Since Ed can be
adequately calculated with knowledge of atmospheric properties, Rrs is a quantity that
directly measures water color. Consequently, for a water pixel with Rrs obtained from a
satellite sensor, a comparison of its spectral dependence to the spectral dependence of
Case-1 Rrs provides a measure if the water belongs to Case-1.
From recent and historical measurements of Chl and optical properties, a relationship
between Chl and Rrs for Case-1 water has been developed. Apply this Case-1 bio-optical
model, for Chl values ranged from 0.02 to 30 mg/m3, Rrs at the SeaWiFS bands were
calculated following the iterative steps described in Morel and Maritorena (2001). Further,
the following spectral ratios are calculated:
RR12 
Rrs ( 412)
R (555)
, RR53  rs
.
Rrs ( 443)
Rrs ( 490)
(1)
Here 412, 443, 490, and 555 are wavelengths in units of nm, and are the center
wavelengths of SeaWiFS band 1, 2, 3, and 5, respectively.
In ocean color remote sensing, RR53 is an indicator of Chl (e.g., the OC2 algorithm
for SeaWiFS), while RR12 is an indicator of relative abundance of CDOM per Chl. For
Case-1 waters, because CDOM co-varies with Chl, a monotonic line exists between RR12
and RR53, as shown in Figure 1 by the blue line. For most natural waters, because CDOM
does not necessarily co-vary with Chl, wide variations of RR12 exist for the same RR53
values, as shown in Figure 1.
To map the global distribution of Case-1 water, a quantitative boundary (though
difficult and somewhat arbitrary) has to be drawn between Case-1 and non-Case-1 waters.
For easier processing, we map Case-1 in such a manner: for a water pixel with values of
CS 1
RR12 and RR53 from remote-sensing measurements, if its RR12 is between (1   ) RR12
and (1   ) RR12CS 1 , then we classify this water belongs to the Case-1 category. Otherwise,
CS 1
it belongs to non-Case-1. Here RR12
is the Case-1 RR12 value that corresponding to the
RR53 value of that pixel (the blue line in Fig.1).
Clearly, the inclusiveness of Case-1 relies on the selection of the value of . Ideally, 
= 0 for “pure” Case-1 water. Practically, a none-zero value has to be used to account for
imperfections from model to measurements. To be inclusive (though still arbitrary), we
initially set  as 0.05, i.e. to allow a 5% deviation of RR12 for the same RR53 value. Note
that this 5% deviation implies a likely error of -30% ( = 5%) to 50% ( = -5%) in the
prediction of aCDOM(443)/aChl(443) ratio for the same Chl. Here aCDOM(443) and aChl(443)
are the absorption coefficients of CDOM and chlorophyll at 443 nm, respectively. For
Case-1 waters, aCDOM(443)/aChl(443) ratio is a fixed value for given Chl as it solely
depends on Chl. The error range of aCDOM(443)/aChl(443) thus indicates a loosely defined
co-variation between the absorption coefficients of CDOM and Chl.
It is necessary to point out that using the RR12 - RR53 relationship alone is a quite
relaxed standard to classify Case-1 water, simply because this relationship to the most
only evaluates if the optical property of CDOM co-varies with Chl as expected by Case-1
bio-optical models. Suspended sediments, a primary factor determines the magnitude of
Rrs(λ) through its contribution to backscattering coefficient, is ignored here (will be
discussed later).
3. Distribution of Case-1 water by the remote-sensing criterion
To know the global distribution of Case-1 waters under the remote-sensing criterion
devised above, the lately reprocessed SeaWiFS global data is acquired from GorDAD.
Seasonally averaged normalized water-leaving radiance ([Lw(λ)]N) of the first five
SeaWiFS bands collected between March 23, 2003 and March 23, 2004 were obtained.
By definition of [Lw(λ)]N, Rrs(λ) of each pixel is the ratio of [Lw(λ)]N to F0(λ). Here F0(λ)
is the solar irradiance on top of the atmosphere with a mean Sun-Earth distance and is
available at GorDAD. From these Rrs(λ), RR12 and RR53 values of each pixel are then
easily calculated.
As an example, Figures 1a and 1b show the ranges and variations of RR12 and Rrs(555)
for each RR53 value of the global surface waters, measured by SeaWiFS in the period of
September 21, 2003 – December 20, 2003. The blue line in both figures indicates the
Case-1 RR12 and Rrs(555) values that corresponding to the RR53 value, respectively. The
cyan and green lines in Fig.1a indicate the 5% deviation of RR12 for the same RR53
value; whereas the cyan and green lines in Fig.1b indicate a 30% deviation of Rrs(555)
for the same RR53 value. When RR53 is perceived as a measure of Chl (the numbers in the
parenthesis), clearly, even for waters with Chl less than 1.0 mg/m3 (a range encompass
most oceanic waters), there are quite wide variations in both RR12 and Rrs(555) for global
waters.
Apply the Case-1 remote-sensing criterion defined earlier, global water is separated
into four categories as depicted in Fig.2. The cyan colored points are for pixels with RR12
values higher than the cyan line; the blue color for pixels (Case-1 water) with RR12
CS 1
CS 1
values between 0.95 RR12
and 1.05 RR12
; the green color are for pixels with RR12
CS 1
values between 0.50 and 0.95 RR12
; and the red color for pixels with RR12 values less
than 0.50. Apply this separation to the global observation, a map of the four
classifications are obtained (see Fig.3a-d for Spring, Summer, Fall, and Winter,
respectively). Generally, by this Case-1 remote-sensing criterion, Case-1 (blue pixels)
take ~40% of the global surface waters. Seasonally, there are more (46%) Case-1 in Fall,
and less in Spring. There are more green pixels in Summer (a result of phytoplankton
degradation bloomed in Spring), and less in Fall. Geographically, blue pixels (Case-1
water) are generally in the sub-tropic regions, whereas green pixels occupy mostly the
northern hemisphere and coastal regions, with 90% of the cyan pixels around the equator.
Red colored pixels only take about 1% of the global surface water, and are generally
around coastal lines, likely a combination of incorrect atmospheric correction and
enhanced CDOM concentrations.
Recall that for each RR53 ratio (an index of Chl), the RR12 value is a relative measure
of CDOM per Chl. Therefore cyan color indicates relatively lower CDOM for the same
Chl compared to Case-1 water, while green color indicates relatively higher CDOM for
the same Chl compared to Case-1 water. The global distribution of these colors
suggesting that there are less CDOM in the tropical Pacific due to photo-bleaching, while
more CDOM in coastal and northern waters, results of land run-off and productivity.
Inversely, if the same empirical Case-1 algorithm for Chl (such as the OC2 SeaWiFS
algorithm) is applied to the global waters, overestimation of Chl would be resulted to
high latitude waters while underestimation to tropical waters, even without consideration
of phytoplankton package effect.
Clearly, the percentage of surface water that belongs to Case-1 depends on the width
of the Case-1 boundaries. If we relax further the standard for Case-1 by selecting  as 0.1
(a 10% deviation of RR12 for the same RR53 value), substantially more surface waters
could be classified as Case-1 water. However, this 10% deviation of RR12 (centered on
the Case-1bio-optical model predicted value) indicates a likely error of -46% ( = 10%)
to 100% ( = -10%) in the ratio of aCDOM(443)/aChl(443) for the same Chl. Such kind of a
range is then over-inclusive compared with the co-variation requirement between CDOM
and Chl for Case-1 waters. Even with this significantly relaxed criterion (plus no
consideration of Rrs values), Case-1 water takes about 70% of the global surface waters
(see Figure 4 and Table 2). Again, tropical Pacific waters and high latitude northern
hemisphere waters do not belong to such a broad Case-1 category. These results and
distributions support further the argument the oceanic waters are not necessarily Case-1
water, and caution needs to taken when apply Case-1 bio-optical models and algorithms
to global waters.
Regionally, by this quantitative Case-1 remote-sensing criteria, the Mediterran and
the Japan sea are hardly belong to Case-1 category, and both are in green color (meaning
more 50% or more CDOM than predicted by the Case-1 model for the same Chl).
4. Summary
In ocean color remote sensing, it is commonly assumed that oceanic waters belong to
Case-1, while coastal waters belong to Case-2, though no clear boundary is drawn
between oceanic and coastal waters. Further, numerous remote sensing algorithms have
been developed for Case-1 water, but the distribution of Case-1 water in global scale is
vague and elusive. To fill this gap, and to gain a clearer knowledge of the global Case-1
distribution, we developed a relaxed Case-1 remote-sensing criterion based on widely
accepted Case-1 bio-optical models. Further, we applied this criterion to the lately
updated global ocean color data collected by SeaWiFS to map the global distribution of
Case-1 water. The results of such an exercise show that depending the inclusiveness (or
boundary) of Case-1 definition, Case-1 water takes ~ 40-70 of the global surface waters,
with most of them in the subtropical and the southern hemisphere. For the four seasons
studies, there are apparent seasonal variations for some specific local regions, such as the
north Atlantic, and the Indian Ocean. For waters in tropic Pacific, due to its lower CDOM
per Chl compared with the Case-1 bio-optical models, they actually do not belong to the
Case-1 water defined quantitatively.
Table 1. Global coverage of different water classes when  is set as 0.05
Water class
Spring
Summer
Fall
Winter
Cyan
31%
24%
32%
34%
Blue (Case-1)
36%
41%
46%
40%
Green
32%
34%
21%
25%
Red
1%
1%
1%
1%
Table 2. Global coverage of different water classes when  is set as 0.1
Water class
Spring
Summer
Fall
Winter
Cyan
12%
10%
12%
12%
Blue (Case-1)
65%
66%
73%
71%
Green
22%
23%
14%
16%
Red
1%
1%
1%
1%