2017 IWA Symposium of Lake and Reservoir Management
Shanghai, China, 22-26 May, 2017
Semi-analytical Modeling of Reservoir Water-Transparency
Chih-Hua Chang*, Wei-Min Huang, Hsueh-Hsien Ti
Department of Environmental Engineering and Global Water Quality Research Center,
National Cheng Kung University, Tainan, Taiwan.
Presenting Author:
Keywords:
Chih-Hua Chang
semi-analytical model; water transparency; Secchi Disk; water quality modeling and management.
Introduction
The water-transparency, achieved by measuring the depth of Secchi Disk (ZSD), is one of the most commonly applied
physical parameter for multidisciplinary water quality management in lakes and reservoirs. Water-transparency is an
important response variable in lakes and reservoirs, indicating the trophic states, the health status of ecosystem, the
tempo-spatial distribution of water quality, as well as the landscape and recreational values. However, few water quality
models address the mechanistic processes required for analytically linking ZSD with other water quality variables or pollutant
loads. Current management measures on reservoir transparency are mostly relied on information provided by empirical
relationships linking optically active component concentration to ZSD. For example, Carlson evaluates trophic states by
linking Chlorophyll-a (Chla) or total phosphorus (TP) concentrations to the level of ZSD using regression models developed
in cold and temperate regions (Carlson 1977). The ability of an observer to see the disappearance of a white disk stepped in
water was a result of the interaction between penetrated sunlight and optically active substances (OASs), which are radiative
transfer processes linking the inherent optical properties (IOPs) of water bodies to the apparent optical properties (AOPs)
remotely sensed by a human eye. Many analytical and semi-analytical (SA) models are developed in oceanic waters to
describe such physical processes, but few have been applied in lakes and reservoirs. This work first established bio-optical
models (BOMs) relating Chla, suspended solids (SS), and total organic carbons (TOC) concentrations to IOPs based on water
samples taken in Sun-Moon Lake, Taiwan. Second, by the integration of the bio-optical models and ocean color SA
approaches determining the radiative transfer processes, a total of 2,400 measurements of ZSD in 22 primary drinking water
reservoirs over the period between 2007 and 2012 were simulated.
Materials and Methods
The BOMs developed in Sun-Moon Lake consist of four optically active components: algae particle, detritus-mineral,
color dissolved organic matter (CDOM) and particulate matter. The spectral adsorption coefficient of algae particle at 440nm,
aph(440), was related to the concentration of Chla; the adsorption due to detritus-mineral at 400nm, adm(400), was related to
the concentration of SS; the adsorption of CDOM at 440nm, ag(440), was related to the concentration of TOC, and; the
backscattering of particulate maters at 550nm, bbp(550), was linked to the level of SS. The BOMs used in this study to
simulate total spectral adsorption (a(λ)) and backscattering coefficients (bb(λ)) are formulated as:
a( )  aw ( )  0 ( )  1 ( )a ph (440)   adm (400) exp[  Sdm (  400)  ag (440) exp[  S g (  440) , and
bb( )  bbw (  )  bbp (550)  550  
n
.
(1)
(2)
Where aw(λ) and bbw(λ) are the adsorption and backscattering coefficients of pure water; α0(λ) and α1(λ) are modified from
(Lee et al. 1998), which are the spectral shapes for aph; Sdm and Sg are the spectral slopes of adm and ag, which are calibrated to
0.014 and 0.016 using in-situ data, respectively, and; n is the spectral shape of bbp. The solar zenith angle (θa) was calculated
by NOAA solar calculator with user input sampling location (latitude and longitude), date and time. The diffuse attenuation
coefficient of downward irradiance (Kd(λ)) was simulated by IOPs, θa and a semi-analytical model (Lee et al. 2005). The
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2017 IWA Symposium of Lake and Reservoir Management
Shanghai, China, 22-26 May, 2017
underwater remote sensing reflectance (rrs(λ)) was estimated by a quasi-analytical algorithm (Lee et al. 2002). In order to
model the spectrally dependent reduction of light from a Secchi disk to a human eye (at the surface) with the increase of
depth, the transparent window (tr) and the perceived color (pc) are defined as the wavelengths at which the minimum Kd(λ)
and the maximum rrs(λ) would occur, respectively. With the Kd and rrs evaluated at tr band and pc band, the ZSD was
simulated by a recently developed mechanistic model for underwater visibility (Lee et al. 2015). The overall SA modeling
scheme for ZSD in reservoirs is described in Figure 1.
Sampling location
Sampling time
OAS
concentration
[Chla], [TOC],
[SS]
NOAA
Solar
Calculator
BOMs
Eqs. 1 and 2
θa
IOPs
a(λ)
bb(λ)
c(λ)
Semianalytical
Kd algorithm
Semianalytical
rrs algorithm
AOPs
rrs(λ)
Kd(λ)
Evaluation of
transparency window
and percieved color
Kdtr, rrspc
Analytical ZSD
model
ZSD
Figure 1 A semi-analytical modeling scheme for linking optically active component concentration to ZSD.
Results and Discussion
As shown on Figure 2, the performance of SA approach proposed in this study was compared to empirical methods,
including the best stepwise regression model trained by the entire dataset (n=2,400), and the Carlson’s model. Results
showing that the SA approach has a higher determination coefficient (R2=0.73) than the best stepwise regression model
(R2=0.71) and Carlson’s model (R2=0.07), and provides stronger relationships with the known values particularly when the
ZSD measurements are extremely low and high. Please noted that the empirical part of SA model, e.g., BOMs, were developed
based on 20 to 35 water samples taken from Sun-Moon lake, which are not included in the test dataset.
Figure 2 Comparisons between known ZSD values and ZSD simulated by (a) SA model, (b) the best stepwise regression model,
and (c) Carlson’s regression model.
Conclusions
To facilitate the water quality management in reservoirs, this research encourages the application of SA model in
identifying key optically active component influencing water transparency.
References
Carlson, R.E. (1977) A trophic state index for lakes. Limnol. Oceanogr. 22(2), 361-369.
Lee, Z.P., Carder, K.L. and Arnone, R.A. (2002) Deriving inherent optical properties from water color: a
multiband quasi-analytical algorithm for optically deep waters. Appl. Opt. 41(27), 5755-5772.
Lee, Z.P., Carder, K.L., Mobley, C.D., Steward, R.G. and Patch, J.S. (1998) Hyperspectral remote sensing for
shallow waters. I. A semianalytical model. Appl. Opt. 37(27), 6329-6338.
Lee, Z.P., Du, K.P. and Arnone, R. (2005) A model for the diffuse attenuation coefficient of downwelling
irradiance. J. Geophys. Res.-Oceans 110(C2).
Lee, Z.P., Shang, S.L., Hu, C.M., Du, K.P., Weidemann, A., Hou, W.L., Lin, J.F. and Lin, G. (2015) Secchi disk
depth: A new theory and mechanistic model for underwater visibility. Remote Sens. Environ. 169, 139-149.
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