Chapter 2 Water quality monitoring using remotely sensed data
2.3 Retrieval of reflectance
Mobley (1994) described the optical properties of natural water are conveniently divided into two mutually exclusive classes: inherent and apparent. Inherent optical properties (IOP’s) are those properties that are independent of the ambient light field.
The two fundamental IOP’s are the absorption coefficient and the volume scattering function which can quantitatively describe the solar radiance transfer process.
Apparent optical properties (AOP’s) are those properties that depend both on the medium and on the geometric structure of the ambient light field, and that display enough regular features and stability to be useful descriptors of the water body. The spectral remote-sensing reflectance is one of the most important AOP. The spectral remote-sensing reflectance, hereafter which is short as reflectance, is used to construct the experience model in this study.
In satellite remote sensing application, the major paths of solar radiation reaching the sensor are depicted in Figure 2-6. The primary solar radiance (path I) accounts for the solar irradiance onto the target object, and then reflected back to the atmosphere, and finally arrives at the sensor. The downwelled solar radiance (path II) is the atmospheric scattered solar radiance incident on and reflected away from the target object before reaching the sensor. The upwelled solar radiance (path III) is the radiance scattered by the atmosphere and directly reaching the sensor without getting
Figure 2-2 Study area in northern Taiwan (The numbers represent the sample sites).
Figure 2-3 The radiometric control area (RCA).
Taiwan
Study Area
2 3
4 5 8 7
Yin-Yang Sea 1 6
Tunnel Outlet RCA
Approximate sampling locations
0
Total suspended solids Chlorophyll-a concentration Figure 2-4 Box plots of water quality data of no-diversion and post-diversion periods.
No-diversion Post-diversion No-diversion Post-diversion
No-diversion Post-diversion No-diversion Post-diversion
SDD (m) Tb (NTU)
TSS (mg/L) Chla (μg/L)
-1.00 0.00 1.00 2.00 3.00 4.00
-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 Ln(Tb)
Ln(TSS)
-1.00 0.00 1.00 2.00 3.00 4.00
-1.00 0.00 1.00 2.00 3.00
Ln(SDD)
Ln(Tb)
-1.00 0.00 1.00 2.00 3.00 4.00
-1.00 0.00 1.00 2.00 3.00
Ln(SDD)
Ln(TSS)
Figure 2-5 Empirical relationships among different water quality parameters (a)Tb vs. TSS (b) SDD vs. Tb(c) SDD vs. TSS.
(c) (a)
(b)
Table 2-2 Methods of water quality analysis.
Water quality variable Methods Unit
Chlorophyll-a conc. NIEA E508.00B μg/L
Turbidity NIEA W219.52C NTU
Secchi disk depth NIEA W221.50A m
Total suspended solid NIEA W210.57A 1030C-1050C mg/L Table 2-3 Dates of water sampling and SPOT image acquisition.
Sampling
10/08/2007 NAa Typhoon Krosab
(10/4~10/7) 16,133,400
11/14/2007 NAa No storm 0
aSatellite images were not collected due to high percentage of cloud cover.
bFlow diversion activated.
Table 2-4 Statistical properties of water quality variables.
Mean Standard
deviation Maximum Minimum
Secchi disk depth (m) 5.40 2.13 10.30 0.50
Turbidity (NTU) 2.20 4.22 29.50 0.38
Total suspended solid (mg/L) 4.36 4.97 28.00 0.40
Chlorophyll-a conc. (μg/L) 0.79 0.69 2.67 0.00
Total number of samples: 61
in contact with the target object.
Mobley (1994) defined the spectral remote-sensing reflectance, in this study is called reflectance, as the water-leaving radiance divided by irradiance onto water surface. Spectral remote-sensing reflectance, which is abbreviated as reflectance in this study, is presented as:
( ) ( )
L = the water-leaving radiance
θ = view angle in sensor-target direction φ = sensor azimuth angle Z
φS =sun azimuth angle σ = the sun angle
E = the solar irradiance reaching water surface λ = wavelength in μm.
The amount of solar radiance reaching the satellite sensor can be expressed as:
(
θ,φZ,λ) (
θ,φS,φZ,σ,λ) ( )
τ2 λ u(
θ,φZ,λ)
S L L
L = ⋅ + (2-3)
where τ2 is the atmospheric transmittance along the target-sensor path and L is u upwelled solar radiance ( also known as path radiance). The water-leaving radiance can further expressed as:
(
θ,φS,φZ,σ,λ)
=ETop= the exoatmospheric solar irradiance
τ1 = the atmospheric transmittance along the sun-target path ED = the downwelled irradiance from the sky dome onto the target
F = the obstruction factor.
The obstruction factor in equation (2-4) accounts for the proportion of irradiance that may be obstructed by adjacent objects or surface slope of the target. If the target object is on a horizontal surface and free of adjacent object obstruction, the factor F equals 1. It is also worthy to note that the sun and view angles are defined with reference to the normal of the target surface. If the target is located on a slope, the sun and view angles will need to be adjusted accordingly. Readers are referred to Schott (1997) for detailed calculation of solar radiances arriving at the sensor.
The reflectance Rrs
(
θ,φS,φZ,σ,λ)
varies with spectral wavelength and orientation angles. If the target object is assumed to be a diffuse reflector with a constant reflectance Rrs( )
λ in all directions, we then have(
θ,φZ,λ)
=LS
(
ETop ⋅τ1( )
λ ⋅cosσ +F⋅ED( )
λ)
⋅ Rrsπ( ) ( )
λ ⋅λ2 λ(
θ,φZ,λ)
Lu
+
(2-5)
On the right hand side of the above equation, only the reflectance Rrs
( )
λ represents the physical property of the target surface. The upwelled radiance Lu does not even get into contact with the target.Environmental monitoring using remote sensing images often requires derivation of physical properties (reflectance, for example) of the target objects from satellite images. Unfortunately, the upwelled radianceLu, the atmospheric transmittance τ1 andτ2, the downwelled irradianceED, and the exoatmospheric solar irradiance ETop
are generally not available for most applications, and we have to resort to other means for estimation of the reflectance.
For most local-scale environmental monitoring applications,Lu,τ1,τ2,ED, and
Figure 2-6 Major paths of solar radiation reaching the satellite sensor. The target object is assumed to be on a horizontal plane.
Sun Sensor
Sky dome above the target object
Target object North φS
φZ
θ σ
I: Primary solar radiance III I II
II: Downwelled solar radiance III: Upwelled solar radiance ETop
ETop can be assumed constant (or spatially invariant) within the study area. While on the contrary, the sun angle σ and the obstruction factor F are dependent on the surface slope of the target, and the reflectance Rrs
( )
λ is dependent on surface cover of the earth. Their values may vary from pixel to pixel within a scene. If only pixels on horizontal surface and free of adjacent obstruction are considered (F = 1), Equation (2-5) may be expressed as:(
θ,φZ,λ)
= remote sensing is the dark object subtraction (DOS) method (Chavez, 1988; Cheng and Lei, 2001; Teng et al., 2008). The basic concept of the DOS method is to identify very dark features within the scene. The minimum scene radiance is set to be the upwelled radiance based on the assumption that it represents the radiance from a pixel with near zero reflectance. If the minimum scene radiance is subtracted from the radiance of each individual pixel, the processed image is then assumed free of atmospheric scattering effect.reflectance estimation scheme through reflectance calibration in a radiometric control area (RCA).
In this study a radiometric control area of approximately 30 m × 60 m was chosen for spectral reflectance calibration. The RCA is a horizontal paved open area with homogeneous and stationary surface reflectance and no adjacent obstruction (see Figure 2-3). It is located in a restricted and free of public access harbor area. The wavelength-depended surface reflectance of RCA is then calibrated using a variable spectral radiometer (VSR) which is equipped with two spectral-variable filters capable of detecting spectral radiances in various 7 nm-wide windows within the 0.40 – 0.72 μm and 0.65 – 1.1 μm ranges respectively (Figure 2-7). The VSR was moved around within the radiometric control area taking multispectral images. When taking images within the RCA, a standard reflectance disk which has been pre-calibrated to have RrsDisk
( )
λ ≈1 over the 0.25 – 1.1 μm wavelength range was also placed within the viewing area. Reflectance of the radiometric control area is then calculated as the ratio of average radiance from RCA to average radiance from the standard reflectance disk, i.e.:( )
λ Disk rsDisk( )
λS RCA RCA S
rs R
L
R = L ⋅ (2-8)
where RrsRCA
( )
λ is the reflectance of RCA, andLRCAS andLDiskS are respectively average radiances received at VSR sensor from the RCA surface and from the standard reflectance disk. For RCA reflectance calibration, the effect of upwelled radiance can be neglected since the VSR is placed near the ground surface. Table 2-5 lists measurements of surface reflectance in the radiometric control area and area average reflectance with respect to various spectral wavelengths are also shown inFigure 2-8. The RCA-average reflectance corresponding to green, red and near infrared SPOT spectral bands (hereafter referred to as the RCA band reflectances) are calculated to be 0.097, 0.113, and 0.161%, respectively. The RCA band reflectances are considered constant since the land surface condition within the RCA is relatively homogeneous and stationary.
Assuming the sea surface is horizontal, the DOS-adjusted radiances of a pixel A in the RCA and a pixel B on the sea surface are respectively expressed by:
(
θ φZ λ)
rsA( )
λ respectively. Combining Equation (2-9) and Equation (2-10) and rewriting the reflectance of sea surface pixel B as:( ) ( )
radiance and reflectance of RCA, and( ) ( )
LS represents the average value of DOS-adjusted radiances within RCA and RrsRCA
( )
λ is the RCA band reflectance. The reflectance calibration ratio( )
varies due to scene variations in orientation angles and atmospheric transmittance.
Table 2-6 summarizes reflectance calibration ratios of individual SPOT multispectral images.