Water depth determination from satellite data
- Optical Model
A number of models can bc used. However, The model of polcyunnd lycu (1975) is considered here. This model is as follows:
R = Rp + ta Rg + ta Ri rb -------(1/n2)exp {-a(secd + Sec ds)|z|-----------------(4)
where
R= radiance at the detector
Rp= atmospheric path radiance
R1= radiance on the sea surface
Rg= radiance from the sea surface
N1= telleetance of the scabed
ta =transmittance of the column of atmosphere below the satellile
a= allennation coffielent of light in water
n= refraetive index of water (approx. 1.33 ).
d'= apparent angle of observation under the water
d's= apparent solar zenith water
Z= depth of water
Case study - penang lsland
A study was carried out on the coastal waters of Penang island using the landsat 3 Multispectral Seanner (MSS) data. The study area is shown in Figure 2. The turage was acqured on 10 January 1979 at about 02:52 hours GMT by the landsat 3 MSS when the hright of the tide was 1.6 in above lowest astronomical tide. Geometrical recttication. Depth used and some results that were abtatned are presented.
- Geometrical rcctification and depth algorithms
- Geometrical rectification
The sub-scene used in the study was geometrically rectified to enable quantllative comparison to be made between the remotely -sensed image and existing maps and charts. The following relationship was used for this pumpose. Where E is the Easting (Longitude), N is the Northing (Lattude). S is the scantiar number and I is the column or plxcl number on the CCT.
P=C1+C2E+C3N+C4E2+C5EN +C6N2 -----------------(5)
P=C7+C8E+C9N+C10E2+C11 EN+C12N2 ---------------(6)
The coordinates of ground control points (gcps) which are well delined on the image were used to determine the values of the coefficients c1 .C2……C12 in these equations between 10 and 30 points were used to perform a least - squares fit to obialn the best values of the coafficients .
- Method of depth determination and depth algorithms
For the remotely -sensed data used in the study. pixel intensittes (digital numbers) were extracted at some points of known depth (calibration depths) in order to algonthus relating plxcl intensitles to the dept. The pixel intensities at these alienation depths were obtained by transforming the geographical positions of these points into scanline and pixcl number (column number) by using equations (5) and (6) and subsequently using computer programs to read the inteusllies in telesant hands at these values of scanline and pixel number, A least squanes mintulsation was carried out relating plxcl intensllies to depth to obtain the best valuers of the unknown coefficients in the algorithms used. Having determined the coefficients. The depth at any point on the particular hange can be obtained by using the values of these covert ion and the plxcl intensely values at this point from the relevant bands.
Ashnple algortlun based on the model described by equreton (1) was used.
1 = A1+A2 exp A3Z -------------------(7)
Equation (7) can usefully he expressed in the allernative form as below
Z = (1/A3[In A2 - In (A1)]-------------------(8)
These equations express the expected exponential relationship between pixel intenslly, I and depth, Z A1 A2 and A 3 are the unknown ceficients.
