Modelling Sea Surface Salinity from MODIS ... - Semantic Scholar

Modelling Sea Surface Salinity from MODIS Satellite Data Maged Marghany, Mazlan Hashim, and Arthur P. Cracknell Institute of Geospatial Science and Technology (INSTEG) Universiti Teknologi Malaysia 81310 UTM, Skudai, Johore Bahru, Malaysia [email protected] [email protected]

Abstract. In this study, we investigate the relative ability of least square algorithm to retrieve sea surface salinity (SSS) from MODIS satellite data. We also examine with comprehensive comparison of the root mean square of bias the difference between second polynomial order algorithm and least square algorithm. Both the least squares algorithm and second polynomial order algorithm are used to retrieve the sea surface salinity (SSS) from multi MODIS bands data. Thus, the basic linear model has been solved by using second polynomial order algorithm and least square estimators. The accuracy of this work has been examined using the root mean square of bias of sea surface salinity retrieved from MODIS satellite data and the in situ measurements that are collected along the east coast of Peninsular Malaysia by using hydrolab instrument. The study shows comprehensive relationship between least square method and in situ SSS measurements with high r2 of 0.96 and RMS of bias value of ±0.37 psu. The second polynomial order algorithm, however, has lower performance as compared to least square algorithm. Thus, RMS of bias value of ± 7.34 psu has performed with second polynomial order algorithm. In conclusions, the least square algorithm can be used to retrieve SSS from MODIS satellite data. Keywords: least square algorithm, second polynomial order algorithm, MODIS Satellite Data, Sea surface salinity.

1 Introduction Remote sensing technology has been recognized as powerful tool for environmental dynamic studies. Ocean surface salinity is considered as major element in marine environment. In fact, the climate change, marine pollution and coastal hazardous are basically controlled by the dramatic changes in sea surface salinity (SSS) [2,5]. From an oceanographic viewpoint, salinity is important because together with temperature, it determines water density and thus is intimately linked to the horizontal circulation of the ocean. It also determines the depth to which water, cooled at the surface in winter, can sink. Through its effect on density, it partially controls the stability of the upper mixed layer of the ocean. This in turn has important physical and ecological consequences. Furthermore, it is one of the prime determinants of the environment in D. Taniar et al. (Eds.): ICCSA 2010, Part I, LNCS 6016, pp. 545–556, 2010. © Springer-Verlag Berlin Heidelberg 2010

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M. Marghany, M. Hashim, and A.P. Cracknell

which fish and other marine life live and modulates air-sea interaction including gas and heat exchange [8]. The conventional method for ocean salinity measurements that acquired by buoys and oceanographic or commercial ships, remain sparse and irregular, with large parts of the global ocean never sampled. In addition, weather conditions can be play tremendous role in achieving the collection of in situ measurements. In these circumstances, scientists have paid a great attention to utilize satellite data for SSS retrieval [2-4,6,10]. Therefore, acquiring SSS from satellite measurements would be greatly useful to oceanographers and climatologists. Radiometric accuracy and sensitivity depend on the position of the pixel in the field of view [4]. In this context, standard mathematical algorithms are required. Previous empirical research provides conclusive evidence on utilizing mathematical algorithm such as least square algorithm to acquire comprehensive and accurately pattern of sea surface salinity (SSS) from different remote sensing sensor i.e. passive and active sensors [11-14]. In this research, we are going to investigate this question that least square algorithm on the basis of all- inclusive concept, would be a better measure of sea surface salinity from MODIS satellite data.

2 Previous Research Scientists have made use of the active passive microwave sensors for acquiring sea surface salinity. Particularly, advances in microwave remote sensing enable precise measurements of the brightness temperature of seawater at L-band ( 1.4 GHz) to be acquired over coastal regions from a light aircraft, whereas the Soil Moisture and Ocean Salinity (SMOS) and Aquarius satellite missions are provided a similar capability over the deep global oceans [6,10]. Modern airborne L-band microwave radiometers therefore, are sensitive enough to detect brightness temperature variations at better than 0.5-K precision under operational conditions, at typical spatial resolutions of 1 km, whereas satellite-borne systems are being designed to provide effective 0.1K precision, after data averaging, on spatial scales of about 100–300 km [2]. In fact, scientists have found that SSS retrieval is function of brightness temperature variations. According to Ellison et al.,[4] the relationship between brightness temperature, sea surface salinity (SSS), sea surface temperature, incidence angle, and antenna polarization for a flat calm sea can be obtained from the so-called “flat sea” empirical emissivity model relationships. Indeed, The brightness temperature at the surface brightness temperature is proportional to the sea surface temperature and the emissivity. Further, Sonia et al., [12] estimated SSS on a global scale, with a precision over the open ocean of 0.2 practical salinity units (psu) in 200 × 200 km boxes on a tenday average. They, therefore, reported that the remotely sensed SSS should be appropriate for assimilation into ocean circulation models which is based on global ocean data assimilation experiment. In the case of SMOS, this precision would achieve by averaging numerous salinity retrievals, as every region of the global ocean can be visited by SMOS at least once every three days. Generally, monitoring surface brightness temperatures, however, from L-band satellite radiometric measurements is particularly challenging because of their limited resolution (typically 30–100 km) and L-band measurements over the coastal ocean are contaminated by the nearby land. In fact, recent global simulations of L-band land brightness temperatures showed a range of about 140 K to 300 K, compared to approximately 100 K for the ocean [6].

Modelling Sea Surface Salinity from MODIS Satellite Data

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Researchers have found that dissolved salts, suspended substances have a major impacts on the electromagnetic radiation attenuation outside the visible spectra range [14]. In this context, the electromagnetic wavelength larger than 700 nm is increasingly absorbed whereas the wavelength less than 300 nm is scattered by nonabsorbing particles such as zooplankton, suspended sediments and dissolved salts [1]. Recently, Ahn et al., [1] and Palacios et al., [13] have derived SSS using colored dissolved organic matter, (aCDOM) from optical satellite data. Ahn et al., [1] have developed robust and proper regional algorithms from large in-situ measurements of apparent and inherent optical properties (i.e. remote sensing reflectance, Rrs, and absorption coefficient of colored dissolved organic matter, aCDOM) to derive salinity using SeaWiFS images. Further, Palacios et al., [13] stated that light absorption by chromophoric dissolved organic matter (a CDOM) is inversely proportional to salinity and linear because of conservative mixing of CDOM rich terrestrial runoff with surrounding ocean water. In this context, Ahn et al., [1] established the robust algorithm based on the absorption coefficients of CDOM, in-situ measurements of salinity that made at 400 nm, 412 nm, 443 nm and 490 nm. Similarly, Palacios et al.,[13] developed synthetic salinity algorithm simple linear (salinity versus a CDOM) and multiple linear (salinity and temperature versus a CDOM) algorithms were applied to MODIS 250 m resolution data layers of sea surface temperature and absorption by colored dissolved and detritus matter (a CDM) estimated at 350 nm and 412 nm from the Garver Siegel Maritorena model version 1 algorithm. Ahn et al., [1] found that 2 the CDOM absorption at 400 nm was better inversely correlated (r =0.86) with salin2 ity than at 412 nm, 443 nm and 490 nm (r =0.85–0.66), and this correlation corre2 sponded best with an exponential (r =0.98) rather than a linear function of salinity measured in a variety of water types from this and other regions. In this context, Palacios et al., [13] stated that light absorption by chromophoric dissolved organic matter (a CDOM) is inversely proportional to salinity and linear because of conservative mixing of CDOM rich terrestrial runoff with surrounding ocean water using MODIS satellite data. The study of Palacios et al., [13] showed high correlation using MODIS during both downwelling (simple, β 1 = 0.95 and r2 = 0.89; multiple, β 1 = 0.92 and r2 = 0.89) and upwelling periods (simple, β 1 = 1.26 and r2 = 0.85; multiple, β 1 = 1.10 and r2 = 0.87) using the 412 nm data layer. Both studies of Ahn et al., [1] and Palacios et al., [13] have agreed that SSS can be derived using optical satellite data based on absorption coefficient of colored dissolved organic matter, aCDOM.

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3 Methodology 3.1 In Situ Measurements The in situ measurement cruises are conducted in two phases: (i) September 2002 which is along the coastal waters of Kuala Terengganu and (ii) October 2003 which is in Phang coastal waters, Malaysia (Fig. 1). In doing so, more than 100 sampling locations are chosen (Fig. 1). The field cruises are conducted separately, area by area on the east coast of Peninsular Malaysia. In fact, it is major challenge to cover a large scale area over than 700 km2 in short period using conventional techniques. The hydrolab equipment is used to acquire vertical water salinity profiles (Fig. 2). Every

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field cruise has been conducted on 6 days in the east coast of Malaysia. For this study the in situ surface salinity (1 meter below sea surface) data are used. In fact, it is expected to have a higher correlation with MODIS reflectance data than middle and bottom salinity column measurements. These data are used to validate the sea surface salinity distributions that derived from MODIS data. In situ measurements are collected near real time of MODIS satellite data overpass. Twenty four sets of Aqua/MODIS level 1 B images are acquired during the in situ salinity measurements.

Fig. 1. Sampling Locations

Fig. 2. Hydrolab equipment is used in this study

3.2 Deriving Sea Surface Salinity Algorithm from MODIS Data The relationship between in situ sea surface salinity (SSS) and radiance in different bands of MODIS can be described by the multiple regression as follows [9,14]

SSS = b0 + b1 I1 + b2 I 2 + b3 I 3 + ............ + b7 I 7 + ε

(1)

Equation 1 can be written as k

SSSi = b0 + ∑ bi I ij + ε i j

(2)

i =1

SSSi is the measured sea surface salinity, b0 and bi are constant coefficient of linear relationship between MODIS radiance data I within multi-channels i and where


in situ sea surface salinity, k= 1,2,3,………..,7 and

ε is residual

error of SSS esti-

mated from selected MODIS bands. The unknown parameters in Eq.2, that are and

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b0

bi may be estimated by a general least square iterative algorithm. This proce-

dures requires certain assumptions about the model error component ε . Stated simply, we assume that the errors are uncorrelated and their variance is σ ε . 2

The least-square estimator of the SE =

bi minimizes the sum of squares of the errors, say

k

∑

( SSS

j =1

i

− b0 −

k

∑

i =1

b i I ij ) 2 =

k

∑

ε

j =1

2

(3)

j

It is necessary that the least squares estimators satisfy the equations given by the k first partial derivatives

∂S E = 0 . Therefore, differentiating Eq. 3 with respect to bi ∂bi

and equating the result to zero we obtain ^

^

k

kb 1 + ( ∑ I ) b 2 j =1

2j

^

k

k

^

k

^

k

+ ( ∑ I 3 j ) b + ... + ( ∑ I 7 j ) b = 3 7 j =1 j =1 ^

^

k

k

∑ SSS j =1

j

k

( ∑ I 2 j ) b + ( ∑ I 2 2 j ) b + ... + ( ∑ I 2 j I 7 j ) b = ∑ I 2 j SSS 1 2 7 j =1 j =1 j =1 j =1 ………………………………………………………………. k

^

k

^

^

k

(∑ I 7 j ) b + (∑ I 7 j I 2 j ) b + ... + (∑ I 1 2 j =1 j =1 j =1

2

7j

k

) b = ∑ I 7 SSS 7 j =1

The equations (4) are called the least-squares normal equations. The

(4) ^

bi found

solving the normal equations (4) are least-squares estimators of the parameters

by

bi .

The only convenient way to express the solution to the normal equations is in matrix notation. Note that the normal equations (4) are just a I x I set of simultaneous linear ^ equations in unknowns the parameter b . They may be written in matrix notation as i

^

Ib i where

= g

(5)

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and

Thus, I is a 7 x 7 estimated matrix of MODIS radiance bands that used to estimate ^ sea surface salinity, and b and g are both 7 x 1 column vectors. The solution to the i

least-squares normal equation is ^

bi

= I

−1

g

(6)

where I-1 denotes the inverse of the matrix I. Using equation 6 to express into equation 2, then, the sea surface salinity SSS is given as

SSS

i

= I 0−1 g 0 +

7

∑

i =1

I i−1 g i I i + ε

(7)

Then, the empirical formula of SSS (psu) which is based on equations 6 and 7 is

SSS (psu) =27.65 + 0.2 I1 - 21.11 I 2 + 14.23 I 3 + 62.12 I 4 + 148.32 I 5 + 1.22.03

I 6 + - 11.41 I 7 + ε

(8)

In this study, polynomial regression algorithm is also examined to retrieve SSS from MODIS satellite data. In this context, SSS is estimated using the multiple regression models in Eq. 1 can be also made up of powers several variables

SSSPol = β0 + β1(SSS) + β2 (SSS )2 + ...... + βn (SSS)n + ε pol

(9)

where SSS is retrieval sea surface salinity from MODIS data using Eq.1, while SSS Pol is sea surface salinity estimated using polynomial regression algorithm and

ε pol is

residual error of SSS Pol estimated. In addition, β0 and β1 , β 2 ,............, β n

are unknown parameters that are calculated using polynomial regression algorithm


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with degree of n. In this study, quadratic model, in two variables SSS and SSSi is given by

SSS Pol = β 0 + β1 ( SSS ) + β 2 ( SSS )( SSSi ) +

β3 ( SSS )( SSSi ) + β 4 ( SSS ) 2 + β5 ( SSSi ) 2 + ε p

(10)

In Eq.10 the variable SSS , SSSi is the interaction between SSS and SSSi . In Fact, a variable that is the product of two others variables is called an interaction. 3.2 Accuracy Estimation Following Sonia et al., [12], ε errors that represents the difference between retrieved and in situ SSS are computed within 10 km grid point interval and then averaged over all grid points having the same range of distance to coast, where the bias ε on the retrieved SSSi is given by: N

ε =

∑

i =1

(SSS i/

pol

− SSS

s itu

) (11)

N

where SSS i / pol is the retrieved sea surface salinity from MODIS satellite data using least square and polynomial regression algorithms, respectively. Further,

SSS situ is

the reference sea surface salinity on grid point i and N is the number of grid points. Finally, root mean square of bias (RMS) is used to determine the level of algorithm accuracy by comparing with in situ sea surface salinity. Further, linear regression model used to investigate the level of linearity of sea surface salinity estimation from MODIS data. The root mean square of bias equals

RM S = [N

−1

N

∑

i =1

( S S S i / p o l − S S S s i tu ) 2 ] 0 .5

(12)

The time integrations is performed to determine the possible improvement of RMS. In doing so, simulations and retrievals were performed within a two-month period and for each grid point, the retrieved SSS was averaged over six days during the MODIS satellite passes.

4 Simulation Results 4.1 Results of in Situ Measurements The salinity water distribution patterns are presented in 2D and 3D plots that have been derived from in situ measurements are illustrated in Figs. 3 and 4. The typical water salinity distributions during the inter-monsoon period of September 2002 of the South China Sea are shown in Figs 3a and 3b, respectively.

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(a)

(b)

Fig. 3. In situ measurements during September 2002 (a) 2D sea surface distribution and (b) 3D salinity pattern variations

(a)

(b)

Fig. 4. In situ measurements during October 2003 (a) 2D sea surface distribution and (b) 3D salinity pattern variations

In September 2002, both 2D and 3D plots show that the water salinity ranges between 28.5 to 33.6 psu (Figs. 3a and 3b) whereas in October 2003, the water salinity ranges between 29.5 to 33.0 psu (Fig. 4). Both Figs 3a and 4a show the onshore waters salinity are lower than offshore. In this context, Figs 3a and Fig.3b are agreed that the onshore water salinity is ranged between 28.5 to 30 psu during September 2002. In October 2003, however, the onshore water salinity is ranged between 29.5 to 31.0 psu (Fig 4). It is clear that the offshore water salinity is higher than onshore within constant value of 33.5 psu in September 2002 and October 2003, respectively. Further, both September 2002 and October 2003 dominated by tongue of low water salinity penetration of 28.5 and 29.5 psu, respectively along the coastal water. This agrees with the studies of Wrytki, [15]; Zelina et al. [16]; Maged and Mazlan [9].


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4.2 Simulation Results from MODIS Data The sea surface salinity retrieved from MODIS data in September 2002 and October 2003, respectively is shown in Fig. 5. It is observed that the offshore water salinity is higher than onshore. The homogenous offshore water salinity pattern occurred in both September 2002 and October 2003 with maximum salinity value of 33.00 psu and 33.8 psu, respectively. The retrieval SSS patterns from MODIS data confirm the occurrences of tongue of low water salinity penetration along the east coast of Peninsular Malaysia. This may be attributed to the proximity of nearshore waters are close to the rivers such as Kuala Terngganu and Pahang Rivers. The maximum amount of rainfall in the September 2002 and October 2003 are 150 and 300 mm, respectively. This high amount of rainfall is not only dilute the salinity of the surface water but also cause a high amount of fresh water discharges from the rivers are located along the east coast of Malaysian waters into the South China Sea. This confirms the studies of Maged and Mazlan [9]; Maged et al., [8]; Maged and Hussin [7].

(a)

(b) Fig. 5. Sea surface salinity estimated from MODIS data (a) September 2002 and (b) October 2003

4.3 Model Validation Fig. 6 shows the comparison between in situ sea surface salinity measurements and SSS modeled from MODIS data. The blue color exists in Fig.6 is represented sample points of regression. Therefore, regression model shows that SSS modeled by equation 8 is in good agreement with in situ data measurements. The degree of correlation

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is a function of r2, probability (p) and root mean square of bias (RMS). The relationship between estimated SSS from MODIS data and in situ data shows positive correlation as r2 value is 0.96 with p