RETRIEVING SEASONAL SEA SURFACE SALINITY FROM MODIS SATELLITE DATA USING A BOX–JENKINS ALGORITHM Maged Marghany and Mazlan Hashim Institute of Geospatial Science and Technology (INSTeG), UniversitiTeknologi Malaysia 81310 UTM, Skudai, Johor Bahru, Malaysia Emails:
[email protected], :
[email protected] ABSTRACT In this study, we investigate the relative ability of a BoxJenkins algorithm to retrieve sea surface salinity (SSS) from MODIS satellite data. The accuracy of this work has been examined using the root mean square of bias of sea surface salinity retrieved from MODIS satellite data. The study shows comprehensive relationship between Box-Jenkins algorithm, least square method, and in situ SSS measurements with high r2 of 0.98, 0.96 and RMS of bias value of ±0.34 psu, and ±0.32 psu, respectively. Thus, lower RMS of bias value of ± 0.32 psu has performed with BoxJenkins algorithm. In conclusions, Box-Jenkins algorithm can be used to retrieve time series of SSS from MODIS satellite data as compared to least square algorithm. Index Terms — Box-Jenkins algorithm, least square algorithm, MODIS satellite data, Sea surface salinity(SSS). 1. INTRODUCTION Remote sensing technology has been recognized as powerful tool for environmental dynamic studies[1]. Ocean surface salinity is considered as major element in marine environment [2]. The scientists, therefore, have paid a great attention to utilize satellite data for SSS retrieval [1]. Therefore, obtaining SSS from satellite measurements would be greatly helpful to oceanographers and climatologists[3]. 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 [1-5,8]. In this research, we are going to investigate this question that the Box-Jenkins algorithm on the basis of all- inclusive concept, would be an excellent measure of seasonal variation of sea surface salinity from MODIS satellite data. Marghany [2], Marghany [3] and Marghany et al., [4] have implement the least square methods to retrieve SSS
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salinity from MODIS satellite data. Nevertheless, they implemented the similar least square methods coefficient parameters with different season data. Indeed, these parameters must be changed from season to season due to seasonal variation of SSS. On contrary, Salah et al., [9] implemented a fallacious linear regression equation to estimate SSS with RMSE of 1.5 psu. In addition, Salah et al.,[9] have also declared that polynomial algorithm can provide a similar SSS as well as linear regression model. Conversely, that study does not show any output results derived using polynomial algorithm. Continuously, Salah et al., [9] used an erroneous formula to retrieve sea surface salinity in the South China Sea coastal waters, along the coastal water of Semporna. Nevertheless, Semporna does not lie in coastal waters of the South China Sea. They used the in situ data that collected along east coast of Sabah; Semporna, to retrieve seasonal SSS changes in east coast of Peninsular Malaysia. However, Semporna is considered as small bay where any SSS in-situ measurements can not be used to retrieve SSS along east coast of Malaysia due to different physical geography locations and sea surface characteristics. In general, Salah et al. [9] study show contradictory SSS pattern with diametrically opposed formulas. These types of studies provide a confusing and wrong information for SSS retrieving from MODIS satellite data, although in-situ measurements are very costly. We hypothesized that the Box-Jenkins algorithm can be used to retrieve accurate time series of SSS from MODIS satellite data. In this research, we are going to investigate this question that the Box-Jenkins algorithm on the basis of all- inclusive concept, would be an excellent measure of seasonal variation of sea surface salinity from MODIS satellite data. 2. DATA ACQUISITION MODIS data acquired in this study were derived from MODIS/Aqua sensor involved high radiometric sensitivity data in 36 spectral bands (Marghany and Mazlan 2010b).
IGARSS 2011
According to Wong et al., [8] these data were ranged between 0.4 μm to 14.4 μm. In addition, MODIS data have 36 bands: the first two bands are imaged at a nominal resolution of 250 m; the next five bands have nominal resolution of 500 m; and the remain 29 bands particularly have 1 km resolution. Further, MODIS data have 4 levels which are: level 0; 1A; 1B; 2; 3; and 4. Level 0 Raw instrument data at original resolution, time ordered, with duplicate packets removed. Level 1A is a reconstructed unprocessed instrument/payload data at full resolution, any and all communications artefacts (e.g. synchronization frames, communications headers) removed 3. METHODS 3.1. Ground survey Study area is located along the east coast of Penssiular Malaysia as part of the South China Sea (SCS) (Figure 2). According to Marghany [2] the location of the South China Sea (SCS) where it is considered as an equatorial, semienclosed sea with a complex topography that includes large shallow regions [4,5]. The study is conducted in two phases: (i) On September 2002 along the coastal waters of Kuala Terengganu and (ii) on October 2003 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. In situ measuremnts have described in details at Marghany [2,3] and Marghany et al.,[4].
Fig.1. Location of in situ measurements [4]. 3.2. Models Least Square Algorithm: Marghany [2] has derived special formulae that is based on least square algorithm. In this context Maged [9] has assumed that the MODIS image radiance I within multi-channels i have a linear relationship with measured sea surface salinity ( SSS ). According to Marghany et al.,[4] retrieval
SSS MODIS is
estimated using the fitted multiple regression model given
as
2018
^
S S S M O D IS = b1 +
k
^
¦bI i
i
(1)
i= 2
where ^
b = H
−1
h (2) Thus, H is a k x k estimated matrix of MODIS radiance ^
bands that used to estimate sea surface salinity, and b and h are both k x 1 column vectors. where H inverse of the matrix H and
ª¦ SSS j º « » «¦ I 2 j SSS j » h=« » «: » «¦ I SSS » kj j ¼ ¬
−1
denotes the
(2.1)
Box-Jenkins algorithm: Three basic models exist, AR (autoregressive), MA (moving average) and a combined ARMA in addition to the previously specified RD (regular differencing) combine to provide the available tools. When regular differencing is applied together with AR and MA, they are referred to as ARIMA, with the I indicating "integrated" and referencing the differencing procedure[7]. The need for seasonal autoregression (SAR) and seasonal moving average (SMA) parameters is established by examining the autocorrelation and partial autocorrelation patterns of a stationary series at lags that are multiples of the number of periods per season. Seasonal differencing is indicated if the autocorrelations at the seasonal lags do not decrease rapidly. There are essentially three stages to a Box-Jenkins procedure: (i) identifying the tentative model. Which of the three categories listed above is identified as the appropriate category is determined by first making the data stationary (usually by differencing the data) and then analyzing the autocorrelations and partial autocorrelations of the stationary data. Note that there are theoretical autocorrelation and partial autocorrelation profiles for each of the possible models. Therefore, determining the appropriate type of model for a specific situation is mainly a matter of matching the observed correlations to the theoretical correlations. (ii) Determining the parameters of the model. This is similar to estimating the parameters in regression analysis. (iii) Application of the model[7]. Consider a seasonal autoregressive process with n observation per season, and let the only nonzero parameters be those with subscripts that are an integer multiple of n. the retrieval seasonal SSS from MODIS satellite data may be given by (3) SSSt = λ1SSSt−n +λ2SSSt−2n +....... +λpSSSt−ps +εt
where
λi is the seasonal autoregressive parameters, and ε t
is random errors. 4. RESULTS AND DISCUSSION
simulate the time series variation of SSS. The northeast monsoon dominated by onshore lower SSS of 28.00 psu than southwest monsoon period. This confirms the study of Ibrahim et al.,[10].
The sea surface salinity derived modeled from MODIS data using multi-linear regression model is shown in Fig.2. Clearly, the existence model provides fuzzy pattern of sea surface salinity. In early stage, sea surface salinity estimated directly using multi-linear regression model are not accurate with RMS of ± 20.34 psu with r2 of 0.1(Fig. 2b). (a)
(b)
Fig. 3. Time Series of monthly SSS variations are retrieved using Box-Jenkins algorithm.
Fig. 2. Modeled sea surface salinity using (a) multi-linear regression model and (b) regression analysis with in-situ measurements. Fig.3 shows the variation of sea surface salinity during northeast monsoon period that simulated using Box-Jenkins algorithm. It is interesting, to find that Box-Jenkins algorithm able to detect lowest sea surface salinity of 28.00 psu which close to coastline of Malaysia.
Fig.4 and Table 1 show the comprehensive relationship between Box-Jenkins algorithm, least square algorithm, and in situ SSS measurements with high r2 of 0.98, 0.95 and RMS of bias value of ±0.34 psu, and ±0.32 psu, respectively. The least square algorithm, however, has lower performance as compared to Box-Jenkins algorithm. Thus, RMS of bias value of ± 0.32 psu has performed with Box-Jenkins algorithm. (a)
(b)
Fig.4. Regression model between in situ SSS and SSS modeled from MODIS by (a) least square and (b) BoxJenkins algorithms. Table 1: Accuracy of the used algorithms Algorithm Box-Jenkins algorithm Least square algorithm Fig. 3. Sea Surface Salinity (SSS) retrieved using BoxJenkins algorithm during northeast monsoon period. Fig.4 shows the trend of seasonal variations of SSS that was retrieved using Box-Jenkins algorithm during the year of 2003. This indicates that Box-Jenkins algorithm is able to
2019
r2 0.98
RMS (psu) ±0.32
0.96
± 0.34
Box-Jenkins is a procedure which uses a variable's past behavior to select the best forecasting model from a general class of models. It assumes that any time series pattern can be represented by one of three categories of models: (i) Autoregressive models: retrieve of a variable based on linear function of its past values; (ii) Moving Average models: retrieval is based on linear combination of past
errors; and (iii) Autoregressive-Moving Average models: combination of the previous two categories[7]. There is a great contrary between recent study and Salah et al., [9]. Indeed, Salah et al, [9] studies did not derive a real sea surface salinity from MODIS data. Further, they implemented improper equation parameters and wide of the mark of geographical location for in situ measurements as reported on Salah et al., [9]. Crooked field measurements will produce confusing pattern of sea surface salinity. Without a doubt, least square algorithm requires accurate input parameters to be run through MODIS data. 5. CONCLUSIONS In general, this study has demonstrated a new approach for deriving new algorithm to retrieve seasonal variation of sea surface salinity from optical remote sensing satellite data such as MODIS. In doing so, Box-Jenkins algorithm is used to derive a new seasonal SSS algorithm for MODIS satellite data. In conclusion, Box-Jenkins algorithm can be used to retrieve time series of SSS from MODIS satellite data as compared to least square algorithm. 6. REFERENCES [1] Y. H.Ahn, P. Shanmugam, J. E. Moon, and J. H. Ryu, Satellite remote sensing of a low-salinity water plume in the East China Sea. Ann. Geophys., 26, 2019–2035, 2008. [2] M. Marghany, “Linear algorithm for salinity distribution modelling from MODIS data”, Geoscience and Remote Sensing Symposium, 2009 IEEE International, IGARSS 2009, Vol.,3. pp: III-365 - III-368,2009. [3] M. Marghany, ”Examining the Least Square Method to Retrieve Sea Surface Salinity from MODIS Satellite Data”. Eur. J. of Sci. Res. 40 (30),377-386,2010. [4] M. Marghany, H. Mazlan and A.P. Cracknell, “Modelling Sea Surface Salinity from MODIS Satellite Data”. Lecture Notes in Computer Science, 2010, Vol. (6016), Computational Science and Its Applications – ICCSA 2010, P 545-556,2010. [5] M. Marghany and H. Mazlan. “MODIS Satellite data for modeling chlorophyll-a concentrations in Malaysian coastal waters. Int. J. of Phys. Sci. 5(10), 1489-1495,2010. [6] C.Z. Hu, T. Chen, P. Clayton, J. Swarnzenski, I. Brock, and F.Muller-Karger, “Assessment of estuarine water-quality indicators using MODIS medium-resolution bands: Initial results from Tampa Bay, fL” Remote Sensing of Environment, 93:423-441,2004. [7] G. E. P.Box,G.M. Jenkins, and G.C. Reinsel, Time Series Analysis, Forecasting and Control, 3rd ed. Prentice Hall, Englewood Clifs, NJ,1994. [8] M.S.Wong,L. Kwan, J.K.Young, J. Nichol, L. Zhangging , N. Emerson, “Modelling of Suspendid Solids and Sea Surface Salinity in Hong Kong using Aqua/ MODIS Satellite Images”. Kor. J. of Rem. Sens. 23 (3):161-169, 2007. [9] T.D. Salah, M.Shattri, A.M. Rodzi, S. Pirasteh, “Monitoring sea surface salinity season variation from MODIS satellite data”. Geoscience and Remote Sensing Symposium (IGARSS), 2010 IEEE International IGARSS 2010, 25-30 July 2010, Honolulu, USA, 628-631.2010.
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[10] Z.Z. Ibrahim, A. Arshad, S.C. Lee, S.B. Japar, A. T. Law, Nik Mustapha, and M. M. Marghany, “East Coast of Peninsular Malaysia”. In: Seas at The Millennium: An Environmental Evaluation. Charles Sheppard (ed.). Elsevier Science LTD London, UK, 2000.