Evaluation of Maximum Likelihood Estimation and regression methods for fusion of multiple satellite Aerosol Optical Depth data over Vietnam44871

978-1-7281-3003-3/19/$31.00 ©2019 IEEE Evaluation of Maximum Likelihood Estimation and regression methods for fusion of multiple satellite Aerosol Optical Depth data over Vietnam Pha

978-1-7281-3003-3/19/$31.00 ©2019 IEEE

Evaluation of Maximum Likelihood

Estimation and regression methods for fusion

of multiple satellite Aerosol Optical Depth

data over Vietnam Pham Van Ha

Center of Multidisciplinary

Integrated Technology for Field

Monitoring

University of Engineering and

Technology, VNUH

Hanoi, Vietnam

hapv@fimo.edu.vn

Ngo Xuan Truong

Center of Multidisciplinary Integrated Technology for Field

Monitoring University of Engineering and Technology, VNUH

Hanoi, Vietnam truongnx@fimo.edu.vn

Dominique Laffly

University Toulouse II Jean Jaurès,

UT2J

Toulouse, France dominique.laffly@univ-tlse2.fr

Astrid Jourdan

Ecole Internationale des Sciences du Traitement de l'Information,EISTI

Pau, France aj@eisti.eu

Nguyen Thi Nhat Thanh

Center of Multidisciplinary Integrated Technology for Field Monitoring University of Engineering and Technology, VNUH

Hanoi, Vietnam thanhntn@fimo.edu.vn

Abstract—This paper applied different data fusion

methods including Maximum Likelihood Estimation

(MLE) and Linear Regression methods on satellite

images over Vietnam areas from Moderate Resolution

Imaging Spectroradiometer (MODIS) and Visible

Infrared Imaging Radiometer Suite (VIIRS) sensors In

comparison with ground station Aerosol Robotic

Network (AERONET), the regression method is better

than Maximum Likelihood Estimator (MLE) Our results

show that the fusion methods can improve both data

coverage and quality of satellite aerosol optical depth

(AOD) Strong correlations were observed between fused

AOD and AERONET AOD (R 2 = 0.8118, 0.7511 for Terra

regression and MLE method, respectively) This paper

presented the evaluation of data fusion algorithm and

highlighted its importance on the satellite AOD data

coverage and quality methods from multiple sensors

Keywords— data fusion, regression, Maximum

Likelihood Estimation, Vietnam, satellite images

I INTRODUCTION Aerosols are the liquid droplets or solid particles

which present in air as fog or smoke It may have

complex effects on clouds and precipitation, air quality

and public health [1] Aerosol Optical Thickness (AOT)

or Aerosol Optical Depth (AOD) is the amount of

aerosol present in the atmosphere AOD has been used

in air quality monitoring application in multiple scale

[2]–[7]

AOD observations can be grouped into two broad

kinds: in situ measurements and satellite remote

sensing Although very useful, in situ measurements are

limited both in time and space Satellites are increasingly used to obtain AOD, taking advantage of technical and scientific developments over the last decades However, satellite AOD data also has its own disadvantages such as coarse temporal frequency, cloud contamination and moderate quality Especially, the high cloud coverage over tropical area such as Southeast Asia has a significant impact on monitoring satellite data in these regions A previous study of Lasko [8] show that the highest cloud cover was observed in Vietnam (monthly average was 72.4%) Therefore, a fusion of multisource satellite AOD data can be an effective solution

AOD can be observed from many different satellites, including MODIS sensor on MODIS Aqua / Terra satellite and VIIRS sensor on Suomi-NPP satellite The Moderate Resolution Imaging Spectroradiometer (MODIS) sensor was launched in

1999 on the Terra satellite and Aqua satellite in 2002 [9] The swath width of MODIS sensor is about 2330

km and orbits cycle is 16 days The MODIS aerosol retrieval algorithm is comprised of two different algorithm including Dark Target and Deep Blue The Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-Orbiting Partnership (Suomi NPP) satellite was launched in October 2011 as a successor to MODIS sensor VIIRS aerosol retrievals are made at 550 nm which can measure both Angstrom Exponent and aerosol type [10]

In remote sensing and satellite imagery research area, data fusion is defined as data combination of

various satellite images The fusion methods are utilized

including optimum interpolation [11]–[13], polynomial

functions [14], weighted or arithmetic average, least

squares and Maximum Likelihood Estimation [15]–

[17]

The maximum likelihood estimator (MLE) is one of

the most widely used methods in statistical inference

MLE is used to estimate the parameter value of a

probability model based on observed data by

maximizing likelihood function In data fusion area,

different statistics information were used for fusing

AOD data [17]

Linear regression analysis is a method of analyzing

the relationship between the response variable and one

or more predictor variables The model parameters are

estimated from data based on the ordinary least squares

(OLS) method Many previous studies used linear

regression methods to integrate AOD data [18]–[20]

In this paper, we integrate MODIS Terra/Aqua

satellite aerosol datasets in Vietnam region using two

different methods: Maximum Likelihood Estimation

(MLE) and linear regression The research questions are

raised as follows: What is the effective data fusion

method which enhances quality, data coverage of

satellite aerosol data over Vietnam area? The research

area and datasets are shown in the next part The

methodology is presented in section III Section IV

presents the experimental including the assessment of

data coverage and data quality of original data and fused

data Finally, the conclusion is illustrated in section V

II STUDY AREA AND DATASETS

The study area is showed in Figure 1 The study was

conducted in Vietnam region which lies on the eastern

edge of the Indochinese Peninsula, near the center of

Southeast Asia, with a latitude of 23º23 'N to 8º27' N

and longitude of 102°10' E to 109°30' E The northern

border with 1400 km is bordered by China, the western

bordered by Laos and Cambodia, and 3260 km by sea

along the east and south

In Vietnam, four seasons are present for the North

including Spring, Summer, Autumn and Winter It can

also be divided into dry season (November - March),

rainy season (May - September) and seasonal change

(April and October) The climate in the Central and the

South is more stable with rainy season (September -

December in the central and May - October in the south)

and dry season is the rest in one year

In this paper, MODIS Terra/Aqua AOD level 2 at 3

km (MOD04_3K/MYD04_3K), VIIRS AOD EDR at 6

km (VIIRS EDR) over Vietnam are utilized to

experiment different data fusion methods

Fig 1 Vietnam boundary and location of AERONET stations TABLE I E XPERIMENTAL DATA

Data Product/

Station

Spatial resolution/

Location

Temporal resolution Period

MODIS Terra AOD MOD04_3K 3 km Daily

2012

-

2016

MODIS Aqua AOD MYD04_3K 3 km Daily

2012

-

2016

VIIRS NPP AOD

VIIRS AOD

2012

-

2016

AERONET AOD

NGHIADO Nha Trang Bac Lieu SonLa

105.800, 21.048 109.206, 12.205 105.730, 9.280 105.800, 21.048

15m

2012

-

2016 MODIS data collection 6 at 3km spatial resolution from 2012 – 2016 are collected from LAADS DAAC system [21]

VIIRS Aerosol Level 2 products onboard the Suomi-NPP satellite are also collected All data at 6 km spatial resolution in period of 2012 –2016 are collected from NOAA website [22]

Finally, station AOD data from AERONET network set up by NASA and PHOTONS are collected for validating original and fused satellite AOD data Currently, seven AERONET stations have been built in Vietnam but only four stations which provide data during 2012 to 2016 All cloud-screened and quality-assured AERONET AOD data (Level 2) at four stations

n

n

n

n

Vietnam

Laos

China

Thailand

Cambodia Son La

Bac Lieu NGHIA DO

Nha Trang

in Vietnam including Nghia_Do, Nha_Trang, Bac_Lieu

and SonLa (see Fig.1) were gathered All collected data

are summarized in Table 1

III METHODOLOGY

A Data preprocessing

Both MODIS Terra/Aqua and VIIRS aerosol

algorithm can produce not only AOD value but also

quality flag for each pixel The quality flag is stored

aerosol product as a separated dataset Quality flag

values range from 0 – 3 where 0 is lowest quality and 3

is highest quality Firstly, we extract

Land_Ocean_Quality_Flag datasets on MODIS

Terra/Aqua AOD images For VIIRS NPP, AOD value

and quality flag data are extracted from

QF1_VIIRSAEROEDR datasets Each raw image must,

be separately converted to a georeferenced image In

this paper, Thin Plate Spline (TPS) method were

applied for georeferencing raw images using GCPs in

the metadata of each image Our previous study [23]

show that TPS function is the best georeferencing

method for satellite images Then, Both MODIS and

VIIRS NPP AOD data were re-projected into grids of 3

km pixel resolution These processes were implemented

by GDAL library (Geospatial Data Abstraction

Library)

For comparing of AERONET with MODIS AOD

and VIIRS AOD, It was converted into 550 nm using

the Angström Exponent (440 nm – 675 nm) as

following equation:

55 0 5 0 ln

5 0 55

.

0

67 0 44

e

m m

µ µ α

µ µ

τ τ

−

−

Where τ0.55μm is AERONET AOD at 550 nm and

τ0.5μm is at 500 nm, respectively α0.44 µm – 0.67 µm

is the Angström Exponent for the range of 440 nm – 675

nm

B Data fusion

Two different methods were used to combine

aerosol data including Maximum Likelihood

Estimation (MLE), and Linear Regression

Maximum Likelihood Estimation (MLE)

In this study, AOD images are combined day by

day For each day, a set of three AOD images are

merged to produce only one consistent merged image

For each pixel of the fused image, AOD values are

calculated as the average of aerosol values from each

sensor base on a given weight The MLE combination

is defined as following equation:

Where AOD, is MODIS Terra AOD value at pixel

i,W ,! is weighting of pixel i on Terra AOD images The weighting is based on information about quality flag of each pixel Quality flags are an indicator of the algorithm team’s for assessment of the AOD data quality In this study, the weighting value and quality flag are directly proportional It means that the weighting value of high-quality flag pixel is greater than the weighting value of medium or low-quality pixel It

is calculated from quality flags as follows:

W = ∑3%=1QF QF

W = ∑3%=1QFQF (3)

W = ∑3%=1QFQF Where WTerra,i is weighting of pixel i, QFTerra,i is quality

flag value of pixel i on Terra AOD images and QFk,i is Quality flag value of pixel i on other sensors (k=1,2,3)

Linear Regression

Based on the quality, the satellite data which was the best quality is used as target data In order to increase AOD image coverage, this method employed other AOD data to retrieve the target data where target AOD values were not available but other AOD values exist Firstly, the data which is the highest data quality is used as target variable In this step, by validating with AERONET data as described in our previous studies [24], [25], MODIS Terra AOD was chosen as a target variable and the empty MODIS Terra pixels were filled

up with values where MODIS Aqua or VIIRS NPP existed

After that, for each day, the pixels which have both MODIS Terra/Aqua or VIIRS AOD value were selected

as training dataset to build the model as following regression equation:

AODTerra = a * AODAqua + b (4) AODTerra = c * AOD VIIRS + d

Where AODTerra, AODAqua and AODVIIRS are value of

satellite AOD (a,c) and (b,d) are regression slope and

intercept Then, regression images of MODIS Aqua and VIIRS NPP are estimated by using regression coefficient Finally, MODIS Terra and all regress images are merged All pixels on Terra without cloud are kept For all cloud pixels on Terra, if it is available

on Aqua Regress image then its values are selected Finally, for the pixels which are cloud on both Terra and Aqua, VIIRS AOD values is used if it does not contain cloud

C Data evaluation

After combination, the spatial coverage of original

images and fused images are also computed for

comparison In addition, fused images are evaluated

with AERONET data to assess the fused image quality

and the accuracy of fusion methods Several fusion

methods are compare using following criteria such as

coefficient of determination (R2), Root Mean Square

Error (RMSE), Relative Error (RE), Mean Fractional

Bias (MFB) and Mean Fractional Error (MFE) as

follows:

()= ∑ *+2*∑ *+2,34,- +̅/,- +̅/*0) ,- 01/ /)

,34 ∑ *02 , - 01/)

,34 (567 = 8 ∑ *+2 ,- 0,/)

,34 9 (7 = |+,- 0,|

+, 100%

5>? = 1 9 @ 0,- +,

A+,+ 0,

2 C

2

,34

5>7 = 9 @ 1 |0,- +,|

A+,+ 0,

2 C

2

,34

Where + D, 0 Dare mean of ground AOD and satellite

AOD, +,, 0,are ground and satellite AOD at time t,

and n is the number of samples

IV EXPERIMENT RESULTS

A Evaluation of data coverage

Figure 2 depicts the monthly averaged of data

coverage original data and fused data for the period

from 2012 to 2016 The data coverage of an image is

calculated as the number of pixels that have valid data

compared to the total number of pixels in the whole of

Vietnam The monthly average of data coverage is

calculated as the average of the data coverage for all

images in the given month The results show that the

data coverage for each month are different, with the

monthly variety trend are similar for both satellite data

The MODIS Terra/Aqua data coverage is relatively

low, approximately 5% to 20% over the months While

data coverage for VIIRS NPP images are relatively

high, approximately from 25% to 75% The data

coverage of the fusion methods is approximately

similar, slightly higher than the data coverage of the

VIIRS NPP image Although the data coverage

increased slightly, however, the quality of the combined

image increased significantly compared to the VIIRS

NPP image (presented in the next section) This shows

that the combined image takes advantage of the original

images simultaneously to increase the spatial coverage

and increase the quality of the data

Fig 2 Data coverage of original images and fusion image over Vietnam region from 2012 - 2016

B Evaluation of data quality

The scatter plots in Figure 3 show the correlation between AOD values of satellite images with AERONET AOD data, including original images (MODIS Aqua, MODIS Terra, VIIRS NPP) and fused images (MLE, Terra regression) On these charts, the horizontal axis is the AOD value of the image, the vertical axis is the corresponding AOD value of the AERONET station

In the original images, MODIS Terra satellite data has the highest determination coefficient (R2 = 0.76), MODIS Aqua and VIIRS satellite image data have lower R2 coefficients (R2 = 0.5824 and 0.6018 respectively) In the fused images, with the same number of samples (n = 680), the highest coefficient of determination (R2 = 0.8118) was observed on Terra regression method, follow by the MLE method (R2 = 0.7511)

Fig 3 Correlation of AERONET data with original and fused data (2012 – 2016)

Table 2 summarizes the evaluation results on quality

of the original and fusion data using a variety of

methods The assessment has been conducted by

comparing AERONET monitoring stations at 4 stations

in Vietnam for the period from 2012 to 2016

For the original data, the yearly data coverage of

VIIRS NPP from 2012 to 2016 was the highest (approx

45.4396% compared to MODIS Terra and MODIS

Aqua are 12.5033% and 10.4254% respectively)

However, considering the data correlation, MODIS

Terra has a better correlation (R2 = 0.7594, 0.5824,

0.6018 corresponding to MODIS Terra, MODIS Aqua

and VIIRS NPP) The error of MODIS Aqua data is the

lowest (RMSE = 0.2806, RE = 73.9%), followed by the

MODIS Terra (RMSE = 0.2379, RE = 74.3%) and the

highest were the VIIRS NPP (RMSE = 0.2667, RE =

99.25%) Both MFB and MFE are within acceptable

range (approximately 42 to 52%)

TABLE II DATA QUALITY OF ORIGINAL AND FUSED IMAGES

Data type MODIS

Aqua

MODIS Terra

VIIRS

Terra Regression Data

coverage 10.4254 12.5033 45.4396 47.9188 48.4046

RE 73.9229 74.325 99.2505 80.5099 72.7096

MFB -0.3506 -0.34 -0.4113 -0.3343 -0.3459

MFE 0.4246 0.4314 0.5253 0.4599 0.4476

For fusion data, both methods offer a better data

coverage and data quality Data coverage of fusion

methods do not differ significantly, with a value of

48.5% However, the correlation between fusion

methods is quite distinct The MLE and AERONET

regression correlations were approximately 0.75, which

is similar to the MODIS Terra image and higher than

the MODIS Aqua and VIIRS NPP images Terra

regression methods has a higher correlation

(approximately 0.8) than the original images and other

methods

In terms of data error, the fusion methods produce a

lower error than the original image AERONET

regression method had the lowest error (58.18%),

followed by Terra regression (RE approx 72-76%) and

MLE (RE = 80%) Both MFB and MFE are in

acceptable levels, showing that the results of the fusion

methods are relatively good

V CONCLUSION

In this paper, several data fusion methods were

applied on MODIS and VIIRS AOD images in

Vietnam AERONET AOD were used to validate these

data fusion methods The results indicate that Terra

Regression method is better than MLE method Data

fusion methods generally increase data coverage and

improve data quality Terra regression model shows the

best correlation while MLE gives the lowest relative

error Therefore, depending of the application so that we can choose the appropriate data fusion method

VI ACKNOWLEDGMENT The author would like to thank the Agence Universitaire de la Francophonie (AUF) for PhD Fellowship This research is also funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.99-2016.22

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