HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-21-2685-2017A multi-sensor data-driven methodology for all-sky passive microwave inundation retrievalTakbiriZeinabtakbi001@umn.eduhttps://orcid.org/0000-0003-1455-1236EbtehajArdeshir M.Foufoula-GeorgiouEfihttps://orcid.org/0000-0003-1078-231XDepartment of Civil, Environmental and Geo- Engineering and St.
Anthony Falls Laboratory, University of Minnesota, Twin Cities, Minneapolis,
Minnesota, USADepartment of Civil and Environmental Engineering, University of
California, Irvine, California, USAZeinab Takbiri (takbi001@umn.edu)8June20172162685270026October20161November201614March20177May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/21/2685/2017/hess-21-2685-2017.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/21/2685/2017/hess-21-2685-2017.pdf
We present a multi-sensor Bayesian passive microwave retrieval
algorithm for flood inundation mapping at high spatial and temporal
resolutions. The algorithm takes advantage of observations from multiple
sensors in optical, short-infrared, and microwave bands, thereby allowing
for detection and mapping of the sub-pixel fraction of inundated areas under
almost all-sky conditions. The method relies on a nearest-neighbor search and
a modern sparsity-promoting inversion method that make use of an a
priori dataset in the form of two joint dictionaries. These dictionaries
contain almost overlapping observations by the Special Sensor Microwave Imager and
Sounder (SSMIS) on board the Defense Meteorological Satellite Program (DMSP) F17 satellite and the Moderate Resolution Imaging
Spectroradiometer (MODIS) on board the Aqua and Terra satellites. Evaluation
of the retrieval algorithm over the Mekong Delta shows that it is capable of
capturing to a good degree the inundation diurnal variability due to
localized convective precipitation. At longer timescales, the results
demonstrate consistency with the ground-based water level observations,
denoting that the method is properly capturing inundation seasonal patterns
in response to regional monsoonal rain. The calculated Euclidean distance,
rank-correlation, and also copula quantile analysis demonstrate a good
agreement between the outputs of the algorithm and the observed water levels
at monthly and daily timescales. The current inundation products are at
a resolution of 12.5 km and taken twice per day, but a higher resolution (order of
5 km and every 3 h) can be achieved using the same algorithm with the dictionary populated by the Global Precipitation Mission (GPM) Microwave Imager
(GMI) products.
Introduction
Capturing the diurnal spatiotemporal dynamics of inundation over coastal
regions, deltaic surfaces, and river floodplains requires high-resolution
observations in both time and space, which are not available from the typical
sparse ground-based sensors. Satellite observations from the visible to the
microwave bands of the electromagnetic spectrum have been widely used for
mapping floods, estimating surface water storages, river discharge values, and
water levels (Smith, 1997). In the visible bands
(∼ 0.4–0.8 µm), natural water reflects a fraction of
incident light depending on the water depth and concentration of the
optically active components such as suspended and dissolved particulate
matter. However, water reflectivity sharply declines and approaches zero in
the near-infrared bands (∼ 0.8–2.5 µm). Thresholding of this
sharp gradient is often used to discriminate water bodies from their nearby
dry soils and vegetated surfaces (Rango and Anderson, 1974; Smith, 1997, 2001, and
references therein; Frazier and Page, 2000; Jain et al., 2005).
In the microwave region of the spectrum, the dielectric constant of water
(∼ 80) is much higher than the dry soil (∼ 4) and thus the
inundated areas are substantially less emissive and radiometrically colder
than the surrounding soils and vegetation covers. Moreover, emission from
smooth water surfaces is more polarized than that from rough soils and
vegetated surfaces (Ulaby et al., 1982; Papa et al., 2006; Prigent et al.,
2007). This polarization signal has also been used through empirical
thresholding approaches to distinguish water surfaces from other land surface
types (Allison et al., 1979; Sippel et al., 1994, 1998; Brakenridge et al.,
2005, 2007).
Flood mapping from space was first accomplished using visible to near-infrared
(VNIR) observations (0.4–1.1 µm), by the multispectral scanner system (MSS)
sensors on board Landsat-1 (Rango and Anderson, 1974;
Rango and Salmonson, 1974; McGinnis and Rango, 1975). In these pioneering
works, flooded areas were mapped where the near-infrared surface reflectance
was below a certain threshold as water absorption is strong in this region.
More recently, Brakenridge and Anderson (2006) showed that the visible red
band 1 (0.62–0.67 µm) and near-infrared (NIR) band 2
(0.84–0.87 µm) from the Moderate Resolution Imaging
Spectroradiometer (MODIS) aboard the Terra and Aqua satellites can be used to
detect water over land surfaces. They mapped several hundreds of flood events
at different sites all over the world by classification of water via
thresholding over the NIR band and the normalized difference vegetation
index, NDVI=(NIR-red)/(NIR+red)
introduced by Rouse et al. (1974). To better discriminate the vegetation from
inundated areas in threshold-based methods, Ticehurst et al. (2013) and
Guerschman et al. (2011) used a new index – called the normalized difference
water index, NDWI=(red-MIR)/(red+MIR)
introduced by Gao (1996) and later modified to MNDWI=(green-MIR)/(green+MIR) by Xu (2006). This
index exploits the mid-infrared (MIR; 1.23–1.25 µm) part of the
spectrum to improve the mapping. In all thresholding methods, the shadows of
terrains and clouds are usually miss-classified as inundated areas.
Therefore, Kuenzer et al. (2015) used the topography and cloud information
data as ancillary variables to obtain improved estimates of the interannual
dynamics of areas covered with water over five deltaic regions with high
annual cloud cover.
The use of passive microwaves (PMW) to map flooded areas was pioneered by
Allison et al. (1979), Giddings and Choudhury (1989), and Choudhury (1991).
Allison et al. (1979) used horizontal polarization of brightness temperatures
(Tb) at 19.3 GHz, from the electrically scanning microwave radiometer (ESMR)
on board the Nimbus-5 satellite, to delineate flooded regions in Australia.
Giddings and Choudhury (1989) reported the 37 GHz vertical and horizontal
polarization differences (i.e., Tb37v-Tb37h), from the Scanning Multi-frequency Microwave Radiometer (SMMR) on board
the Nimbus-7 satellite, as the most responsive channel to identify the
seasonal changes in the extent of floodplains over South America. Temimi et
al. (2005) used the empirical basin wetness index (BWI) defined by Basist et
al. (1998), to obtain real-time water surface fraction (WSF) in the Mackenzie
River basin, using multi-frequency information at 19, 37, and 85 GHz. To
minimize the contamination effects of atmospheric emission and variations of
surface temperatures, Brakenridge et al. (2007) exploited the ratio of Tb
values over inundated and dry surfaces at 36 GHz and presented promising
results over several river sites all over the globe, using the PMW
observations by the Advanced Microwave Scanning Radiometer – Earth Observing
System (AMSR-E). De Groeve (2010) also used the same method and
instrument to map floods for several hundreds of locations for the Global
Disaster Alert and Coordination System.
While visible and shortwave-infrared bands often provide sub-kilometer
resolution for inundation mapping, their capability is very limited in a
cloudy sky. This limitation is usually very restrictive over
prone-to-flooding watersheds and deltas in tropical regions with
a high-frequency of heavy precipitation events. For instance, a long-term
analysis of Landsat data revealed that due to cloud contamination, only
30 % of overpasses are useful for inundation mapping (Melack et al.,
1994). Because of this limitation, most of the related satellite products,
including the MODIS inundation products, are available mostly in monthly,
seasonal, and/or annual timescales (Ordoyne and Friedl, 2008). However,
microwaves can penetrate clouds – and to some extent hydrometeors in
frequencies ≤37 GHz – to provide water inundation mapping in almost
all weather conditions. Unfortunately, due to the coarse resolution of
microwave data, e.g., (47×74) km2 at 19 GHz to (13×16) km2 at 183 GHz for the SSMIS), only large water bodies can be
detected and sub-pixel inundated areas cannot be directly identified (Smith,
1997). Presently, there exist several sensors on board different satellites
that overlap in the spatial and time domains that sample land–atmosphere
signals at different wavelengths of the electromagnetic spectrum. Therefore,
it is imperative to integrate these multi-sensor observations to overcome
their individual shortcomings and improve retrievals of land–atmosphere
parameters and the extent of flooded areas (Prigent et al., 2001, 2007;
Crétaux et al., 2011; Temimi et al., 2011; Schroeder et al., 2010).
In this paper, we develop a method to retrieve sub-pixel inundation fraction
(“inundation” referring to regions where water covers the land surface,
excluding permanent water bodies) only from passive microwave observations
based on a set of paired VNIR and passive microwave training samples. In
particular, as training samples, we use global observations of VNIR data from
the MODIS on board Terra
(launched in 2000) and Aqua satellites (launched in 2002) and passive
microwave data from the Special Sensor Microwave Imager and Sounder (SSMIS) on
board Defense Meteorological Satellite Program (DMSP) satellites F16–F18. Several years of observations (2000–present)
by these two sensors allow us to collect adequate overlapping data to link
coarse-scale SSMIS passive microwave data to high-resolution MODIS VNIR data
in the form of an organized dataset. Obviously, this collection of almost
coincident observations does not contain direct information about surface
inundation in a cloudy sky, as the radiative signals in VNIR wavelengths
cannot penetrate clouds. However, over land, it is well understood (see
Ferraro et al., 1986; Grody, 1991; Wilheit et al., 1994) that hydrometeors and the
atmospheric profile do not significantly affect the low-frequency
< 60 GHz brightness temperatures. Therefore, the information content of
the dataset over low-frequency channels is independent of the atmospheric
profile and can be used to a good degree of accuracy to recover inundated
surfaces under cloudy conditions as well. It should be acknowledged that
there is an uncertainty for the inundation retrieval under heavy rainy/cloudy
skies when only the information in the clear-sky dataset is used. However, we
expect that this uncertainty will be small since the information of the
underlying surfaces in low-frequency channels of the collected dataset
remains almost the same over different atmospheric conditions.
The collected dataset has a large number of linked pairs of inundation
fraction data from MODIS data SSMIS multi-frequency brightness temperatures.
For algorithmic development, the dataset is organized into two fat matrices:
the brightness temperature and inundation dictionaries. For an
observed pixel-level brightness temperature, the proposed passive retrieval
algorithm uses the nearest-neighbor search to isolate a few vectors in the
dictionary of brightness temperatures and their corresponding inundation
fraction and then use them to estimate the unknown inundation fraction. The
proposed retrieval algorithm is applied to estimate daily inundation fraction
at spatial resolution of 12.5 km over the Mekong in 2015. The main
motivation for selecting this delta as a case study is that approximately
90 % of the Mekong region is covered by clouds during the rainy season
(Leinenkugel et al., 2013), which severely hampers the use of inundation
mapping in the VNIR bands. We retrieve the inundation fraction twice per day
using the proposed algorithm over the Mekong Delta and compare the results
with the flood products of VNIR data during clear skies. We also evaluated
the results against the daily and monthly water level data obtained from
11 gauges over the Mekong Delta (Fig. 1) to examine consistency of the
retrievals with the regional inundation patterns.
Map and digital elevation of the Mekong River basin
(area = 795 000 km2) and its delta. The study area is delineated by a pink
rectangle. The 11 stations (from Mekong River Commission) that monitor the
water level are also marked by pink stars.
This paper is organized as follows. Section 2 explains the a priori
dataset and the formation of the dictionaries and Sect. 3 provides detailed
information about the retrieval algorithm. Implementation of the method and
validation are explained in Sect. 4. Section 5 presents concluding remarks
and directions for future research.
Study area and dataset
The 60 000 km2 Mekong Delta is in South Vietnam (see Fig. 1) with a
tropical monsoon climate system. The delta with its agricultural industry is
one of the most important sources of food supply to Southeast Asia. This
critical region is home to nearly 20 million people, approximately 22 %
of the population of Vietnam, and is one of the most densely populated
regions in the world. The area has been exposed to exacerbated erosion due to
human activities and increased sea level rise and lowland flood events in the
recent decades (e.g., Syvitski et al., 2005; Ericson et al., 2006; Nicholls
and Cazenave, 2010; Tessler et al., 2015). Improved quantification of (near)
real-time inundation of the Mekong Delta can help (1) to improve flood
forecasting by identifying the inundated and thus soil saturated zones and
(2) to identify erosional and depositional hotspots that can improve
geomorphologic and ecosystem modeling. The proposed retrieval algorithm is
applied to estimate sub-daily inundation fraction at resolution of 12.5 km
over some of the lower regions of the Mekong Delta in calendar year 2015
(Fig. 1).
Two sources of information are used to build a dataset that connects almost
coincident VNIR water inundation data and multi-frequency passive microwave
data. The VNIR data consist of the daily NASA standard MODIS near-real-time
(NRT) water product (MWP-3D3ON; i.e., 3-Days imagery, three observations, and no
shadow masking) with approximately 250 m spatial resolution (Nigro et al.,
2014) from both Terra and Aqua satellites. The Terra and Aqua satellites both
have a sun-synchronous orbit. They rotate around the earth in opposite
directions: Terra has an ascending orbit with the local equatorial crossing
time of 10:30 LT and Aqua has a descending orbit with the local equatorial
crossing time of 01:30 p.m. MWP products are binary information of
inundation based on the Dartmouth Flood Observatory (DFO) algorithm, which
uses a thresholding scheme on MODIS observations at band 1
(0.62–0.67 µm), band 2 (0.84–0.87 µm), and band 7
(2.10–2.15 µm). To minimize the contamination effects of cloud and
terrain shadows, we focus on 3-day composite MWP products (3D3ON). Clearly,
the use of the 3-day composite MODIS-MWP data can affect daily inundation
retrievals; however, in the context of the presented algorithm this is the
best choice because, daily MODIS-MWP composites are very uncertain due to the
terrain shadows and clouds (Nigro et al., 2014). Typically, there are
numerous missing pixels in the daily products, which reduce the sample size
dramatically. These errors are significantly reduced in 3-day composite
products, as it is less likely that clouds (and their shadows) stay at the
same spot during a 3 day period (Nigro et al., 2014).
The microwave data are obtained from the DMSP SSM/I-SSMIS Pathfinder Daily
Equal-Area Scalable Earth Grid (EASE-Grid; see Armstrong and Brodzik, 1995)
brightness temperatures distributed by the National Snow and Ice Data Center
(NSIDC). These datasets are at four central frequencies 19, 22, 37, and
91 GHz. All channels are vertically and horizontally polarized except
channel 22 GHz. The effective resolution of the highest frequency channel is
∼ 12.5 km while low-resolution channels are projected onto a grid size
of ∼ 25 km. DMSP SSM/I-SSMIS brightness temperature data products are
from observations by the SSM/I and SSMIS radiometer on board the DMSP F8, 11,
13, or 17. Since December 2006, the F17 satellite has been the only
operational satellite from the DMSP series, which carries on board the SSMIS
instrument with equatorial crossing times of 05:30–06:30 a.m. and
17:30–18:30 p.m. for the descending and ascending orbits, respectively. It
is important to note that because these satellites revisit every point on
Earth at the same local time, repeatedly, the paired MODIS-MWP with DMSP
SSMIS data have a fixed diurnal time difference in the entire dataset. Since
the MODIS-MWP data are from the combination of Terra and Aqua observations,
their time tag is advantageous in the sense that it allows us to enrich the
number of samples for the diurnal cycle of inundation dynamics.
The first step for building the a priori dataset is to match the different
space–time resolutions of the multi-sensor information. To unify the spatial
resolution of the microwave data, the brightness temperatures of the three
lower-frequency channels are mapped onto the latitude–longitude grids of the
high-frequency channel of 91 GHz with a resolution ∼ 12.5 km, using a
nearest-neighbor interpolation. Then the clear-sky MWP data are also upscaled
from 250 m to 12.5 km and projected onto the same grids. In the process of
upscaling the binary MWP data, we assigned to each upscaled pixel a scalar
inundation fraction number f that represents the ratio of the number of
inundated sub-pixels to the total number of sub-pixels within a pixel size of
12.5 km. For matching the timescales of Tb and MWP values, the Tb values
are averaged over a 3-day time window to minimize the possible effects of
cloud contamination in the VNIR data. Figure 2 demonstrates schematically the
process of producing the explained dataset.
A schematic showing construction steps of the a priori dataset for
dictionaries. The top slab is the upscaled MODIS-MWP and the other slabs are
the brightness temperature data at seven frequency bands. Each vector on the
left is created by stacking a pixel-level information of the multi-frequency
brightness temperatures by the SSMIS radiometer and their corresponding
inundation fractions from the MWP product at 12.5 km resolution. This
process is repeated for each orbit to generate a large number of vectors and
form separate dictionaries for ascending and descending orbits using all
satellite overpasses in 5 years from 2010 to 2014. N=n×m is the
number of collected vectors for 1 day in a year. The same process is
conducted for each day in 5 years (2010–2014) to create the dictionaries
with M=∑i=15×365Ni vectors.
The retrieval algorithm
The proposed retrieval algorithm uses the link between two available
coincidental datasets, passive microwave (SSMIS) and VNIR (MODIS-MWP), to
retrieve inundation in the cloudy days. First, the overlapped clear-sky
pixels of MODIS-MWP and SSMIS for 5 years (2010–2014) are collected over the
study area to create two coincidental dictionaries: the SSMIS dictionary and
the MODIS-MWP dictionary. The SSMIS dictionary consists of 8-dimensional
vectors of brightness temperature (Tb), where 8 is the number of frequency
channels, and the MODIS-MWP dictionary consists of scalar values of
inundation fractions for each corresponding pixel in Tb. In other words, the
inundation fraction for each Tb in the brightness temperature dictionary is
known. The algorithm uses the information embedded in these two dictionaries
to estimate the unknown inundation fractions for each Tb observation vector.
First, it searches the brightness temperature dictionary to find the K most
similar vectors in the Euclidean sense to the Tb observation vector through
the K-nearest-neighbors algorithm. Then, for these K-nearest-neighbors,
the corresponding known scalar values in the inundation fraction dictionary
are picked. If the ratio of the number of inundated vectors in K-nearest
neighbors is greater than a threshold (which will be explained later), this
pixel is called inundated and the algorithm goes to the estimation step. In
the estimation step, the coefficients that can optimally estimate the Tb
observation vector based on its K-nearest neighbors are calculated through
a least-squares regularization approach. Those coefficients are then used to
linearly combine the K known inundation fractions that are associated with
the neighboring Tb vectors for calculating the unknown inundation fraction.
The above detection and estimation steps are repeated for each orbit at
a pixel level of 12.5 km over the study area. The algorithm is mathematically
described in what follows.
To organize the dataset in an algebraically tractable manner, M vectors of
microwave brightness temperatures bi=Tb1i,Tb2i,…,TbniT∈Rn at n frequency channels are collected. These vectors form
the column space of an n-by-M matrix B=b1|b2|…|bM∈Rn×M, called a brightness temperature dictionary, where M≫n. Analogously, the corresponding inundation fraction values fii=1M can be collected in the column space of the
inundation dictionary F=f1|f2|…|fM∈R1×M. For each vector
bi in the dictionary of brightness temperatures there is an
inundation fraction fi from MODIS-MWP. The collection of these pairs
from historical observations forms the two dictionaries B and
F. The algorithm follows two sequential steps: a detection and an
estimation step. In the detection step, for each observed vector of brightness temperature
bobs, the algorithm first finds its
K-neighboring brightness temperatures in B in the Euclidean
sense and stores them in the column space of Bs∈Rn×K. Then, knowing the column indices of the
neighboring brightness temperatures, it isolates their corresponding
inundation fraction values in Fs∈R1×K. In this step, if at leastp×K number of
nearby inundation fraction values in Fs are non-zero,
the algorithm assumes that bobs is over an inundated pixel
and attempts to estimate the fraction of inundation in the estimation step.
Here, p∈(0-1) is the detection probability parameter. It should be
also noted that the K-nearest-neighbor algorithm in this paper does not
directly constrain its search to any specific time or location. In other
words, for every pixel-level vector of Tb, the K-nearest-neighbors
algorithm searches the entire dictionary regardless of any specific time or
spatial coherency.
In the estimation step, the method assumes that bobs can
be estimated by a linear combination of a few column vectors of
Bs as follows:
bobs=Bsc+e,
where the vector c∈RK contains a set of
representation coefficients to be estimated and e∈Rn
is the error vector. Clearly, for an observed vector of brightness
temperatures bobs, the goal is to estimate its unknown
inundation fraction value f^. We assume that the two paired
dictionaries Bs and Fs represent
similar manifolds in a geometric sense that their local structures can be
approximated well with the same linear model. This allows us to assume that
the representation coefficients in vector c from Eq. (1) can be used
to estimate the inundation fraction f^ as follows:
f^=Fsc.
As a result, using a classic-weighted least-squares method, the
representation coefficients c can be estimated as
c^=argminc‖Wbobs-Bsc‖22,
where W is a weight matrix (to be discussed later in this section)
that characterizes the importance of each channel in the retrieval scheme.
The number of K-nearest neighbors is often larger than the number of
frequency channels, k≫n, making Bs a rank-deficient
matrix and the above problem ill-posed. To make the optimization problem
(Eq. 3) well-posed, we use a
mixed ℓ1–ℓ2-norm regularization as follows:
c=Argminc‖Wbobs-Bsc‖22+λ1‖c‖1+λ2‖c‖22subject to c0,1Tc=1,
which has been successfully used for passive microwave precipitation
retrievals (Ebtehaj et al., 2015a, b). The non-negativity of the coefficients
assures positivity of the brightness temperatures and the sum-to-one
constraint enforces an unbiased estimation. The regularization involves both
the ℓ1-norm ‖c‖1=∑i=1Kci and the ℓ2-norm c2=(∑i=1Kci2)12. The
parameters λ1 and λ2 in Eq. (4) are
regularization parameters that enforce a trade-off between the two
regularizations ℓ1 and ℓ2. In this mixed regularization,
the ℓ1-norm leverages sparsity in the solution (i.e., forces some of
the elements of c to be zero) while the ℓ2-norm increases
the stability of the solution as the neighboring brightness temperatures in
Bs are likely to be highly correlated (see Zou and
Hastie, 2005). In effect, due to the use of a mixed regularization, this
regularization promotes group sparsity (i.e., some blocks of the
representation coefficients are zero) while it keeps the solution
sufficiently stable. In other words, it acknowledges the fact that there are
a few clusters of nearby brightness temperatures that can properly explain
the observation. By enforcing the ℓ1-norm we select vectors that are
parts of clusters of brightness temperatures, while the ℓ2-norm
handles the potential correlation between those clustered neighbors and makes
the problem sufficiently stable. The proposed algorithm is summarized in a
flowchart shown in Fig. 3.
Flowchart of the inundation retrieval algorithm for N pixels in
each orbit, where Knn stands for the K-nearest neighbor. See text for definitions of the notations and detailed
explanation.
As previously noted, in the current implementation of the proposed retrieval
algorithm, we focus on (almost) coincidental observations of the brightness
temperatures and inundation fractions by the SSMIS and MODIS instruments,
respectively. The dictionaries B and F are constructed
using 5 years of overlapping data (2010–2014) over the Mekong Delta
(latitude: 0–10∘ N and longitude: 100–110∘ E) at 12.5 km
grid resolution (Fig. 1).
To build the dictionary, only the clear-sky MODIS-MWP products were
considered. At resolution 12.5 km, we labeled a pixel as clear-sky when less
than 50 % of the VNIR data at resolution 250 m is flagged as non-cloudy.
Because the MODIS sensor has a much higher resolution than the footprint of
SSMIS and because the number of cloud-free samples over the Mekong are very
limited, a threshold above zero is deployed to keep a certain number of
partially cloudy pixels and make sure that the dictionary will not be
undersampled. For choosing the threshold, we conducted some sensitivity
analysis (not shown here) and found a 50 % threshold, as a fair
probability choice, results in a minimum of potential biases.
(a) The systematic difference between passive microwave
observations from the ascending (solid lines) and descending orbits (broken
lines) as a function of five different sub-pixel intervals of inundation
fractions. (b) July to December daily average of absolute differences between the
ascending (TbA) and descending (TbD) brightness temperatures at
vertically polarized 19 GHz channel. The values of TbA-TbD mainly capture the coastal regions with significant variability in
their surface emissivity values due frequent diurnal tidal effects.
Since the DMSP satellites have two different equatorial crossing times, here,
we use two sets of dictionaries for Tb values in the ascending (day
or morning) and descending (night or evening) orbits. From all the available
coincident observations, we randomly chose 2 × 106 pairs of
brightness temperatures and inundation fractions in each ascending and
descending dictionary. The purpose of stratifying the dictionaries into
ascending and descending orbits is to exclude the effects of Tb modulations
from the retrieval process caused by the systematic diurnal variation of
surface temperature. In other words, the same inundation fraction has
different PMW spectral signature in a daytime versus a nighttime overpass
largely due to the diurnal variability of skin temperature, precipitation,
and soil moisture (see Mears et al., 2002; Ramage and Isacks, 2003; Norouzi
et al., 2012). Figure 4a presents the systematic difference between the Tbs
of the ascending versus descending tracks for various ranges of pixel-level
inundated fractions. In effect, in this figure, the Tbs in the dictionaries
are grouped into five intervals based on their corresponding inundation
fraction (from 0 to 1) in F. Then for each interval, the average
of Tb values is shown. The plot clearly demonstrates that the daytime Tbs are
thermally warmer than their nighttime counterparts and this difference
begins to shrink when the inundation fraction increases. It is worth noting
that the difference between ascending and descending brightness temperatures
is larger over the low-frequency channels (≤37 GHz) as they respond
more to the land surface structural variability than the higher-frequency
channels that capture atmospheric signatures. Figure 4b depicts TbA-TbD where TbA
and TbD stands for ascending and descending overpasses,
respectively. It can be observed that high values of TbA-TbD depict the
coastlines, i.e., regions with the transient presence and/or absence of water
over land.
The normalized coefficients of variation (right panel) of the
brightness temperatures (Tb) (left panel) averaged over the entire dataset
for different intervals of inundation fractions. Here,
Tb¯ denotes the average of brightness temperatures over the
inundation fractions. The coefficients of variation of each channel are used
to determine the channel weights for the retrieval algorithm. Channels 19 H GHz and 37 V GHz are the most responsive channels to the variability of
inundation fraction and are given higher weights.
The probability of detection, p∈(0-1), determines if a pixel is
inundated or not if the number of inundated vectors in K-nearest neighbors
is ≥p×K. We found that the inundation detection with K≥50
gives a reasonable rate for the probability of hit and false alarms. In other
words, the probability of detection does not change significantly for a
larger number of nearest neighbors. In the estimation step, to characterize
the weight matrix W∈Rn×n, we used the
coefficients of variation of each channel in response to changes in the
inundation fraction (see Fig. 5). In other words, we assume that those
channels that exhibit more variability with respect to changes in inundation
fraction contain more information about inundation and shall be given more
weight in the estimation process. One might ask why it is important to
consider the high-frequency channels (e.g., 91 V, H GHz) despite the fact
that they show minimal sensitivity to the inundation fraction (Fig. 5) and
land surface emissivity compared to lower-frequency channels. The
high-frequency channels mainly capture the information content of the
atmospheric profile. Therefore, incorporating them in the proposed retrieval
framework allows us to indirectly consider the effect of atmospheric
conditions by narrowing down the search for K-nearest neighbors to those Tb
candidates that best match both the underlying land surface emissivity and
the atmospheric conditions.
Inundated map of the Mekong Delta in the wet (July–December) and
dry (January–June) seasons for the ascending orbits. The results of the
proposed retrieval algorithm are presented using the ascending dictionary
(top row) against the upscaled MODIS near-real-time (NRT) water product
(MWP) data (bottom row). Overall, a good agreement is observed with some
overestimation of inundated areas by the proposed algorithm compared to
MODIS-MWP data around the river banks.
For implementation of the algorithm, the regularization parameters are set as
λ1=λ(1-α) and λ2=αλ,
where α∈(0,1). Here, through cross-validation studies, through
cross-validation we empirically found that λ=0.001 and α=0.1 provide a reasonable balance between sparsity and stability of the
solution in Eq. (4). It should be noted that Eq. (4) is converted to a
constrained quadratic programming problem and solved using an iterative
Newton's method with MATLAB optimization Toolbox (see Coleman et al., 1999).
Results, validation, and discussion
The inundation fractions were estimated during the wet period of calendar
year 2015 from July to December when the water levels across the delta begin
to rise and eventually recede (see Fig. 6). The wet season of the region is
largely characterized by heavy precipitation as a result of the interactions
of two monsoons including the Indian monsoon and the East Asia–western North
Pacific summer monsoon (Delgado et al., 2012).
To study the performance of the detection step we computed the probability of
hit P(f^>0|MWP>0) and false alarm P(f^>0|MWP=0) of the algorithm outputs. Our analysis indicates that the
probability of hit is around 0.92 for both the dry and wet season,
demonstrating the capability of the algorithm in detecting the inundated
areas. However, the probability of false alarm is around 0.12 for the dry
season and reaches the value of 0.34 for the wet season, which might be due
to the generalization of the algorithm and MODIS missing data during the wet
season. The MODIS daily data, especially in the wet season, contain a large
number of missing values due to cloud blockages and frequent heavy rains over
the study area. In fact, while we were collecting the overlapping data for
constructing the dictionaries, we observed that over 88 % of the MWP
products have some missing portion in the 12.5 km resolution. As a result,
it is very likely that the MWP data underestimate the actual inundation
fraction of regions with prolonged precipitation events.
Scatterplots of daily inundation fractions (f) from the retrieval
algorithm against those from MODIS-MWP in wet (a) and dry seasons (b) shown
in Fig. 6. The scatterplots demonstrate larger inundation fractions from the
retrieval algorithm in July to December (a) compared to MODIS-MWP data.
However, in January to June, when there are fewer clouds, the inundation
fractions from the proposed algorithm are more correlated with the MODIS-MWP
data, with only a slight underestimation of their variability.
Figure 6 shows that the algorithm is capable of identifying hotspots of
inundation when its outputs are compared with the MODIS-MWP; however, the
algorithm slightly overestimates the inundation fractions for some pixels
farther from the coastlines, most of which are completely dry in MWP. Here
for brevity, we only show the results for ascending overpasses, while similar
spatial patterns are observed for descending overpasses. Figure 6 also shows
some overestimation of inundation fractions near the riverbanks of major
rivers. This might be due to the high soil moisture content (≥ 0.8)
during the wet season that increases the dielectric constant of the soil up
to 30–50 (Alharthi and Lange, 1987), which is close to the dielectric
constant of the water surfaces (75–80). Another reason is the cloud
coverage. Since the riverbanks are inundated less frequently than the
coastlines, it is possible that these few inundation events were missed by
MODIS because of the cloud blockages. There is also some underestimation in
the inundation fractions from the proposed algorithm over the hillslopes far
away from the riverbanks compared to the MODIS-MWP product. Those
sporadically inundated areas, which appear on the MODIS-MWP map (Fig. 6b, c),
can be due to the terrain shadows that are misclassified as water. While we
cannot directly prove the above assertion within the scope of this
paper, the elevation map (Fig. 1) indicates that those hillslopes are
very unlikely to get inundated.
Comparison of inundation fractions from MODIS-MWP and the proposed algorithm
at daily scale is also challenging. This is because daily MODIS data are
often severely corrupted by cloud coverage. On the other hand, under a clear
sky, the MODIS-MWP inundation fractions are more precise than the results of
the retrieval algorithm. To better illustrate this issue, scatterplots of
daily inundation fractions from our retrieval algorithm against those from
MODIS-MWP in wet and dry season are displayed in Fig. 7. The scatterplots
further demonstrate larger inundation fractions from the retrieval algorithm
in July to December (Fig. 7a). In the wet season, there are also a lot of
non-zero retrieved inundation values on the y axis that have corresponding
zero inundated pixels in MODIS-MWP data. However, in January to June, when
there are fewer clouds, the inundation fractions from the proposed algorithm
are generally more correlated with the MODIS-MWP data but slightly
underestimated (Fig. 7b). This underestimation probably also exists in wet
months but is masked because of the all-sky retrieval capability of the
proposed algorithm in the presence of the clouds and heavy rains. The reason
for this underestimation might stem from the choice of 50 % threshold for
selecting the clear-sky pixels. In other words, there are a set of brightness
temperatures for which the corresponding MODIS data are partially cloudy and
potentially underestimate the actual inundation fraction. As a result, it is
likely that those pairs will be isolated, used in the retrievals, and
eventually lead to some underestimation in passive microwave retrievals.
As previously mentioned, the interannual climatology of the Mekong Delta is
highly affected by two tropical monsoons that characterize the seasonal
patterns of precipitation, river stages, and water levels (Delgado et al.,
2012). To better understand whether the results of our retrieval algorithm
follow the regional climatology, the monthly percentage of inundated area
over the Mekong Delta is calculated and shown against the monthly water level
data in Fig. 8a. The monthly water level data are obtained by averaging over
all 11 stations shown in Fig. 1. The specific goal is to compare the monthly
variability of the algorithm outputs with the MWP products and investigate
whether they are consistent with the regional variations of the surface water
level (river stage), which is considered a surrogate for the extent of
inundation. It should be acknowledged that this approach is not a direct
validation; however, it can provide insight into the performance and
climatological consistency of the proposed model as the surface water level
data are positively correlated with the extent of the inundated surfaces.
The monthly inundated areas of the Mekong Delta calculated from
the proposed retrieval algorithm and MODIS near-real-time (NRT) water
product (MWP) data in comparison with ground-based monthly water level data.
(a) Comparison of the total inundated surface of the Mekong Delta from MWP
products and the retrieval algorithm from ascending and descending
dictionaries. From visual inspection, it is obvious that the retrieval
algorithm can better follow variations of the water levels compared to MWP.
More inundation over the dry season is reported by MWP products than the wet
season, which contradicts the causality between rivers' stages and the
extent of inundated areas. (b) The total fraction of land surface areas that
are labeled as missing in MWP product because of atmospheric contaminations.
The larger deviations of the MWP products from water level data during the
wet months might be attributed to the larger percentage of missing values.
The seasonal variations in the monthly percentage of the total inundated
surfaces from the proposed model follow the trend of monthly water level data
better than the standard MWP products (Fig. 8a). We can see that during the
wet months of June to November, the MWP data report much less inundated area
than the outputs of the proposed algorithm, whereas this pattern is reversed
during the dry months of January to March. As previously noted, we suspect
that the differences in the wet season are due to the large portion of
missing data in the MWP products because of the high cloud coverage in the
rainy season (Fig. 8b). For quantitative comparison of the outputs of the
algorithm with MWP, a Euclidean distance between normalized version of the
algorithm outputs and water level data is calculated and compared with its
MWP counterpart. The Euclidean distance between water level and the retrieved
inundation from ascending and descending orbits is 3.46 and 3.56,
respectively, while this distance for MWP and water level data is about 7.89,
which is more than twice the distances calculated from the microwave
retrieval results. This indicates the superior performance of the proposed
inundation fraction retrievals as compared to the MWP products, chiefly
because of its all-sky skills during the rain dominant seasons.
When is compared to MODIS-MWP, the inundated area obtained by the retrieval
algorithm in the dry months (Fig. 8a) shows some underestimation. One reason
for this underestimation is the general limitation of the empirical Bayesian
estimation method regarding the extreme events (see Coles and Powell, 1996,
and the references therein) and we suspect that it is not just limited to the
months of January to March but it affects the retrievals at other months to a
lesser extent, as well. This limitation arises by the sample scarcity of
large flooding scenarios during the warm months of the year, which probably
lead to the underestimation of inundation fractions related to those events
by our retrieval algorithm. We expect that by improving the
representativeness of the dataset – especially for extreme events in the
summer months – this shortcoming can be significantly improved.
A closer look at Fig. 8a also reveals slightly larger inundated surfaces in
each month for the ascending (evening overpasses) compared to the descending
(morning overpasses) tracks. This small difference between the ascending and
descending retrievals can be attributed to the expected diurnal patterns of
the precipitation over the Mekong Delta. Indeed, it is well documented (Gupta
2005) that localized convective precipitation events are more likely during
the evening, which can increase the extent of the inundated areas. To further
assess the proposed algorithm performance at a daily scale, we compare the
dependence of the total area of ascending daily inundation fractions of the
algorithmic outputs with the average daily water level data, using Spearman's
rank-correlation coefficient. The rationale is that a stronger rank
correlation of an inundation product with the water level data implies an
improved retrieval. The correlation coefficient between the daily water level
of the rivers and the total inundated surfaces of the Mekong Delta is equal
to 0.22, which drops to -0.38 for the MWP products. To go beyond a rank
correlation, we also examined the dependence structures across different
ranges of inundation and water level quantiles using an empirical copula (see
Appendix A1).
Copulas provide an effective non-parametric way for simple representation of
multivariate joint distributions of high-dimensional random variables to
describe their dependence structure. When dependence of two random variables
increases, their bivariate “L-shaped” cumulative copulas tend more to the
origin. In Fig. 9, the axes show the marginal quantiles of daily inundation
fractions versus those of water level elevations and the contours trace the
cumulative copulas. To characterize the dependence of water level and
inundation as a function of topography, we divided the study area into two
sub-regions covering the steeper upper parts (above the Phnom Penh gauge in
Fig. 1) and the flatter downstream region. The copula analysis for each
region was presented separately in Fig. 9. As is evident, the empirical
copula of the total daily inundation fraction from the proposed algorithm
shows higher degree of dependence to the water level, as compared to MWP,
especially for the quantiles with less than 0.8 cumulative probability for
both upstream and the downstream regions. However, comparing the downstream
(Fig. 9a) and the upstream (Fig. 9b) regions, we see an increased dependency
of the retrievals with the water levels in the upstream region. This
observation seems to be consistent from a geomorphological point of view,
because over a steeper region of the basin the hill slopes are naturally
steeper and any small water variability can give rise to significant water
extension of inundated areas. However, over fat floodplains water levels and
extent of inundations may not be strongly correlated as small changes of
water levels may give rise a large extension of flooded surfaces.
The empirical copula (joint probability distribution of quantiles)
of the average daily water level and total daily inundated areas from the
proposed retrieval algorithm (red curves) and MODIS-MWP data (black curves)
for 2015. These plots indicate that our products have stronger dependence to
water levels than the MWP products (more L-shaped curves) for both the
downstream (a) and upstream (b) regions of the Mekong
Delta. The shaded areas (which quantify the difference between the degree of
dependence of our products and the MWP products to the daily water levels)
are larger in the upstream region, indicating an enhanced performance of the
proposed algorithm to retrieve inundation fraction where potential inundation
areas are better defined due to topography, e.g., around major riverbanks.
Conclusions and future directions
In this paper, we introduced a methodology to retrieve inundation from space
for almost all-sky conditions to reduce the gaps that exist in using
satellite data in visible to microwave bands. The key idea of the proposed
method was to explore the links between overlapping daily high-resolution
observations in the visible and near-infrared bands from the MODIS and the
lower-resolution passive microwave observations from the Special Sensor
Microwave Imager and Sounder (SSMIS) sensor. The developed multi-frequency
inundation retrieval algorithm uses the K-nearest matching method in
conjunction with a sparsity-promoting regularization technique. The proposed
method demonstrated promising results in resolving the spatial patterns of
inundation, compared with the MODIS-MWP data. Over the months with high
cloud coverage, the monthly results are consistent with the seasonal
dynamics of water level variation, which is controlled by tropical monsoons
in the Mekong Delta. Analysis also showed that, at a daily timescale, the
outputs of the algorithm exhibit stronger dependency with the water level
data than the MWP data.
There were three major sources of uncertainty in the proposed retrieval model
in this paper. The first one related to the use of the 3-day composite
MODIS-MWP data (daily products of MODIS-MWP were avoided due to missing
values and cloud blockages), which might have introduced some bias in the
daily retrievals due to mismatch of timescales. This source of error can be
significantly reduced if the MODIS dictionary is populated with more accurate
daily products. The second source of error related to the lack of adequate
fully clear-sky samples in our dictionary and therefore the need to define a
cloud coverage threshold in order to increase the sample size. Using
partially cloudy MODIS data was the main reason for some observed
underestimation of inundation fractions, especially in the dry months
(Figs. 7 and 8), which can be mitigated by increasing the sample size. The
last source of error was more related to the general limitation of the
Bayesian estimation method regarding the retrieval of extreme events (see
Coles and Powell, 1996, and references therein). This limitation is due to
scarcity of large floods in the dictionary, which can be treated by adding
more scenarios of extreme events to the dataset from different geographic
locations.
One of the limitations of the proposed algorithm (because of the spatial
resolution of microwave data used in this paper) was its lack of information
about the spatial patterns of inundation within the 12.5 km pixels. The
spatial pattern of the estimated inundation fractions can be further enhanced
by using the guidance of a high-resolution topographic data (see Galantowicz,
2002). The database can also expand to include some high-resolution
cloud-free imageries from newly launched satellites, such as Sentinel-2, which can
aid in capturing the high-resolution inundation areas. Finally, expanding the
dictionary to include data from the passive microwave channels of the new
satellites, such as Global Precipitation Mission (GPM) Microwave Imager
(GMI),
will increase the spatial resolution of the retrievals to approximately
5 km. In this paper, the seasonality and also different land surface classes
have not been directly taken into account in the retrieval algorithm. Future
research should include the stratification of the dictionary based on
different land surface types and time periods (e.g., seasons).
MATLAB code available at
ftp://ebtehaj.safl.umn.edu/Codes/ShARP_Demo/. The dictionary of
overlapped MODIS-MWP and SSMIS and also the resulting database are publicly
available upon request (email to takbi001@umn.edu). The data that have been
used to create the dictionary are available at
https://floodmap.modaps.eosdis.nasa.gov/ (NASA Goddard's Hydrology
Laboratory, 2016) and
ftp://sidads.colorado.edu/pub/DATASETS/nsidc0032_ease_grid_tbs/global/
for or MODIS-MWP and SSMIS data, respectively.
Copula
Let X1 and X2 denote two random variables with marginal
cumulative distributions F1(x1)≡P[X1≤x1] and F2(x2)≡P[X2≤x2] with the
cumulative joint distribution function F(x1,x2)≡PX1≤x1,X2≤x2. According to the Sklar's
theorem (Nelsen, 1999), the cumulative joint distribution F(x1,x2)
of X1 and X2 is equal to the cumulative joint distribution
function C(u1,u2) of the quantiles u1=F1(x1) and
u2=F2(x2) by
Fx1,x2=PX1≤x1,X2≤x2=PX1≤F1-1(u1),X2≤F2-1(u2)≡CU1≤u1,U2≤u2=Cu1,u2,
where Cu1,u2, is the cumulative copula with
uniform marginal random variables F1(x1) and F2(x2) on
the interval [0,1]. The multivariate density function f(x1,x2),
if it exists, can be calculated by taking the derivative of C and F, which
results in the following:
f(x1,x2)=c(u1,u2)⋅f(x1)⋅f(x2)=cF(X1),F(X2)⋅f(x1)⋅f(x2).
It shows the copula density function c(u1,u2) separates the joint
distribution function f(x1,x2) from its marginal probability
distribution functions f(x1) and f(x2); therefore, it can
capture the probabilistic dependence between the two random variables x1
and x2 by quantifying the strength of the relationship between their
corresponding quantiles.
Acronyms and abbreviations.
SSMISSpecial Sensor Microwave Imager and SounderSSM/ISpecial Sensor Microwave ImagerDMSPDefense Meteorological Satellite ProgramMSSMultispectral scanner systemVNIRVisible to near infraredMODISModerate Resolution Imaging SpectroradiometerNIRNear infraredMIRMid-infraredPMWPassive microwavesESMRElectrically scanning microwave radiometerSMMRMulti-frequency Microwave RadiometerBWIBasin wetness indexWSFWater surface fractionAMSR-EAdvanced Microwave Scanning Radiometer - Earth Observing SystemNRTNear-real timeNSIDCNational Snow and Ice Data CenterDFODartmouth Flood ObservatoryMODIS-MWPMODIS near-real-time (NRT) water productCDFCumulative probability functionMNumber of vectors of microwave brightness temperatures BkNumber of nearest neighborsBBrightness temperature dictionaryfInundation fractionFInundation dictionarybobsObserved vector of brightness temperatureKNumber of nearest neighborsBsSub-dictionary of BFsSub-dictionary of FcVector of representation coefficientsf^Estimated inundation fractionWWeight matrixnNumber of frequency channelspDetection probability ∈(0,1)ℓ1& ℓ2Regularizations normsλ1 & λ2Regularization parameters
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported by the NASA Global Precipitation Measurement Program
under grants NNX13AG33G and NNX16AO56G. It was also partially supported by
NSF under the Belmont Forum DELTAS project (EAR-1342944) and the LIFE project
(EAR-1242458). The MODIS-MWP data over the Mekong Delta were kindly provided
by Dan Slayback from the NASA Goddard Space Flight Center. The first author would
like to thank Professor Robert Brakenridge for his advice on this research
during the AGU Fall Meeting 2015. Edited by:
M. McCabe Reviewed by: two anonymous referees
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