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  • View in gallery

    Examples of topographic variables in the Amazon (0°–5°S, 55°–60°W).

  • View in gallery

    Scheme of the datasets used in the downscaling procedure.

  • View in gallery

    (a) MODIS floodability index, (b) our topography-based index, (c) a visible observation from Google Earth, and (d) a flood water occurrence from Landsat for two regions (left and right) in Vietnam.

  • View in gallery

    Illustration of the downscaling procedures in the Amazon (0°–5°S, 55°–60°W).

  • View in gallery

    Transformation of the floodability index (the original GIEMS LR box is delimited by solid lines).

  • View in gallery

    Global probability inundation map from GIEMS-D3.

  • View in gallery

    Inundation dynamics for (a) October, (b) November, (c) December, (d) January, (e) February, (f) March, (g) May, and (h) June of the 1993/94 wet season over Llanos de Moxos in northern Bolivia (17°–12°S, 68°–62°W).

  • View in gallery

    Histogram of inundated area (%; from 0 to 1) over the Amazon basin (see Fig. 9).

  • View in gallery

    Inundation maps over the Amazon basin showing (top) mean min and (bottom) mean max for (left) GIEMS, (center) GIEMS-D15, and (right) GIEMS-D3.

  • View in gallery

    Left y axis shows time series from 1993 to 2007 of surface water extent (km2) over the Amazon basin (see Fig. 9) from GIEMS-D15 (max value), GIEMS-D15 (min value), GIEMS-D3, and GIEMS. Right y axis denotes river discharge (green) observed at Óbidos station (HYBAM data).

  • View in gallery

    Comparison between SAR-derived and GIEMS-D3 inundation maps over the Amazon. The GSWO inundation occurrence from Landsat is also represented.

  • View in gallery

    Confusion matrices for both inundation states, as shown in Fig. 11.

  • View in gallery

    MODIS-derived and GIEMS-D3 inundation maps, for January and October 2006, over the Inner Niger Delta. A map in the visible wavelength (from Google Earth) is also provided for comparison purpose, together with the GSWO from Landsat.

  • View in gallery

    (a) Landsat, (b) MODIS, (c) SAR, (d) GIEMS-D3, (e) Google Earth, and (f) GSWO view over the Mekong River for a spring month (around May).

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A Global Dynamic Long-Term Inundation Extent Dataset at High Spatial Resolution Derived through Downscaling of Satellite Observations

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  • 1 LERMA/Observatoire de Paris, UPMC, CNRS, Paris, France
  • | 2 Columbia Water Center, Columbia University, New York, New York
  • | 3 Estellus, Paris, France
  • | 4 Center for Limnology, University of Wisconsin–Madison, Madison, Wisconsin
  • | 5 Department of Geography, McGill University, Montreal, Quebec, Canada
  • | 6 Laboratoire d’Etudes en Géophysique et Océanographie Spatiale, Université de Toulouse, CNES, CNRS, IRD, UPS, Toulouse, France
  • | 7 Indo-French Cell for Water Sciences, Indian Institute of Science, Bangalore, India
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Abstract

A new procedure is introduced to downscale low-spatial-resolution inundation extents from Global Inundation Extent from Multi-Satellites (GIEMS) to a 3-arc-s (90 m) dataset (known as GIEMS-D3). The methodology is based on topography and hydrography information from the HydroSHEDS database. A new floodability index is introduced and an innovative smoothing procedure is developed to ensure a smooth transition, in the high-resolution maps, between the low-resolution boxes from GIEMS. Topography information is pertinent for natural hydrology environments controlled by elevation but is more limited in human-modified basins. However, the proposed downscaling approach is compatible with forthcoming fusion of other, more pertinent satellite information in these difficult regions. The resulting GIEMS-D3 database is the only high-spatial-resolution inundation database available globally at a monthly time scale over the 1993–2007 period. GIEMS-D3 is assessed by analyzing its spatial and temporal variability and evaluated by comparisons to other independent satellite observations from visible (Google Earth and Landsat), infrared (MODIS), and active microwave (synthetic aperture radar).

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Filipe Aires, filipe.aires@obspm.fr

Abstract

A new procedure is introduced to downscale low-spatial-resolution inundation extents from Global Inundation Extent from Multi-Satellites (GIEMS) to a 3-arc-s (90 m) dataset (known as GIEMS-D3). The methodology is based on topography and hydrography information from the HydroSHEDS database. A new floodability index is introduced and an innovative smoothing procedure is developed to ensure a smooth transition, in the high-resolution maps, between the low-resolution boxes from GIEMS. Topography information is pertinent for natural hydrology environments controlled by elevation but is more limited in human-modified basins. However, the proposed downscaling approach is compatible with forthcoming fusion of other, more pertinent satellite information in these difficult regions. The resulting GIEMS-D3 database is the only high-spatial-resolution inundation database available globally at a monthly time scale over the 1993–2007 period. GIEMS-D3 is assessed by analyzing its spatial and temporal variability and evaluated by comparisons to other independent satellite observations from visible (Google Earth and Landsat), infrared (MODIS), and active microwave (synthetic aperture radar).

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Filipe Aires, filipe.aires@obspm.fr

1. Introduction

Wetlands and temporarily inundated areas are widely recognized to be of crucial importance for many aspects. For instance, 1) security and risk managements are highly dependent on inundations (Winsemius et al. 2015); 2) food security and rice paddy cultivation rely, in certain regions of the world, on surface inundation; 3) wetlands are an important component of the terrestrial water cycle and are crucial for water management; 4) wetlands represent 30% of the methane emissions (Ciais et al. 2013), a very powerful greenhouse gas for climate change; and 5) wetlands are host to ecosystems vulnerable to changes in hydrology. However, global distribution and dynamics at high spatial resolution are still not available to satisfy the needs of a large community of users, such as hydrologists, water and disaster managers, or climate scientists. Global, frequent, and high-resolution characterization of surface water extent is beyond the capabilities of current satellite observations.

Moderate Resolution Imaging Spectroradiometer (MODIS) observations have been used to derive global products every 2 days (http://oas.gsfc.nasa.gov/floodmap/), but of course, visible/infrared observations suffer from the presence of clouds (about 70% of Earth’s surface at any time) and vegetation. However, this type of data is of great value to the community to detect open water. In Yamazaki et al. (2015), a global water body map at 90-m resolution is proposed from Landsat imagery. This dataset exploits multitemporal acquisitions in order to delineate permanent from temporal water-covered areas. However, the full dynamics of the wetland maps is not proposed. Pekel et al. (2016) recently proposed a new dataset, Global Surface Water Occurrence (GSWO), also from Landsat but using more images, which allows it to better describe the dynamics and probability of occurrence. Two limitations are that Landsat measurements are sensitive to vegetation and cloud presence. Synthetic aperture radar (SAR) has the potential to retrieve inundations at high spatial resolution, as demonstrated by Santoro et al. (2010) using the Environmental Satellite (Envisat) Advanced Synthetic Aperture Radar (ASAR) or recently using the Sentinel-1 mission (Pham et al. 2016, manuscript submitted to Remote Sens. Environ.). However, the past or current availability of the data has not yet allowed for producing a global high-spatial-resolution inundation dataset. There is clearly a need to invest more time in retrieval algorithms and potentially perform data fusion in order to obtain a global, long-term, reliable, and high-resolution dataset of inundation extent. The NASA–CNES Surface Water and Ocean Topography (SWOT) mission, planned for launch in 2020, is specifically designed to provide high spatial resolution and temporal sampling of the continental surface waters (both height and area) (Prigent et al. 2016), thanks to an interferometric Ka-band radar (Rodriguez 2012). Meanwhile, efforts have to be pursued to provide the community with the best possible information about the spatial and temporal variations of these key variables.

A monthly-mean water surface extent has been derived at a low spatial resolution (0.25° × 0.25° equal-area grid) over a 15-yr period (1993–2007) by combining satellite observations in the visible, near-infrared, and passive/active microwaves (Prigent et al. 2007, 2012): the Global Inundation Extent from Multi-Satellites (GIEMS). At ~25 km, this dataset resolution is compatible with climate models and some global land surface models (Bousquet et al. 2006) or for regional applications (Papa et al. 2015), but it is certainly not suitable for local applications requiring higher spatial resolution. Before the launch of a dedicated mission such as SWOT, downscaling of the GIEMS dataset to a finer spatial resolution could provide a high-spatial-resolution estimation of the global water surface extent on a monthly basis. Furthermore, it will be seen in perspective that the downscaling of GIEMS could help extend the future high-spatial-resolution inundation datasets from SWOT or Sentinel-1 in the past.

Techniques to downscale inundation maps have been developed in the past. For instance, Schumann et al. (2014) developed a methodology to downscale model outputs from coarse to fine resolution. Global river flood risk assessment has also been performed by using a downscaling procedure of the water elevation/depth in order to obtain the hazard probability distributions (Winsemius et al. 2015). In general, downscaling procedures require ancillary information at high spatial resolution to disaggregate the coarse information to a better resolution. Two downscaling techniques of GIEMS have already been developed, using high-spatial-resolution observations from satellites, in the visible/infrared with MODIS (Aires et al. 2014) and in the microwaves with the SAR (Aires et al. 2013). However, visible/infrared observations are not exploitable under cloudy conditions and SAR observations are not yet available frequently all over the globe. To obtain a long-term global inundation estimate at high resolution, another source of auxiliary information has to be explored. Topography is naturally related to inundation potential and accurate digital elevation models (DEMs) derived from satellite radar observations are available globally. Fluet-Chouinard et al. (2015) adopted the Shuttle Radar Topography Mission (SRTM)-derived topographic information trained on a global land-cover map to produce an inundation probability map at 15-arc-s resolution (~500 m). The downscaled inundation map was then generated by distributing the inundated area of the coarse ~25 km GIEMS pixels among the corresponding ~500 m pixels having the highest probabilities of inundation, and a ~500-m resolution map of the minimum and maximum inundation extents at global scale (GIEMS-D15) has been calculated (http://www.estellus.fr/index.php?static13/giems-d15).

Here, we propose an evolution of this latest downscaling methodology, also based on topography information, with special attention to the optimization of the topographic variables and their use in an innovative neural network inundation probability model. A novel smoothing procedure is also put in place in order to avoid erroneous discontinuities in the high-resolution inundation patterns at the edges between low-resolution grid cells. The downscaling methodology is applied globally over 15 years of GIEMS data availability, with a monthly time step, to obtain a global and dynamic inundation dataset at even higher spatial resolution (~90 m). The method is tested over the densely vegetated basin of the Amazon River, over rice-growing regions in the Mekong region, and over the semiarid Inner Niger Delta.

Section 2 presents the databases used in this study. The downscaling technique is introduced in section 3. The main features and characteristics of the downscaled database are highlighted in section 4. Evaluation is presented in section 5 by comparing to other high-resolution inundation datasets. Finally, section 6 gathers the conclusion and the perspectives of this study.

2. Databases of water surfaces and topographic variables

a. GIEMS

A multisensor technique has been developed to estimate surface water extent and dynamics at the global scale (Prigent et al. 2007, 2012). It benefits from the complementary sensitivities of different satellite observations to surface characteristics (e.g., water, vegetation, and soil) to minimize limitations and uncertainties related to measurements by individual instruments. Passive microwave observations are particularly sensitive to the presence of surface water, even under vegetation canopy. However, additional observations have to be used to subtract, from the signal, the contribution of confounding factors, such as vegetation, and to avoid confusion with other surface types, such as dry sand. The following satellite observations were used to generate GIEMS:

  • passive microwaves from the Special Sensor Microwave Imager (SSM/I) measurements between 19 and 85 GHz;
  • active microwave backscattering coefficients at 5.25 GHz from scatterometers; and
  • visible and near-infrared reflectances and the derived NDVI.
The methodology is described in detail in Prigent et al. (2001). The passive microwave observations are processed to suppress the modulation of the signal by surface temperature and by atmospheric effects. The inundated pixels are identified with an unsupervised classification algorithm that merges the three sets of satellite observations and a mixture model that quantifies the fractional inundation in each pixel. The method is globally applicable without any tuning for specific environments. Note that the GIEMS estimates include all surface waters such as rivers, lakes, and rice paddies. The inundation is expressed as the fractional inundation within each 773 km2 pixel of the equal-area grid of 0.25° resolution at the equator. In this study, low-resolution (LR) boxes refer to this grid. Regional assessment of this database using SAR data indicates that the approach realistically captures wetland complexes but can underestimate small wetlands comprising less than 10% fractional coverage of a grid cell (<80 km2) or overestimate wetlands of more than 90% of fractional coverage because of its coarse spatial resolution. GIEMS is available to the scientific community (http://lerma.obspm.fr/spip.php?article91lang=en or http://www.estellus.fr/index.php?static13/giems-d15). It is widely used and has been thoroughly evaluated (see, e.g., Prigent et al. 2007).

b. GLWD

The Global Lakes and Wetlands Database (GLWD) from Lehner and Döll (2004) represents a comprehensive dataset of global surface water area, including small and large lakes, reservoirs, smaller water bodies, rivers, and a good representation of the maximum global wetland extent. GLWD was generated through a compilation and assimilation of existing maps and charts. It is considered to be the most extensive water mask of its kind (Nakaegawa 2012). The “level 3” dataset of GLWD used here provides a global 30-arc-s-resolution grid describing 12 different surface water types (Table 1). GLWD is adopted in this study for the training of the flooding probability.

Table 1.

The 12 inundation classes of GLWD. Classes 1–3 correspond to open water, 4–12 to wetlands.

Table 1.

In addition, it is used to help compensate for the underestimation of GIEMS for small water fractions. As mentioned, GIEMS does not detect well the water fraction below 10% of a pixel (see previous section). To partly compensate for this underestimation, when the surface of the permanent water bodies (sum of classes 1–3 in Table 1) within a GIEMS pixel is higher than the GIEMS predicted surface water, the GIEMS value for that pixel is replaced by the GLWD corresponding fractional inundation [this idea was already used in Fluet-Chouinard et al. (2015)].

c. HydroSHEDS topography and hydrography dataset

The Hydrological Data and Maps Based on Shuttle Elevation Derivatives at Multiple Scales (HydroSHEDS) project (http://www.hydrosheds.org) provides a DEM and a suite of hydrographic parameters derived from the SRTM dataset at resolutions ranging from 3 arc s to 5 min, in a consistent format from 56°S to 60°N (Lehner et al. 2008). The HydroSHEDS hydrologic conditioning smooths sampling errors that otherwise interrupt flow and hydrographic connectivity in the original SRTM DEM. High-resolution (HR) pixels will refer to the 3-arc-s pixels of the HydroSHEDS grid. This resolution will be used in the following for the GIEMS-D3 downscaled product. HydroSHEDS also provides a flow direction dataset (derived from the DEM) that indicates, for each HR pixel, the direction of the steepest descent. North of 60°N latitude, the dataset is supplemented with the HYDRO1k database (USGS 2016), an older global DEM at 1-km resolution. The topographic information is therefore much coarser in these boreal regions. Tests have been conducted using HYDRO1k instead of HydroSHEDS, and downscaling results seem to be robust.

A total of 11 variables were computed from HydroSHEDS hydrography and topography. Our downscaling methodology makes use of the following variables:

  • Flow accumulation. The global flow accumulation provides the number of contributing upstream pixels to any pixel in the map.
  • Slope. The flow direction in HydroSHEDS provides the steepest descent direction for each HR pixel. The slope at each pixel is defined as the elevation difference in this steepest-descent direction.
  • Distance and elevation difference from the nearest river. River pixels were defined with flow accumulation values exceeding a certain threshold. In this study, three different thresholds were used: 500, 10 000, and 100 000 HR contributing pixels (i.e., in the flow accumulation sense). Those thresholds correspond to small, medium, and large rivers and result in nine different distance-based variables. Pixels with flow accumulation values over 500 represent 2.82% of all terrestrial pixels, pixels over 10 000 represent 0.67%, and pixels over 100 000 represent 0.21%.

For each HR pixel, the distances from and the elevation above the nearest river (of each size) can then be computed. Three variables per pixel and per river size are defined:

  • Distance to the nearest river, following the flow direction (denoted “distance to the nearest river” in this paper). It is defined as the number of pixels between the given pixel and the river, following the flow direction. Figure 1a represents this variable over a 5° × 5° zone in the Amazon basin.
  • Elevation over the nearest river, following the flow direction.Figure 1b represents this variable in the same Amazon basin. The elevation difference from a river efficiently supplements the distance information: a pixel close to a river following the flow directions is more likely to be inundated if it is rather low above the river.
  • Absolute (or geodesic) distance to the nearest river.Figures 1c and 1d represent this variable in the Amazon basin. This distance and the previously defined distance play complementary roles in the relationship between a pixel and the river network. The closest river in the sense of the geodesic distance is not always the closest river according to the flow directions. This is, for example, the case when there is a hill between the pixel and the closest river in the sense of the geodesic distance: the flow direction will lead to another river.
Fig. 1.
Fig. 1.

Examples of topographic variables in the Amazon (0°–5°S, 55°–60°W).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

Figure 1 gives an overview of the river networks, depending on the flow accumulation thresholds. The selection of different river sizes allows capturing the various scales of the hydrology network. The relations to the largest rivers (e.g., the geodesic distance represented in Fig. 1d) reflect the global aspect of the network, whereas the relations to smaller rivers (e.g., the geodesic distance represented on Fig. 1c) capture the local topographic information. This topographic information at three different spatial scales will allow the floodability index to provide a hierarchy of inundation at different scales.

3. Downscaling procedure

The downscaling procedure uses various datasets (see Fig. 2) and its methodology, broadly inspired by the approach of Fluet-Chouinard et al. (2015) (with several improvements that will be presented below), follows three consecutive steps:

  1. A statistical model is first trained to predict the state of an HR pixel (flooded or not flooded) given its topographic variables. The output of this model is a static floodability index representing an estimate of the probability for the HR pixel to be flooded.
  2. For each LR box, the GIEMS database provides the fractional inundation from which the number n of HR flooded pixels is directly derived. The inundated HR pixels are simply chosen to be the n pixels within the LR box with the highest floodability index.
  3. A smoothing procedure was applied to prevent the appearance of edges and discontinuities at the border between adjacent LR boxes.
  4. A topography-based extrapolation scheme was finally used to retrieve inundation along the coast without the ocean contamination of the coarse satellite observations using in GIEMS.
The scheme of Fig. 2 synthesizes the several steps and datasets used in the downscaling approach of this study. All these components will be described in the following.
Fig. 2.
Fig. 2.

Scheme of the datasets used in the downscaling procedure.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

a. Floodability index model

First, for each HR pixel, we define a floodability index model estimating its probability to be flooded. A probabilistic framework is introduced. Let X be the vector of the topographic attributes of a given HR pixel and C its state from the GLWD classification: C = 1 if flooded according to GLWD, 0 otherwise. We assume that follows a random distribution. Using this probabilistic framework, a natural floodability index is
e1
This conditional probability can be modeled using an artificial feed-forward neural network (NN) with the vector of topographic variables x as inputs and the inundation probability estimate as output. NNs are universal approximators (Hornik et al. 1989) and can therefore estimate this function with an arbitrary precision (provided that enough neurons are chosen on the hidden layer and that enough samples are available; see appendix A).
The probability to be flooded, for a randomly selected pixel (among GLWD pixels) over the globe, is very small (i.e., the event is rare; here and in the following, curly brackets will be used for probabilistic events or ensembles of them). If the training dataset is built on randomly selected pixels, only a small fraction will be flooded and the network will tend to neglect them and consider them as noise. Training our network over a balanced dataset composed of 50% flooded and 50% dry pixels is therefore suggested. However, the NN might not estimate the conditional probability anymore if the training dataset is artificially balanced. Appendix B shows nevertheless that a neural network trained over a balanced dataset will estimate
e2
where is a probability measure, equivalent (in the sense of the measure theory) to , under which both realizations of C are equiprobable: . Is this new conditional probability useful for the downscaling? In fact, only the hierarchy induced by the floodability index matters for the downscaling. Appendix B shows that and are linked by a strictly monotone function that will induce the same hierarchy for the downscaling. Training the probability index network with a balanced dataset ensures that the neural network will not neglect the flooded areas, while providing a reliable floodability index.

The floodability index was modeled using an NN with one hidden layer of 10 neurons and one output neuron. All transfer functions are tan-sigmoids. The network output was linearly rescaled between 0 and 1 to obtain a probability estimation (see appendix A). The network is trained using binary outputs (inundated or not), but doing so will conduct the network to predict in its output a real value between 0 and 1 that estimates the probability to be flooded or not (Bishop 1996). This NN is trained using the Levenberg–Marquardt back-propagation algorithm over a balanced sample of 10 000 000 pixels randomly selected all over the globe (with 50% of inundated pixels).

b. Sensitivity of the floodability index to the topographic variables

It is not known a priori which of the topography variables are more important in determining the floodability of HR pixels. In Bwangoy et al. (2010), an analysis and variable selection is performed over the Congo basin. We carried out a similar evaluation of variables but at the global scale instead. We aim at a model that performs well at a global scale, so a study needs to be performed to identify the best topography information, on average, in every environment.

What are the more relevant topographic variables to define the floodability index described above? To answer this question, a “forward variable selection” is run to rank the variables (see Guyon and Elisseeff 2003). This procedure is executed as follows:

  1. The process starts with an empty variable set S.
  2. While S does not contain all the topographic variables, for each variable υ not in S, train an NN with inputs and whose targets are the states (flooded or not flooded) given by GLWD, and then add to the set S the variable υ that induces the smallest classification error: .
  3. Finally, S gives a ranking for the topographic variables that reflects their importance.
The resulting variable ranking is presented in Table 2, and it is optimized at the global scale so that it is the best compromise to link, globally, the topography and presence of inundation. The elevation over the nearest river plays a dominant role, well before the slope and the two types of distances (geodesic and following the flow). It is nevertheless interesting to note that the distance to the nearest river following the flow contributes more to the model than the geodesic distance, as expected since it more aptly represents the surface inundation dynamics. The mean-square error (MSE) in Table 2 is performed at a global scale and can therefore be misleading. A small decrease of MSE can be negligible at the global level but be significant regionally. A global MSE decrease can also hide that local errors increase. Therefore, verifications have been made to ensure that the global trend reflects also the local error variation.
Table 2.

Variable ranking using forward selection.

Table 2.

c. Evaluation and limitations of the floodability index

The downscaling procedure described in this study relies on the topography information. It was seen in the introduction that other sources of information on the inundation at high spatial resolution could be used instead, such as satellite observations from SAR or visible/infrared instruments, but that it was difficult to have a good spatiotemporal coverage with this type of data. The question is then, is topography information enough to describe complex hydrological systems and therefore accurately perform the downscaling at a global scale?

To answer this question, Figs. 3 (left and right) represent two different regions in Vietnam. Figure 3a represents the frequency of inundation given by MODIS visible/infrared observations using a detection algorithm similar to Sakamoto et al. (2007). Cloud contamination was reduced by using a cloud flag, and the floodability index from MODIS is defined as the inundation frequency over one year of data. The hydrologic network is well represented and is coherent with the visible image in Fig. 3d. The floodability index from the topography information (Fig. 3b) is in good agreement with the MODIS index. The similarities are striking in this natural environment, meaning that topography is a major control on inundation patterns, and that our floodability index of section 3a is able to exploit the topography information in an adequate manner. Figure 3d shows that the visible imagery confirms the good representation of the hydrology system in this region.

Fig. 3.
Fig. 3.

(a) MODIS floodability index, (b) our topography-based index, (c) a visible observation from Google Earth, and (d) a flood water occurrence from Landsat for two regions (left and right) in Vietnam.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

On the contrary, large discrepancies can be noted in the Fig. 3 (right) for another region in Vietnam. The river network is satisfactorily reproduced by the topography-based index, but the southwest and northeast regions have a too large floodability index, due to, for instance, a low elevation of HR pixels compared to their closest river. The southwest region is an extensive rice paddy area; its inundation is driven by man-made decisions and less by topography constrains. Furthermore, GIEMS is overestimating flooding here because of the saturation of the microwave signal in moisture-saturated soils. The surface water occurrence from Landsat (Pekel et al. 2016) is also represented for both regions. The spatial pattern is quite similar to MODIS retrieval, confirming the good GIEMS-D3 retrieval in the east of the region, but an overestimation of flooding in the west.

This comparison of MODIS and topography floodability indices is independent from the GIEMS database. It clearly shows that some (most) regions have natural inundation controlled by topography, but that other regions have an anthropogenic behavior with a hydrology more independent to the topography. The topography downscaling will be appropriate in the first case but not in the second one. This clearly shows the necessity to combine approaches when performing such an inundation downscaling at the global scale, in particular by using satellite data as in Aires et al. (2013, 2014).

d. Application of the floodability index to provide the high-resolution inundation maps

Figure 4b shows the resulting floodability index in the Amazon basin (0°–5°S, 55°–60°W), with very realistic fine structures related to the topography. The pixels located in the Amazon River get a floodability index close to 1 whereas pixels outside of it show much smaller values.

Fig. 4.
Fig. 4.

Illustration of the downscaling procedures in the Amazon (0°–5°S, 55°–60°W).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

Using the previously computed floodability index and the GIEMS estimates for a given month (shown in Fig. 4a), it is now possible to derive high-resolution inundation extents. The number of flooded HR pixels n within each LR box is first computed, given the inundation extents from GIEMS. The HR pixels are then ranked following their decreasing floodability index. The HR pixels with the highest floodability index are the n first inundated pixels. This procedure preserves exactly the coarse-resolution inundation extents of GIEMS LR boxes and respects perfectly the floodability hierarchy within each LR box. The GIEMS estimate for the Amazon basin for June 2000 is presented in Fig. 4a, along with the resulting downscaled product in Fig. 4c; it can, however, be noticed that the methodology induced significant edge effects between adjacent LR boxes (see, e.g., 56°W in longitude and 2.5°S in latitude). This discontinuity issue has to be solved.

e. Smoothing of the downscaled inundation map

1) Smoothing procedure

A smoothing procedure has to be developed to remove the edge effects present in Fig. 4c. As any smoothing procedure, the original data are modified, but the objective of the methodology presented here is to preserve as much as possible the initial water extent from GIEMS, while ensuring a smooth transition in the HR pixel maps.

The simpler solution is to smooth out directly the GIEMS inundation by reallocating inundated area across adjacent LR boxes, based on their communal floodability index distribution. This is, for instance, the solution used in Fluet-Chouinard et al. (2015) (i.e., the moving-window thresholding). This solution has two limitations. First, in order to obtain a smooth enough inundation map, the smoothing might require one to reallocate inundation quite far from its original LR box. Second, the smoothing of the LR box inundations does still not warrant in all cases that the HR pixels will have a smooth transition from an LR box to another.

To limit these two issues, a novel smoothing procedure is introduced here based not on the smoothing of the LR inundation boxes, but on the smoothing of the floodability index used in the downscaling process (Fig. 4b). The floodability index is transformed by multiplying it with a coefficient that depends on the distance to the center of the original LR box. Figure 5 presents this process:

  • Figure 5a shows the original floodability index. The GIEMS pixel to be downscaled is indicated (black square).
  • Figure 5b shows the smoothing coefficient by which the floodability index will be multiplied. This coefficient is equal to 1 on the circumscribing disk of the pixel. Outside of the disk, this coefficient decreases following , where r is the distance to the disk and is the width of the LR box.
  • Figure 5c presents the transformed floodability index, obtained by multiplying the floodability index of Fig. 5a with the coefficient of Fig. 5b.
This spatial convolution of the floodability index is compatible with the nature of the satellite observations used in GIEMS, with the fields of view of the satellite instruments having typical Gaussian patterns with energy coming also from outside the delimited LR box.
Fig. 5.
Fig. 5.

Transformation of the floodability index (the original GIEMS LR box is delimited by solid lines).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

The surface water of a given LR box is not exclusively allocated inside the box, but can also be allocated outside. Water surfaces can now be allocated outside of the initial LR box if the floodability index is high enough, but the process favors reallocation of the water surfaces in the close neighborhood of the initial pixel. However, the HR pixels neighboring the initial LR box can already be inundated from reallocation by a neighboring box, and this raises a new problem. To avoid this issue, the smoothing procedure follows two steps:

  1. For each LR box p with inundation extents , the transformed floodability index around box p is used to allocate the water . During this allocation, the HR pixels of the neighbor LR box are not taken into account if they are already inundated. After this step, only the water surface within box p is kept. Only a water surface is allocated inside the box: the surface remains to be allocated.
  2. After this first step, each LR box is considered one by one again. For each box p, the remaining water surface is allocated, over the p and its neighboring boxes, using the transformed floodability index in addition to the surface water allocated during the first step. In this way, no inundated surface is lost or is artificially generated.

2) Evaluation of the smoothing procedure

The smoothing procedure induces obvious disagreements between the original low-resolution dataset and the new high-resolution database (when upscaled to the low resolution). Even if the total inundation surface remains constant in our smoothing scheme, the reallocation of inundation among LR boxes needs to be investigated. The absolute value of the difference of inundation surfaces from the reallocation has been computed for each LR box and then reported as a proportion of the total box area. Table 3 shows that the reallocation fraction remains under 5% for more than 85% of the LR boxes, and only 7% of the inundated LR boxes have a difference higher than 10%. The disagreements can therefore be considered as admissible because the reallocation fractions remain (for a huge majority) below the incertitude of GIEMS estimates.

Table 3.

Distribution of the reallocation differences introduced by the smoothing procedure. The disagreements are measured as the inundation surface difference, in absolute value, reported as proportion of the LR box area.

Table 3.

4. A new global dynamic long-term inundation extent dataset at high spatial resolution derived through downscaling of satellite observations

In this section, results are presented to illustrate the characteristics of GIEMS-D3: its spatial resolution at 3 arc s (i.e., 90 m), global spatial coverage, monthly time resolution, and long-term duration from 1993 to 2007.

a. Inundation probabilities

Downscaling of each month of the 1993–2007 period results in 180 monthly maps of inundation, which, when combined, reveal the frequency of inundation of each pixel during that period. Figure 6 represents this frequency of inundation at the global scale and at the 90-m resolution. The major global floodplain regions appear clearly: the large hydrologic network in the Amazon, the dense river system in northeast India, or the big lakes in the United States or Canada. More subtle hydrological systems are harder to observe in such a global map, as it is not easy to perceive the level of detail in GIEMS-D3 from this figure. Therefore, five zooms over interesting basins were added in the figure: Mississippi, Ob, Okavango, Sudd, and South America. These zooms are performed at two spatial scales to illustrate the GIEMS-D3 spatial resolution. Regions have been chosen to be contrasted: some with high vegetation (Amazon) and others with less (Okavango); some that suffer from frequent cloudiness (Amazon) and others that do not (Okavango); some with high-elevation contrast (Sudd) and others that are quite flat (Amazon); and most with a natural hydrology, yet others such as the Mississippi that are controlled by humans.

Fig. 6.
Fig. 6.

Global probability inundation map from GIEMS-D3.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

b. Dynamic behavior

Compared to GIEMS-D15, this new database is dynamic, with a monthly-time-scale resolution. Figure 7 shows the evolution of the inundation for the 1993/94 wet season over a region in South America. The inundation frequency map in the same region was represented in Fig. 6, but Fig. 7 shows the smooth transition of the inundation spatial pattern, from month to month. The hydrological network is well respected but the seasonality is strong and coherent. No discontinuity can be noted between the LR boxes. Note that 1) this inundation retrieval is performed in a high vegetation environment and high cloud cover, so no visible/infrared information could be used here (such as MODIS data) to obtain such temporal dynamics, and 2) no repetitive SAR information is available in this region. GIEMS-D3 is able to exploit the multisatellite LR inundation estimates from GIEMS and downscale them at very fine spatial resolution (3 arc s or 90 m) in a coherent way.

Fig. 7.
Fig. 7.

Inundation dynamics for (a) October, (b) November, (c) December, (d) January, (e) February, (f) March, (g) May, and (h) June of the 1993/94 wet season over Llanos de Moxos in northern Bolivia (17°–12°S, 68°–62°W).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

5. Evaluation of the downscaled product

a. Comparison with GIEMS and GIEMS-D15 over the Amazon basin

The GIEMS-D3 results are first compared to the GIEMS original dataset and its first downscaled version (D15). The coherency of GIEMS-D3 with GIEMS has been evaluated at the global scale, but in this section, results are presented over the Amazon basin to facilitate their representation (see spatial domain in Fig. 9). In Fig. 8, the histogram of inundated area is represented: the number of high-resolution pixels with lower inundation areas (up to 10%) are largely increased due to the correction of GIEMS with the permanent bodies from GLWD (see section 2b).

Fig. 8.
Fig. 8.

Histogram of inundated area (%; from 0 to 1) over the Amazon basin (see Fig. 9).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

Figure 9 represents the spatial inundation extent over the Amazon basin considered in this section, for the mean minimum (Fig. 9, top) and mean maximum (Fig. 9, bottom), for the GIEMS, GIEMS-D15, and GIEMS-D3 databases. Again, it can be noticed that GIEMS-D3 (as well as GIEMS-D15) includes many more LR boxes with low inundated area (<10%). As a consequence, some smaller hydrological features have appeared. This is true for both the mean, minimum, and maximum maps. However, the overall inundation map of GIEMS is preserved in the D3 version, meaning that the downscaling procedure developed in this paper follows well the original estimates. GIEMS-D3 seems to present fewer linear edges and an overall smoother hydrological representation than the GIEMS-D15 version. It appears that GIEMS-D3 presents a smoother inundation surface while reallocating less area than GIEMS-D15 because of the newer reallocation method (see section 2e).

Fig. 9.
Fig. 9.

Inundation maps over the Amazon basin showing (top) mean min and (bottom) mean max for (left) GIEMS, (center) GIEMS-D15, and (right) GIEMS-D3.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

The time series of surface water extent (km2) over the Amazon basin are presented in Fig. 10 for the GIEMS, GIEMS-D15, and GIEMS-D3 datasets. Since GIEMS-D15 has no monthly dynamics, only the constant mean minimum and maximum values are shown. This figure demonstrates the advantage of dynamical GIEMS-D3 data over the static version GIEMS-D15. The seasonal and interannual dynamics of GIEMS are well preserved by GIEMS-D3. A positive bias is obvious, which corresponds to the GLWD correction of GIEMS, as mentioned previously. The GIEMS-D3 and GIEMS-D15 minima and maxima are close; differences result from a different GLWD correction of GIEMS in the D3 and D15 versions. Furthermore, if the maximum number of inundated pixels over all the months of the record were counted, we would achieve similar results as the GIEMS-D15 maximum of about 400 000 km2. The river discharge is also represented in Fig. 10. We used the in situ monthly discharges observed at Óbidos, Brazil, which is the closest gauge to the mouth of the river (800 km from the ocean) and available for 1993–2007 at the Environmental Research Observatory (ORE) Geodynamical, Hydrological and Biogeochemical Control of Erosion/Alteration and Material Transport in the Amazon Basin (HYBAM) website (http://www.ore-hybam.org/). The correspondence between GIEMS-D3 surface area and this river discharge is very good, with a 0.89 correlation with a 1-month time lag.

Fig. 10.
Fig. 10.

Left y axis shows time series from 1993 to 2007 of surface water extent (km2) over the Amazon basin (see Fig. 9) from GIEMS-D15 (max value), GIEMS-D15 (min value), GIEMS-D3, and GIEMS. Right y axis denotes river discharge (green) observed at Óbidos station (HYBAM data).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

Figures 810 illustrate the benefits of GIEMS-D3: correction of GIEMS with added information from GLWD, spatial coherency with the original GIEMS, and preservation of the monthly temporal dynamics. All these advantages are available at the high spatial resolution (90 m).

b. Evaluation over the Amazon basin using two SAR images

Hess et al. (2003) used SAR imagery to obtain an inundation mapping of the Amazon basin at approximately 100-m resolution. Two inundation states are available: low-water stage (data acquisition between August and September 1995) and high-water stage (data acquisition between May and August 1996). To evaluate the downscaling accuracy, GIEMS-D3 maximum (between August and September 1995) and minimum (between May and August 1996) have been estimated in its 3-arc-s resolution. Figure 11 compares the SAR-derived inundation map from Hess et al. (2003) and the downscaled inundation maps for both inundation states. It shows that both maps (SAR derived and downscaled) have the same geographical patterns. The difficulties of GIEMS to detect small inundation surfaces (less than 10% of a LR box) are flagrant here: there are many more small rivers on the SAR-derived maps. However, it can also be noted that the SAR estimates have numerous isolated inundated HR pixels. Those are likely instrument noise and speckles inherent in this kind of satellite observations. Part of the difference between the downscaled and SAR estimates is assumed to be related to this SAR noise.

Fig. 11.
Fig. 11.

Comparison between SAR-derived and GIEMS-D3 inundation maps over the Amazon. The GSWO inundation occurrence from Landsat is also represented.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

The GSWO inundation occurrence from Pekel et al. (2016) is also represented in Fig. 11 for comparison. The main hydrological structures are very similar. Finer hydrological structures can be observed with GSWO in regions where the inundation fraction is low. This was to be expected since GIEMS can miss inundation when the water fraction is lower than ~10% (Prigent et al. 2007). However, the Landsat visible observations essentially retrieve the open water. Therefore, the GIEMS estimate is more likely to describe the full seasonal variations, even under vegetation, and as a consequence, the inundation extent is higher for GIEMS-D3.

Table 4 shows that the total inundated surfaces of both inundation maps (SAR derived and downscaled) are close. The major difference is observed for the high-water period where the SAR estimate gives 22.5% additional inundated surface. This is not due to the downscaling algorithm but is rather caused by GIEMS/SAR differences (Aires et al. 2013).

Table 4.

Total inundation surfaces over the Amazon basin (0°–8°S, 54°–72°W) for the SAR-derived and GIEMS-D3 inundation maps

Table 4.

Rather than comparing absolute values, classification errors can be interpreted using confusion matrices [for a precise definition of their values, see Powers (2011)]. Figure 12 provides the confusion matrices for the SAR-based and the downscaled GIEMS-D3 classification. The true positive rates and the positive predictive values are close to 50% for both cases: this means that when a classifier (SAR based or downscaled) classifies a pixel as flooded, the other classifier will classify it as flooded 50% of the time. The matrices show also that when a pixel is classified as dry by a classifier, it will be labeled as dry by the other one 9 times out of 10. The Cohen’s kappa between both classifiers (Cohen 1960) is for the low-water and for the high-water stage. Those values are generally considered as a moderate agreement between classifiers (Landis and Koch 1977). Therefore, the two classifications do not agree perfectly, and this is to be expected:

  1. The two inundation classifications use different and independent satellite observations. The SAR estimates are actually a composite image over several months whereas the downscaled map is for a particular month.
  2. SAR estimate is not perfect (due to the limitation of the classification scheme, the ambiguity of the observation or instrumental noise).
  3. The uncertainties related to GIEMS are about 10%. As a consequence, confusion matrices show a moderate agreement mostly because of the GIEMS/SAR disagreement, not because of a specific problem with the downscaling scheme.
The two inundation states in Fig. 11 show that the downscaling is performing well and the hydrological structure is well represented and similar in both cases.
Fig. 12.
Fig. 12.

Confusion matrices for both inundation states, as shown in Fig. 11.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

c. Evaluation over the Inner Niger Delta using MODIS data

The downscaled database is here compared to the wetland mapping from Bergé-Nguyen and Crétaux (2015) over the Inner Niger Delta. This mapping is derived using satellite optical observations from MODIS. This classification is available from 2000 to 2013 at an 8-day temporal resolution and approximately 500-m spatial resolution. Figure 13 shows both MODIS-derived and downscaled inundation maps during the dry and the wet season. The downscaled map differs significantly from the MODIS-derived map for two reasons. First, the low-resolution dataset (GIEMS) is overestimating the inundation surface during the wet season. Second, the spatial pattern of the inundation differs significantly. This is due to the fact that the floodability index does not reproduce the spatial patterns of the MODIS observations. It means that for this region, the topographical information is not sufficient to derive the inundation location in agreement with regional satellite observations. Even if the topography plays a preponderant role in the geographical distribution of wetlands, additional information (e.g., wetlands with no drainage, rice paddies, or presence of marshes) is sometimes needed to provide an accurate mapping of inundations at high spatial resolution. The Google Earth visible image shows well that vegetation is associated with the maximum extent of the hydrological structures from MODIS or GIEMS-D3. The GSWO inundation occurrence from Pekel et al. (2016) is also represented in Fig. 13. Again, the Landsat imagery appears to detect mainly open water, and the seasonality is rather limited.

Fig. 13.
Fig. 13.

MODIS-derived and GIEMS-D3 inundation maps, for January and October 2006, over the Inner Niger Delta. A map in the visible wavelength (from Google Earth) is also provided for comparison purpose, together with the GSWO from Landsat.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

d. Evaluation over the Mekong River using SAR, MODIS, and Landsat data

To further evaluate the GIEMS-D3 inundation dataset, Fig. 14 shows the inundation pattern over the Mekong River for a spring month (around May, depending on availability). It was already seen in Fig. 3 that the floodability index used to perform the downscaling is not reliable over this region mainly due to standing water not related to topography, such as rice paddies. It is also known that the GIEMS dataset might overestimate the inundation area in tropical moisture-saturated soils (Adam et al. 2010).

Fig. 14.
Fig. 14.

(a) Landsat, (b) MODIS, (c) SAR, (d) GIEMS-D3, (e) Google Earth, and (f) GSWO view over the Mekong River for a spring month (around May).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0155.1

A Landsat image for that month was obtained because enough noncloudy pixels could be compiled together. Obtaining continuous observations is clearly a challenge for this instrument. Large hydrological features such as wide rivers and canals can be observed, in good agreement with the Google Earth visible image. MODIS suffers from cloud and vegetation contamination as well, and its spatial resolution is coarser. Large hydrological structures are also observed but some details are missed compared to the Landsat image. A large structure in the northeast part of the region is observed with MODIS but not with Landsat. The canals (i.e., linear structures) are not detected; this is obviously a limitation of the MODIS 500-m pixel resolution.

The SAR estimates have very high spatial resolution and are less sensitive to vegetation and cloud contamination. However, before the launch of the Sentinel-1 satellite in April 2014, only scarce estimates (in time and space) were available from the Envisat SAR, for instance. The SAR is able to detect well the linear features corresponding to the man-made canals. More details are present, but isolated pixels can also be related to speckle noise. Larger inundation is being seen by the SAR than by the Landsat estimates, possibly because Landsat was not able to see through vegetation and therefore detected mostly open water.

Finally, GIEMS-D3 retrieves well the big river structures, but with an overestimated width. Using microwave observations, GIEMS can detect standing water through vegetation, but it is also known that GIEMS can overestimate inundation (Adam et al. 2010). The canals are not retrieved, meaning that the SRTM DEM from HydroSHEDS is not describing these features. Newly available DEMs could improve the downscaling, but there is no DEM yet able to resolve correctly such small irrigation canal systems. Large structures similar to what was obtained with MODIS can also be observed in the northeast part of the region.

6. Conclusion and perspectives

In this paper, we developed an extension of the downscaling technique presented in Fluet-Chouinard et al. (2015) based on topographic and hydrologic information from the SRTM/HydroSHEDS dataset. A number of modifications and refinements to the method were made: 1) additional input variables were taken into account, 2) the floodability index is given by a nonlinear NN model that estimates the inundation probabilities from the topography information, 3) the smoothing procedure that ensures a smooth transition between the low-resolution boxes has been improved, and 4) a topography-based extrapolation scheme was used to retrieve inundation along the coasts without the ocean contamination of the coarse satellite observations used in GIEMS. The downscaled GIEMS-D3 is expected to be of good quality where the original GIEMS is of good quality (inundated fractions higher than 10% and lower than 90%) and in regions where inundation is controlled by topography. The new downscaling technique is robust enough to downscale the full dynamical record of the GIEMS dataset at the monthly scale, from 1993 to 2007, to the high spatial resolution of 3 arc s. This GIEMS-D3 dataset is the first global long-term and dynamical dataset at such high spatial resolution (90 m).

As any surface product, it is difficult to validate such a dataset because of the lack of in situ data or reliable and independent satellite data. To evaluate GIEMS-D3, we first evaluated the topography-based floodability index to show that it is reliable in natural and topography-driven hydrology domains (such as in the Amazon, observed by SAR), but not adequate for human-influenced regions (e.g., Vietnam rice paddies, observed using MODIS data) or more complex hydrologic systems (e.g., Inner Niger Delta also observed by MODIS data). Evaluation was also performed using a suite of datasets in the visible [Google Earth, official Landsat product, and GSWO from Pekel et al. (2016)], the active microwave of SAR from Hess et al. (2003) and Pham et al. (2016, manuscript submitted to Remote Sens. Environ.), and the visible and near infrared from MODIS (Bergé-Nguyen and Crétaux 2015; Pham et al. 2016, manuscript submitted to Remote Sens. Environ.). The downscaled product compares well to the static GLWD dataset and its dynamics reproduce perfectly, by design, the temporal behavior of GIEMS that has been widely evaluated and exploited in literature (Papa et al. 2015; Zhuang et al. 2015; Ringeval et al. 2010). However, the downscaling technique is not designed to correct the GIEMS estimates, so any errors in the original low-spatial-resolution version of GIEMS will be inherited in the downscaled product.

Perspectives are numerous. First, for anthropized environments or when the terrain is flat or the hydrological structure is not controlled by elevation (as in the Inner Niger Delta), other sources of information should be used to improve upon our current approach. We have seen that MODIS visible/infrared observation or active microwave SAR data can be exploited to retrieve surface inundations. This type of information has already been used to perform the downscaling of GIEMS: see Aires et al. (2014) for the exploitation of SAR information with an image processing downscaling approach based on a neighboring system and Aires et al. (2013) for a PCA-based representation of inundation patterns derived from a MODIS record and used to downscale GIEMS. The fact that the two approaches (i.e., topography or use of independent high-spatial-resolution satellite datasets) exploit a floodability index should facilitate the fusion of these two sources of information into a unique, optimized, and global dataset. It would be possible to benefit from the data fusion of GIEMS-D3 and other independent datasets such as the Landsat ones (Yamazaki et al. 2015; Pekel et al. 2016).

There are several ways we can exploit new satellites to further develop GIEMS. First, the current GIEMS processing requires a large range of ancillary datasets, and GIEMS is so far limited to 2007 because of the lack of one source of information. Efforts are underway to develop a methodology that will depend upon a reduced number of data sources. This will allow producing a climate quality record from 1978 to present, based primarily on carefully intercalibrated observations from SMMR, SSM/I, and SSMIS observations. GIEMS-D3 can be used to support or be combined with data from recent missions such as Sentinel-1 and Sentinel-2 (Pham et al. 2016, manuscript submitted to Remote Sens. Environ.), or to prepare future missions such as SWOT (Rodriguez 2012; Prigent et al. 2016). It should help identify interesting validation campaigns, assess the sensitivity of hydrology models to this kind of high-resolution data (e.g., assimilation experiments to estimate river discharges), feed the SWOT simulator, or measure signal-to-noise ratio constraints. Furthermore, GIEMS-D3 could be calibrated on the SWOT or Sentinel inundation estimates (when they will be available) in order to extend, into the past (back to 1978), the recent but limited available record. Other DEMs could be used instead of or in combination with HydroSHEDS, for instance, the newer version of SRTM at 30-m resolution. It should be noted that the comparison of GIEMS-D15 (450 m) and GIEMS-D3 (90 m) showed the robustness of the downscaling methodology, but it is expected that higher-resolved DEMs can lead to better downscaled products. It should be noted that new DEM can also correct some artifacts. Future DEM versions may include corrections from artifacts, vegetation noise, or tree heights (e.g., Simard et al. 2011). They will be adopted in the further GIEMS downscaling versions.

Applications using GIEMS-D3 are numerous, including estimation of flood risks for insurance purposes or security alert systems, water management, and ecology (particularly important for natural wetlands that shelter very sensitive animal species). GIEMS-D3 can also be used as a forcing for global or regional hydrology models that aim to increase their spatial resolution (Wood et al. 2011). Inundation extent can also be used to estimate water volume changes (Papa et al. 2013; Frappart et al. 2012) and river width (Yamazaki et al. 2014) and to exploit this information in hydrology models to estimate river discharges (Decharme et al. 2012). The exchange of freshwater between continents and the ocean is one of the most important indicators of the water cycle.

Acknowledgments

The authors thank NASA for their support at Columbia University for the project entitled “Downscaling of flooded fraction derived from low-resolution microwave measurements” (Contract NNH13CH27C) led by John Galantowitch at AER, Inc. We would also like to thank the French spatial agency [Centre National d’Études Spatiales (CNES)], and in particular Selma Cherchali, for funding in 2012/13 a study related to this work, in the framework of the SWOT mission. We are grateful to Simon Munier and Pierre Gentine for interesting discussions. The MODIS inundation dataset was provided by Bergé-Nguyen and Crétaux (2015), and the SAR data in the Amazon come from Hess et al. (2003). Images from the Global Surface Water Occurrence (Landsat) are courtesy of the European Commission Joint Research Centre; we thank Jean-François Pekel and colleagues for making them available. We thank also three anonymous reviewers for their help and comments, which helped significantly in the improvement of this manuscript.

APPENDIX A

Posterior Probability Estimate Using Neural Network Classifier

Consider the random variable couple , where X is a vector and (in our case, X corresponds to the topographic variables and C to the class, flooded or not, of a given pixel). We want to predict given a vector x, the corresponding class c. To do so, consider a neural network classifier that takes x as input and whose output is obtained when the network weight is adjusted to minimize the square-error cost function:
eq1
where is a training set of independent, identically distributed (iid) realizations of .
Because of the iid assumption, the law of large numbers guarantees that converge almost surely to
eq2
By applying the “tower property” of the conditional expectation (where indicates statistical expectation),
eq3

Note that y appears only in the first member of the last sum. Hence, is minimal when . Feed-forward neural networks with as few as one hidden layer are universal approximators (see Hornik et al. 1989). That means that y can approximate the function to any desired degree of accuracy on the condition that the network has enough neurons on his hidden layer.

More information about the estimation of posterior probabilities using neural networks can be found in Richard and Lippmann (1991).

APPENDIX B

Probability Estimates over Balanced Datasets

When the training set is balanced, the empirical risk becomes
eq4
where and are composed of randomly selected pixels within the dry and flooded ones, respectively. This risk converges almost surely to
eq5
Here, the minimizer of is not as in appendix A. However, we can show that this minimizer is in fact , where is a probability measure, equivalent to , which verifies . We note and . Let us define the random variable
eq6
Z verifies and , and we can therefore define , which is a new probability, equivalent to . We have . This new probability equilibrates the distribution of C. We compute now
eq7
Therefore, the minimizer of is . We can now show that both posterior probabilities are linked by a strictly monotone function:
eq8
where is a strictly monotone function.

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