# A New Surface Waters Downscaling Approach Applicable at Global Scale

Thu-Hang Nguyen, Filipe Aires

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## To cite this version:

Thu-Hang Nguyen, Filipe Aires. A New Surface Waters Downscaling Approach Applicable at Global Scale. Remote Sensing, 2024, 16 (24), pp.4664. 10.3390/rs16244664. hal-05375538

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Article

# A New Surface Waters Downscaling Approach Applicable at Global Scale

Thu-Hang Nguyen †,(1) and Filipe Aires *,†,(2) ID

(1) LERMA, Observatoire de Paris, Sorbonne Université, PSL University, CNRS, F-75014 Paris, France;
codemau@gmail.com

(2) CNRS, LIRA, Observatoire de Paris, Sorbonne Université, PSL University, F-75014 Paris, France;
filipe.aires@obspm.fr

* Correspondence: filipe.aires@obspm.fr

† These authors contributed equally to this work.

**Abstract:** A surface water extent downscaling framework was developed in the past using a floodability index based on topography. We presented here a new downscaling approach including several improvements. (1) The use of a new Floodability Index (FI), including better integration of auxiliary permanent waters (i.e., presence of water during the whole time record). By using this updated FI, the new downscaling became a true data-fusion with permanent water databases originating mainly from visible observations. (2) Some discontinuities between low resolution cells have been reduced thanks to a new smoothing algorithm. (3) Finally, a coastal extrapolation scheme has been presented to deal with coarse resolution data contaminated by the ocean. This new and complex downscaling framework was tested here on the GIEMS (Global Inundation Extent from Multi-Satellite) database but the approach is generalizable and any surface water database could be used instead. It was shown that this new downscaling procedure (including several processing steps, algorithms and data sources) is a significant improvement compared to the previous version thanks to the new floodability index and the downscaling processing chain. Compared to the previous version, the downscaling results (GIEMS-D) were more coherent with the permanent water database and preserved better the original low-resolution information (e.g., mean sea level error water fraction (0-1) of 0.0041 for the old version, and 0.0018 for the new version, over flooded areas in the Amazon). GIEMS-D has also been evaluated at the global scale and over the Amazon basin using independent datasets, showing an overall good performance of the downscaling.

**Keywords:** surface water; wetlands; downscaling

## 1. Introduction

Passive and active microwave measurements can be used to detect and observe surface water below vegetation due to their penetrative ability. However, while there exist some comprehensive datasets with global and long-term coverage from passive microwave products (e.g., the Global Inundation Extent from Multi-Satellites (GIEMS) [1–3] or the Surface Water Microwave Product Series (SWAMPS) [4]), so far, there has not been any such dataset from the active microwave or Synthetic Aperture Radar (SAR) products. SAR data application towards a global scale is yet at the analysis stage for building prototype techniques, over some locations [5–7]. High-quality datasets at the global scale may be generated from remote sensing data in combination with other information sources (e.g., the Global Dataset of Lakes and Wetlands (GLWD) [8]), but they are often a static product that do not provide water dynamic information. Surface water data from passive microwave products, therefore, is currently the only choice for monitoring surface water globally, beneath vegetation, over long time periods [19]. However, these datasets are provided at poor spatial resolutions. To be employed for applications requiring high resolution, they

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**Citation:** Nguyen, T.-H.; Aires, F. A
New Surface Waters Downscaling
Approach Applicable at Global Scale.

*Remote Sens.* **2024**, *1*, 0.

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4.0/).
need to be downscaled. Downscaling not only allows for more detailed surface water observation but also paves the way to data-fusion with other high-resolution datasets [9].

Several downscaling approaches have been proposed for surface water, but most of them focused on regional areas [10–12]. Ref. [13] produced a high-resolution flood-potential map over the Mississippi-Missouri confluence from elevation, land-cover, and historic flood extent data to downscale the inundation map of the great flood of 1993, derived from passive microwave observation of the SSM/I. For another severe flood, also in the Mississippi basin, ref. [14] downscaled the inundation map derived by MODIS from 500 m to 30 m using SRTM DEM. Water was allocated from low- to high-elevation 30 m pixels, until the accumulated water area equals the low-resolution measurement. While some studies use topography information for downscaling, such as the two above-mentioned, others can be based on statistical strategies. Ref. [10] developed an image-processing technique that used 500 m SAR-derived minimum and maximum water extent maps as reference to increase the resolution of a 0.25° (25 km at equator) dataset (GIEMS) over the Amazon basin. In arid areas where surface water is less obscured by clouds and vegetation, high-resolution optical data can be useful for downscaling low-resolution data. Accordingly, ref. [11] performed a principle component analysis on a time-series of MODIS inundation estimates to obtain High Resolution (HR) surface water patterns used to perform the downscaling of GIEMS over the Niger Delta (a semi-arid area) from a resolution of 0.25° (about 25 km) to 500 m. With the approaches proposed in these two later studies, the downscaled maps had hydrological patterns close to that of the reference data (SAR and MODIS, respectively) [15,16], and the water dynamics were preserved when compared to the low-resolution data. However, there is a need for HR observational references, which are not available at the global scale.

In [17] a first downscaling approach at a global scale based on topography was implemented. This study introduced a downscaling technique using an inundation probability map to increase the resolution of GIEMS from 0.25° to 15" (≈500 m), resulting in the release of GIEMS-D15 which is a static map of three inundation states (mean annual minimum, mean annual maximum, and long-term maximum). The technique was then improved further by using a floodability index based on a neural network model in a latter study [18], resulting in GIEMS-D3 with a resolution of 3". Since the downscaling scheme was more robust, it could be used at the monthly time resolution of GIEMS to obtain a long time-series at high spatial resolution. An evaluation of GIEMS-D3 conducted in [19] showed that this dataset had a better ability to detect water and to provide water dynamics below vegetation and during cloudy weather conditions compared to optical datasets, at the global scale.

The downscaling methodology proposed here is an evolution of the [18] work. Notable improvements are: (1) *Coherency of downscaling with permanent waters*—A priori permanent surface water was not included in the previous version of the floodability index. This was as a true difficulty for the coherency of the resulting downscaled products with known and well-located permanent waters (with issues such as mis-allocation or double-counting). A new floodability index was built in [9] and is exploited here for the downscaling. (2) *Improved continuity between cells*—Discontinuities were present in the previous downscaling results and required to be improved, to favor the use of the database at the local and regional scales. (3) *Better treatment of coastal cells*—The oceanic contamination of coastal Low Resolution (LR) cells was a true issue in previous downscaling. For instance, values of the LR GIEMS coastal cells were just scaled down to 80% of their value in [17].

The downscaling technique presented in this paper is generalizable and can be applied to any LR data, and with different floodability index. For illustrative purpose, we use here the new improved topography-based floodability index produced in [9] to downscale the GIEMS database. The downscaling will be done globally, and then its results will be evaluated with existing surface water datasets over some areas. The quality of the results depends highly on the new floodability index, and in particular in the permanent water database that was incorporated in it. For a detailed evaluation of this floodability index, the reader is referred to [9].
The datasets used in this study will be described in Section 2. How the downscaling is implemented will be introduced in details in Section 3. Section 4 presents the downscaling results and their evaluation.

## 2. Datasets Used in This Study

The datasets described in this section have their main characteristics presented in Table 1.

<table><caption>**Table 1.** Principal characteristics of the datasets used in this study</caption><thead><tr><th>Dataset</th><th>Ref.</th><th>Attribute</th><th>Sensor</th><th>Scale</th><th>Res.</th><th>Time</th></tr></thead><tbody><tr><td>Floodability Index (FI)</td><td>[9,18]</td><td>Hierarchical floodability ranking</td><td>Topography</td><td>Global</td><td>90 m</td><td>Static</td></tr><tr><td>Global Inundation Extent from Multi-Satellite (GIEMS)</td><td>[1–3]</td><td>Monthly inundation fraction</td><td>Passive microwave (main)</td><td>Global</td><td>0.25°</td><td>1993–2007</td></tr><tr><td>Global Surface Water (GSW)</td><td>[20]</td><td>Monthly water extent, occurrence, max extent, etc.</td><td>Optical</td><td>Global</td><td>30 m</td><td>1984–2015</td></tr><tr><td>Global Stream-flow Indices & Metadata archive (GSIM)</td><td>[21,22]</td><td>River discharge</td><td>in situ</td><td>Stations</td><td>Point</td><td>Various</td></tr><tr><td>SAR</td><td>[23]</td><td>Veg. types + dual-season flooding state</td><td>SAR</td><td>Local</td><td>3"</td><td>1995–1996</td></tr><tr><td>SAR</td><td>[24]</td><td>inundation classes</td><td>ALOS PALSAR</td><td>Amazon</td><td>3"</td><td>late-2006 to mid-2010</td></tr></tbody></table>

### 2.1. Global Inundation Extent from Multiple Satellite (GIEMS)

GIEMS dataset provides global estimates of surface water extent and dynamics over 15 years (1993–2007) [1,2]. In particular, GIEMS presents monthly inundation fraction over an equal-area grid with a resolution of 0.25° at the equator (about 773 km²). GIEMS was derived from multiple satellite observation, including (1) the passive microwave emissivity from SSM/I, (2) the active microwave backscattering from ERS-1 satellite, and (3) the visible and near-infrared reflectances from AVHRR. A multi-wavelength algorithm was developed to exploit all these measurements: It detected water using primarily the passive microwave, used the active microwave to estimate the contribution of vegetation to the passive microwave signal, and separated bare soil and inundation in semi-arid areas using the Normalized Difference Vegetation Index (NDVI) derived from the optical. Combining different types of observation enables them to complement each other and thereby limit their individual problems. GIEMS tends to underestimate the low- and overestimate the high-fractional inundation. Still, in general, it was shown to be consistent
with existing independent datasets across various environments and at different latitudes. The development of GIEMS is described in detail by [1,2]. Note that a new version of GIEMS (GIEMS2) is available [3] but would not change the results presented here (The database is available under request to catherine.prigent@obspm.fr).

## 2.2. Floodability Index

The floodability index is a proxy of the probability for one pixel to be under surface waters [18]. It estimates the relative probability of a pixel to be inundated compared to its pixel neighbors (at 90 m resolution). For the downscaling objective, the absolute value of the FI is not important, instead the local hierarchy of pixels (i.e., from the more likely inundated pixels to the less likely ones) is what is used to allocate the water fraction given by the LR specifications.

The floodability index is based on topography and hydrography information using a neural network method [9]. By construction, it is totally coherent with permanent water information due to the use of permanent water database in several stages of the floodability index. Permanent waters are defined as waters that are present in each step of the full time record of a reference database (here Landsat). Often, these permanent waters have no vegetation (rivers, lakes, reservoirs) so they can be monitored with visible observations. The permanent water database originated from [25,26] and updated thereafter (personal communication from Dai Yamazaki). It is extracted from the global database of river width at 3-s resolution. The river width data is obtained from multiple data sources, including Global1 arc-second Water Body Map (G1WBM), Global Surface Water Occurrence (GSWO), and Open Street Map. This database is advantageous since it describes even small canals for some regions and prevents virtual drainage due to a possibly misleading topography. The river width is calculated and assigned for river-center-line pixels. Pixels that are permanent water but not in the center-line are also noted. Hence, a permanent water mask was derived. The permanent water mask is not perfect: For instance, it is static by design so evolving river structures can be representative of later years but not fully coherent with earlier years. Permanent waters detection is based mostly on visible observations so vegetation issues can be problematic for seasonally vegetated places. Furthermore, water management can have a strong impact on surface waters and this is not easily handled in any permanent water mask. The coherency of our downscaling with this permanent waters is however essential because it avoids the double-counting of water bodies. The permanent water information is integrated in the floodability index, which will be useful in the downscaling of LR data (0.25°).

## 2.3. Datasets for Evaluation

### 2.3.1. Global Surface Water (GSW)

Derived from Landsat observations, the GSW dataset is a comprehensive global dataset that presents the spatial and temporal dynamic of open surface water and characterizes its long-term changes [20]. It covers a period of 32 years (1984–2015) at a resolution of 30m. Monthly water extents were mapped (water/dry/non-valid), from which the Global Surface Water Occurrence (GSWO) was derived. GSWO represents the frequency of water presence over the whole period. For a given pixel, some months of the year (e.g., dry season without clouds) can have more valid observations than others (e.g., rainy season). Only valid observations are included in the water occurrence calculation. Thus, to avoid the dominant contribution of some months of the year into the general frequency, the normalization by month is performed: The frequency of water presence is first calculated for each month of the year, then the average of all the months is performed [20]. Note that this dataset, based on visible observations, cannot monitor surface waters in the presence of clouds (which can be 100% of the time in some locations and seasons) and below strong vegetation such as forests [19]. GSW can therefore only provide an information on open waters.
### 2.3.2. Global Streamflow Indices and Metadata Archive (GSIM) River Discharge

Surface water extent is often more or less related to river discharge. Thus, analyzing the relationship between the downscaled water extent with river discharge is also a way to evaluate the performance of the downscaling. Here, we use the GSIM for the river discharge information. The GSIM database, compiled from 12 data sources, provides daily streamflow time-series of 30,935 stations, accompanied by metadata including basic information such as river name, catchment size and boundary [21,22]. The GSIM is accessible on https://doi.pangaea.de/10.1594/PANGAEA.887477. Depending on the data source, time-series of different stations cover different periods of time. To be compatible with GIEMS data, only stations that have data within 1993–2007 were kept, and daily data are aggregated to produce monthly data. More filters will be applied to select appropriate stations for the evaluation but will be described in more details later on.

River gauges provide *in situ* measurement that are used as a reference, but of course, they are associated with errors. GSIM compiles data from 12 data sources and the diversity of instruments and the way they are used to estimate river discharges can introduce differences. This means that systematic biases and variable uncertainty ranges could be observed, in the evaluation phase, for different gauge networks.

### 2.3.3. SAR Derived Flooding State and Wetland Extent over the Amazon Basin

Ref. [23] produced a 3-arcsecond-resolution map of wetland extent, vegetation types, and dual-season flooding states in the lowland Amazon basin using JERS-1 SAR images. The low-water season was October–November 1995 and the high-water season was May–June 1996. Firstly, segmentation and clustering techniques were implemented on backscattering coefficient to delineate wetland extent in the study area. Next, a rule set based on dual-season backscattering values was applied to wetland pixels to label their vegetation cover types and flooding states. Both attributes are integrated into one single map, but only the flooding state is retained for our study. Several limitations of the SAR retrieval of surface waters exist: (1) retrieval is very difficult below trees so underestimation of surface water is inevitable; (2) speckle noise and uncertainties are present in retrievals; (3) we have only here a low and high state estimated over a couple of months in a particular year, so comparison with monthly estimates cannot be perfect. However, SAR can provide the overall hydrology network over the Amazon region and this is a valuable independent information for evaluation of any new product.

Another dataset originating from SAR that is used in this study is the time-series of Amazon wetlands extent maps of [24] at a 3 arcsecond resolution. The L-band ALOS PALSAR ScanSAR data acquired from late-2006 to mid-2010 were collected and classified into inundation classes, including non-inundated, open water, inundated vegetation, and slope exceeding 18 m/pixel. We aggregated the data into binary for water/dry states, and calculated the water occurrence over time that can be used to evaluate the downscaled GIEMS data.

## 3. Downscaling Methodology

For clarity purpose hereafter, let *HR* denote “high-resolution”, and *LR* denote “low-resolution”. We call the LR grid element as a “cell” (e.g., GIEMS cell), and the HR one (i.e., at the target resolution for the downscaling) as a “pixel”. Each cell encloses a number of pixels. The general principle of downscaling LR data is that if a cell is *n*% inundated, water will be allocated to the *n*% pixels with highest floodability index, which are predicted to be more likely to be inundated than the other pixels in the neighborhood. However, in practice, the downscaling process is not as simple and it is worth noting three general ideas:

First, LR data detects water presence whether it is permanent or not. Thanks to the availability of permanent water distribution in the floodability index [9], the constant presence of permanent water is ensured in the downscaled maps. Also, its implicit existence in LR data can be clarified, ameliorating the water allocation of the downscaling process, hence a better delineation of transitory water. With a good idea of permanent water,
we could ensure the coherency of our downscaled surface waters with these permanent waters, a *posteriori*. Instead of that, we prefer here to integrate the permanent water information inside the floodability index. This is an *a priori* information that is exploited in the downscaled product. “Data fusion” is more optimal, and facilitates the use of the floodability index for the downscaling.

Second, the downscaling cannot be done independently on each cell. Otherwise, there would be edge effects that would result from inconsistencies in the LR maps or the inadequacy of the floodability index. These edge effects are the discontinuities in the HR downscaled maps. The discontinuities might not be an important issue at the LR scale, but they are not acceptable at the HR scale. A smoothing technique allowing for a smooth transition of water from one cell to its neighborhood cells is therefore necessary.

Third, over coastal areas, LR cells are partly on land and partly in the ocean. Ocean contamination in the retrieval of water fractions makes values of coastal cells less reliable. In fact, the satellite measurement cannot be isolated into a unique cell, the information comes from an elliptic Gaussiant power distribution, so the value in a coastal cell can largely be impacted by not well geolocated oceanic surfaces around it. It is therefore decided here to not rely on them. Downscaling will therefore be carried out only on inland cells, then inland water will be extrapolated to map the inundation over coastal cells. The floodability index is a practical tool to do this coastal extrapolation.

In the following subsections, these 3 general ideas will be developed. In Figure 1, an overall and general scheme presents the several steps involved in our downscaling framework.

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Overall scheme of the downscaling framework. The several steps will be described in detail in the following sections.</figcaption></figure>

### 3.1. *Fusion of Permanent Water Information*

The permanent water information that is integrated inside the floodability index [9] is an essential element of the downscaling: (1) The LR data can sometimes underestimate the water presence; this often happens with GIEMS, for instance, in places with scarce water [2]. The availability of permanent water information can partly compensate for such underestimations. (2) In the case of good LR estimation, it is preferable to allocate the water first in the permanent water pixels and then allocate the remaining water fraction to the transitory water pixels: Permanent water pixels are constantly inundated, while transitory water pixels switch their inundation status based on seasonality, or in arid environments where waterbodies are dry for months/years and can become wet for very sudden duration.
The distinction between permanent and transitory water pixels indeed has not been exploited enough in previous studies. [17] compensated GIEMS underestimation of low fractions using permanent water area estimated on the Global Dataset of Lakes and Wetlands (GLWD) [8]. After this correction of LR total area, water was allocated to pixels based only on the floodability index, regardless of permanent water information. This can raise a problem as a transitory water pixel can have a higher floodability index than a permanent one nearby because the floodability index is not perfect. In [18], the same permanent water map used in this manuscript was used. But the correction of the GIEMS LR estimates was done first, and the downscaling was done afterwards without imposed coherency with the permanent mask. This was therefore not optimal.

Here, we propose a new procedure that fuses HR permanent water information into the downscaling itself to solve the LR data underestimation and better allocation of the downscaling on permanent water pixels. Illustrated in Figure 2, we calculate the fraction of permanent water (from the HR estimates) over the LR grid ($LR_{perm}$) and consider two cases:

* If the LR fraction is higher than the permanent water fraction ($LR > LR_{perm}$), we derive the amount of transitory water ($LR_{trans} = LR - LR_{perm}$) and allocate it to transitory pixels.

* If the LR fraction is lower than the permanent water fraction ($LR \le LR_{perm}$), no water is allocated ($LR_{trans} = 0$), we just keep the permanent waters in the downscaling.

The original LR data is updated with $LR_{trans}$ before any water allocation. The new LR value can be summarized by: $LR_{trans} = max(LR - LR_{perm}, 0)$. In all cases, permanent waters are introduced in the resulting HR map; they are always present even if the LR data underestimates the water presence.

Since the floodability index is built up around this permanent water emphasizing coherency, the water allocation over transitory water pixels is also constrained towards coherency around the permanent water.

## 3.2. Smoothing Approach

A smoothing procedure helps obtain water distribution continuously on the HR map, without edge effects between adjacent cells. However, it is critical to constrain the smoothing to preserve the LR information: the original inundation fraction is maintained as much as possible for each cell, and the total global water area remains unchanged.

Ref. [17] proposed a smoothing technique called Moving Window Thresholding (MWT): For each cell, a certain ratio of water is restricted to be allocated inside it, and the remaining can go beyond the pixel to its vicinity. Ref. [18] pointed out two limitations of the MWT and introduced a new method: smooth the floodability index *before* the downscaling, instead of directly smoothing the water fraction. For each cell with its surrounding window, the floodability index is multiplied with a smoothing coefficient to produce the *Transformed Floodability Index* (TFI). The TFI is used as the basis to allocate the water amount of the central cell across the window. The smoothing coefficient (Equation (1)) acts as a weight indicating the relative contribution of each HR pixel in the window to the central LR cell value. The closer the HR pixel to the central cell, the greater the impact is. Among two pixels with the same floodability index, the one inside the central cell is given priority to be allocated with water, over the one outside.
<figure><img src="image_7.png" /><figcaption>**Figure 2.** The HR permanent water information from the floodability index (top left) is used to downscale the permanent part of the LR data. First, HR (binary) permanent water is upscaled to fractions in each LR cell. Then, if the LR inundation fraction is lower than the permanent water fraction (LR ≤ LR<sub>perm</sub>), the transitory water fraction LR<sub>trans</sub> is set to zero, otherwise the permanent water fraction is subtracted from LR value (LR<sub>trans</sub> = LR – LR<sub>perm</sub>). HR permanent water is projected in the downscaling map, and it is the LR<sub>trans</sub> that will be allocated to HR transitory pixels based on the floodability index.</figcaption></figure>

$$ \delta = 1 - \left[ \frac{r}{d \times (1.5 - w)} \right]^x \qquad (1) $$

where:

* δ—smoothing coefficient

* r—distance of HR pixel to central disk

* w—factor defining size of central disk

* d—width of central cell
$x$—decreasing rate to be adjusted

Note that this process allows doing the smoothing with circles instead of squares, which is much preferable for smoothing purposes. We adopt this smoothing technique with $w = \sqrt{2}/2$ (the central disk is the circumscribed circle of the central cell, Figure 3) and $x = 2$. The values of these two parameters were chosen after multiple tests on 24-months downscaling experiments. The two parameters gave the best compromise between smoothing effect and water conservation. Figure 4 shows the edge effects when downscaling without smoothing and how they are solved when a smoothing procedure is implemented.

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Sketch representing the parameters in Equation (1) for the smoothing process.</figcaption></figure>

For instance, it can be seen on Figure 4 (lower left map), in the South-Eastern part of the map, that a river section is missing. This is because the GIEMS surface water estimates are under-evaluating the surface water on this LR cell. If a downscaling is done independently for each LR cell, then discontinuities like this are likely to happen. The smoothing is in charge to assure some continuity between the LR cells, and it can be seen on the right bottom map how the smoothing has corrected this issue.
<figure><img src="image_9.png" /><figcaption>**Figure 4.** Downscaling with/without the smoothing procedure. Top-left: LR data to be downscaled. Top-right: floodability index. Bottom-left: downscaled data with edge effects as no smoothing procedure is used. Bottom right: edge effects have been removed thanks to the smoothing procedure.</figcaption></figure>

### 3.3. Coastal Extrapolation

Inundation retrieval are contaminated by the ocean over coarser cells. To reduce this problem, ref. [17] computes the area of ocean in each cell (based on a mean sea level), subtracts them from the LR values, then further reduces the obtained values by 30%, as a guess for reducing ocean contamination. This *ad hoc* adjustment was a rather crude process, showing the necessity to correct GIEMS coastal-contaminated cells, but no easy solution was found at that time.

A more sophisticated coastal extrapolation process was considered in [18]. In that paper, the extrapolation method was not described due to paper length limits, but the results presented were obtained using a new coastal extrapolation method. The basic idea in [18] was to infer the value of coastal cells from inland cells by using the floodability index on the coastal cells. This extrapolation strategy did not use the original coastal LR estimations (considered to be too unreliable) and aimed at replacing them. On each inland cell used for extrapolation, a floodability index threshold was determined for water determination. These thresholds were then weighted-averaged to derive the floodability index threshold to be used in the coastal cell. Then, all the pixels in the coastal cell with floodability index higher than the derived threshold were set to water. The extrapolated coastal cell became then an inland cell and could be used to extrapolate other coastal cells.

Another solution could be to intervene directly in the LR retrieval scheme, by using the higher microwave frequencies (37 GHz used by GIEMS) with better spatial resolution (despite the lower quality than if using all the channels) to reduce the coastal areas when generating LR data. In such case, a coastal extrapolation would still be required, but in a much more limited coastal area. An advantage would be to use real observations and not an extrapolation of remote observation using topography. This is outside of the scope of
this work but could well be pursued in the future and combined with the solution proposed
here.

We propose here instead a new refined coastal extrapolation approach based on an
evolution of that in [18]. The water is extrapolated to a coastal cell depending on its
neighbors, not through the LR water fraction, but through the HR water allocation at their
"frontiers". The process, illustrated by Figure 5a, includes the following steps:

* Define the Land-frontier(s) of the coastal cell. A Land-frontier is an entire edge of a cell or part of it that has contact with an inland cell. In Figure 5, the cell with bold black border is a coastal cell that will be extrapolated from inland cells (gray borders).

* Count the number of water pixels on each Land-frontier on the side of land cells ($N_{land}$).

* For smoothness between the land and the coastal cells, the amount of water at their frontier should be balanced. Thus, select $N_{land}$ pixels at the Land-frontier on the side of the coastal cell with highest floodability index. The minimum floodability index of the selected pixels is then defined as the threshold for that Land-frontier (T).

* After obtaining the threshold T for each Land-frontier, interpolate the threshold t for each pixels inside the coastal cell.

* Inside the coastal cell, a pixel with a floodability index higher than its threshold t is set to water.

The process starts from cells that are more surrounded by land (i.e., longer Land-frontier). After being extrapolated, a coastal cell becomes a land cell and can be used to extrapolate remaining coastal cells. Figure 5b shows an example of the order in which coastal cells will be extrapolated.

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Coastal extrapolation scheme. (a) Process: From the HR water allocation at the Land-frontiers of the coastal cell (cell with bold black border), a threshold of floodability index *T* is defined for each Land-frontier, then a threshold *t* is derived for each HR pixel in the coastal cell. A pixel with floodability index higher than its threshold *t* is set to water. (b) Order in which coastal cells are extrapolated (from blue to red): The cells that have more contact with Land cells are extrapolated first. The cells processed first can then be used to extrapolate the following coastal cells.</figcaption></figure>

## 4. GIEMS Downscaling Assessment

### 4.1. *Comparison with Previous Versions*

The downscaling technique developed in this study can be applied to many LR
datasets. In this study, it is tested to downscale GIEMS data from 0.25° to 3 arcsecond. The
downscaling results will first be compared with the predecessor GIEMS-D3 to check the
improvements, before the downscaling results are evaluated by independent datasets in
next sections. Please note that D3 is not the version of GIEMS, D3 refers to its resolution in
arcsecond. GIEMS-D3 database was first introduced in ref. [18] but the present paper gives
a new version of GIEMS-D3 (at same time-spatial resolution). The comparison has been
done in many places over the world, showing that the new version has better performance
than the previous one, but for illustrative purpose, we will only show here two typical
cases.
Figure 6 shows the downscaling of a single month (December 1994) around the Congo river. The GIEMS low resolution surface water fraction can underestimate the water area when compared to permanent water data from visible observations. We therefore correct GIEMS fractions to be coherent with this a priori permanent water information to obtain “corrected GIEMS” values. The corrected GIEMS are slightly different in the two downscaling versions (Figure 6a,d) because of two separate data sources for GIEMS correction (see Section 3.1). Two advantages of the new downscaling version over the old one can be seen here. Firstly, the new version preserves better the permanent water (Figure 6b,e). A clear example is the Tumba Lake (0.8° S, 18.1° E) which is not inundated in the old version. Secondly, the new version appears to preserve better the LR information while still having an adequate smoothness of water transition between LR cells. The downscaling results (i.e., HR maps) are upscaled into the LR grid (Figure 6c,f). When confronting the upscaling data against the corresponding corrected GIEMS, the new version shows a less significant change (Figure 6f,d) than the old version (Figure 6c,a). Quantitatively, the Mean Square Errors (MSEs) are computed by averaging the squared difference between the upscaling data and the corrected GIEMS. $MSE_{new} = 0.0018 < MSE_{old} = 0.0041$ over the whole site, and $MSE_{new} = 0.0031 < MSE_{old} = 0.0084$ over flooded areas. Note that the change of water allocation is inevitable by the smoothing procedure, we can just try to limit it.

After downscaling all GIEMS monthly data (180 months from 1993 to 2007), the water occurrence was calculated (i.e., number of months with water presence divided by 180). The two versions (GIEMS-D3 and new GIEMS-D) are compared around the Sagara Lake in Figure 7. In the old version (Figure 7a), water is not present in 100% of the lake. This resulted from the imperfection of the old floodability index. Water was not always allocated to the lake but instead to the channels around (which are zoomed). That is why those channels have very high water occurrence, unlike in the new version of the downscaling and GSWO, where they appear at fewer percentage levels. Such a case is not common, but it is a good illustration of the improvement of the new version over the old version of downscaling. Note that the area shown here occupies ≈3×3 GIEMS cells, so the water transfer between the lake and channels is possible during the downscaling (by smoothing procedure). In GSWO, the lake has not an occurrence of 100% either, it is seemingly because of some aquatic vegetation on the surface as can be seen in the Google image (Figure 7d). Since the permanent water mask (Section 2.2) is largely based on visible observations such as Landsat (also used on GSWO), if such vegetation occurs during the season, these pixels should be shown has non-permanent waters. However, it is difficult to know exactly what is happening: drying or water below vegetation. Clearly, the quality of the downscaling is dependent on the *a priori* permanent water. Its quality might not be perfect, but it is the best that is available so far and an overall satisfactory *a priori* information is needed when working at the global scale. The downscaling tests in Figure 7 shows however how the integration of the permanent water information in the floodability index is useful to truly have a coherency with the downscaled product.
<figure><img src="image_11.png" /><figcaption>**Figure 6.** Downscaling of on single month (12/1994) over the Democratic Republic of the Congo and the Republic of the Congo: **a)**, **d**) GIEMS is corrected by GLWD in the previous version and by permanent water integrated in the floodability index in the new version (*Corrected GIEMS = max(GIEMS, reference permanent water fraction)*); **b), e)** downscaling results; **c)**, **f)** upscaling of the HR results; **g)** Google Earth extraction for this region. MSE<sub>c,a</sub> = 0.0041 and MSE<sub>d,f</sub> = 0.0018 over the whole site. MSE<sub>c,a</sub> = 0.0084 and MSE<sub>d,f</sub> = 0.0031 over flooded areas.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Water occurrence from the downscaling of GIEMS around the Sagara Lake using a) the old version versus, and b) the new version. c) GSWO from optical observations at 30 m resolution [20]. d) Google satellite image.</figcaption></figure>

## 4.2. Global Evaluation

### 4.2.1. With GSWO

The global water occurrence from the new GIEMS downscaling (that we will call here GIEMS-D) is presented in Figure 8, and is compared to that from GSWO [20]. Note that for display purposes and to reduce the computational load, all the data were aggregated in this figure to the 0.05° resolution. Water occurrence from GIEMS-D and GSWO are correlated at a 0.78 level, reaching 0.80 when considering only inland areas, and 0.58 when considering only coastal areas. The GIEMS-D and GSWO share the same spatial patterns of water distribution, but the water occurrence reported by the GIEMS-D is generally higher than GSWO. This disparity can be explained mostly by their different origins. An optical sensor (like Landsat, the source of GSWO) is able to observe efficiently only open water due to vegetation cover and cloud contamination in some seasons of some locations. Meanwhile, microwave observations (at the origin of GIEMS-D) can detect water even below vegetation canopy thanks to the penetration ability of long-wavelength radiation. The presence of vegetation above water surface is undoubtedly common on Earth (e.g., forest plants, wetland plants, or crops) [8]. In [27], it is shown that over the Amazon, for instance, there are large extent of the water by flooding during the wet season. It is shown that GIEMS is able to see better this seasonality than visible observations. SAR data is able to better see it too but not as well.
<figure><img src="image_13.png" /><figcaption>**Figure 8.** Water occurrence global map from GIEMS-D (top) and GSWO (bottom).</figcaption></figure>

The distribution and correlation of the two data are shown in a different way in Figure 9, with scatterplots showing the different surface water fractions over several land cover types. Little water is found over bare soil, sparse vegetation, or urban areas in both datasets. For wetlands and water bodies, the two datasets are largely in agreement with each other, from low to high water occurrences. Over forest and cropland, it is not surprising that water occurrence higher than 50% is rarely reported by GSWO, and GIEMS-D is almost systematically higher. In areas with moss, lichen and herbaceous, one might notice a small part of the samples where water occurrence is very high according to GSWO but very low according to GIEMS-D. Our inspection found that it happens in and around the Greenland coasts. The inland of Greenland with snow and frozen water was almost always masked by GIEMS as the signature of snow and ice is very strong and makes it impossible or very difficult to detect surface water accurately. With such absences of inland water, the coastal extrapolation using the floodability index logically derived no water in the coastal areas. Overall, Figures 8 and 9 show that the downscaling seems to be reasonable at the global scale when compared to GSWO. The downscaling cannot be perfect everywhere, but what is obtained can be explained and potentially improved in the future.
<figure><img src="image_14.png" /><figcaption>**Figure 9.** Distribution of GIEMS-D versus GSWO occurrence (%) over all land covers and over some surface types. With higher vegetation, more samples can be seen in the upper-left part sections, meaning more water for the GIEMS-D estimates.</figcaption></figure>

### 4.2.2. With river discharge

Surface water area and river discharge can be related to each other [28,29]. Depending on the environments, this correlation can be high or low. In a basin, if all flooding water flows simply through the drainages to the gauging location, even with a time lag, the correlation between water extent and river discharge should be high. However, in many basins, it is not that straightforward. On the way from flood area to the gauging location, many processes and events can occur, such as heavy rain or human intervention such as water extraction. There is no more direct link between water extent and river discharge in such cases, hence correlation between them can be low.

Monthly water extent from GIEMS-D was extracted for each basin in the GSIM database Section 2.3.2. Three quality flags were used to select basins and associated stations for the downscaling evaluation:

* The time-series must have at least 60 months with simultaneous valid data of river discharge and GIEMS-D surface waters, as too much missing data can reduce the confidence of the analysis.

* The basin must have variation in both river discharge and water extent over time, otherwise, it is not of interest because it contains only permanent water or constant flow and no correlation can be derived.

* The basin must have a surface area larger than 10% of a GIEMS cell area (>77 km²) as GIEMS tends to underestimate surface water when inundation fraction is less than 10% so discarding small basins is a way to avoid GIEMS errors.

After this basin filtering, 2293 stations, corresponding to 2293 basins, were kept. Correlation between river discharge and GIEMS-D water extent was calculated for each basin, with 0 to 4 months lags (GIEMS-D surface water anomalies preceding river discharge), and the highest coefficients among these 5 time-lags were mapped in Figure 10. India is striking with many very high correlation stations. South West Africa and North Europe are found with many low correlations. In other areas, the correlation ranges from very low to very high. Note that low correlation does not always mean that the downscaling is not reliable: as explained above, depending on the environment and other factors, water extent and river discharge may not be directly related to each other. The Land Use/ Land Cover within these watersheds is likely experiencing changes through time, this can have impact on both the water surfaces and the river discharges, reducing temporal correlation. Furthermore, the temporal correlation on the monthly time series monitors well the seasonality, but the water management can have very significant negative impact on these correlations.
<figure><img src="image_15.png" /><figcaption>**Figure 10.** Correlation between GIEMS-D water extent and GSIM river discharge over 2293 basins. The distribution of correlation coefficient is shown on the bottom left corner. Four locations (A, B, C, D) are selected to look into details in Figure 11.</figcaption></figure>

We choose some interesting basins to look in more detail (Figure 11). Monthly water extent was additionally extracted from the GSW database for more references. The use of GSW was only possible in two out of the four basins due to the high number of GSW missing data. For instance, the GSW monthly water data product cannot be directly used over basins (A) and (B) due to frequent appearance of missing data. Therefore, a special data filling approach had to be applied: First, water probability and maximum water extent were computed over the basin for each month of the year ($P_m$ and $ME_m$, respectively, with $m$ from January to December). Then, for each month of the time series, if the GSW water mask has missing data for less than 70% of the basin area, the gaps are filled using the corresponding $P_m$ and $ME_m$. Note that the GSW monthly water extents are much lower than GIEMS-D values so they are amplified 10 times when plotted for better visualization of their dynamics. From the time series of GIEMS-D water extent, GSW water extent (if available), and river discharge (left column in Figure 11), the seasonality (central column) was derived by taking the average of all years for each month of the year, and the de-seasonalised normalized anomalies (right column) were obtained by taking the difference of monthly values against corresponding seasonality values, normalized by standard deviation of the whole time series.

Case A is a big basin of the Mississippi Delta. Both GIEMS-D and GSW water extent have good correlation with river discharge (coefficient of 0.80 and 0.76, respectively). The river discharge seasonality is only slightly better with GSW than GIEMS-D, since GIEMS-D appears to have a one-month delay for the seasonal peak. Please note that management in the Mississippi basin is very important (including levees, backwater events, and land-leveling procedures for irrigation). For instance, water supply and water retention can be present for rice cultivation in this area, which can distort natural correlation between water area and river discharge. Therefore, topography-based only downscaling might not be ideal in such regions. However, the link between surface water area with river discharge is quite large with a correlation of 0.8. Among many basins in India, case B has a relatively lower correlation between GIEMS-D extent and river discharge (0.6). Again, this might be partly related to water supply and water retention for rice cultivation. The elevated phases of GIEMS-D and river discharge are both in the second half of the year. However, it occurs faster with GIEMS-D than with river discharge. Due to crops on the land surface, GSW shows extremely less water compared to GIEMS and very little dynamics (the GSW line fluctuates insignificantly even though the values have been amplified by 10); its correlation with river discharge is also low (0.35), and seasonality is missing. Case C is the biggest available basin in the Amazon, and case D is the biggest in the Congo. Both cases have very good correlation between GIEMS-D and river discharge (0.88 and 0.86, respectively) and similarity in seasonality, with river discharge peaking two months after GIEMS-D in the Amazon. In all cases, the anomalies are less correlated between GIEMS-D and river
discharge but still at a significant level (with coefficient of 0.63, 0.49, 0.56, and 0.59 for A, B, C, and D, respectively). In general, GIEMS-D extent can be a reasonable description of the seasonality of the river discharge, with a lag more or less depending on the river location. Also, good links with extreme events shows that there is a true link between the two variables. Using river discharge for the evaluation of the surface water is not easy because their link is very complex. However, it is a way to compare in relative terms the quality of two surface water datasets (i.e., GSW and GIEMS-D).

<figure><img src="image_16.png" /><figcaption>**Figure 11.** Comparison of GIEMS-D and GSW water extent with GSIM river discharge over 4 basins. Left column: data accumulated over each basin. Central column: data averaged for each month of the year, representing seasonality. Right column: difference of monthly values against corresponding seasonality values, normalized by standard deviation of the whole time series. GSW values are amplified 10 times for better visualization. Numbers floating in the plots are correlation coefficients of water extent (blue for GIEMS-D, green for GSW) and river discharge.</figcaption></figure>

### 4.3. Local Evaluation: A Case Study in the Amazon Basin

From the SAR dataset produced in [23], the flooding states in the dry season (October & November 1995) and the wet season (May & June 1996) are extracted, regardless of land cover type. From the downscaling of GIEMS, the maximum inundation extent of October and November 1995, and that of May and June 1996 are derived to match with the reference SAR data. Figure 12 shows the agreement and disagreement between the two datasets. On both seasons, the main streams of river and tributary (in dark blue) are well detected by both datasets. Many very small channels are detected by the SAR, much less by GIEMS. This can be explained by the underestimation of the low-resolution GIEMS for small water fraction areas. Both datasets mean to indicate sometimes the same channels, but those objects are shifted between the two datasets, for instance as seen in cell B zoom of the figure. The two datasets are provided in the geographic coordinate system (EPSG:4326-WGS84). Still, when overlaying them on the Google satellite image, the objects in GIEMS-D match well with the Google image, contrarily to the SAR data. Some projection corrections could be used, but the older SAR data seems to have more issues of this nature than GIEMS-D, probably due to the complexity of the SAR data (e.g., topography errors can translate into spatial shifts). In the high season, the cell seems to be split quite obviously into two parts:
In one part, GIEMS is dominant (orange beside dark blue); while in the other the SAR is (green beside dark blue). However, this again just shows the disagreement between low-resolution GIEMS and SAR. The quality of the downscaling, in any season, should be doubted only where the water allocation is vague by the two datasets (mixing orange and green), for example cell A zoom in both seasons.

<figure><img src="image_17.png" /><figcaption>**Figure 12.** Comparison of GIEMS-D and SAR [23] in dry (left) and wet (right) states. Two zooms are provided over regions A and B. Google images are given to show the density of vegetation and the challenge to detect surface waters.</figcaption></figure>

Some statistics to compare the two datasets in the domain are provided below. Please note that some geolocalization errors are present (mainly on the SAR data) and that a quantitative comparison of the datasets suffers from systematic errors. Results are rounded with no decimals to reflect this imperfection of the quantitative measures.

* Agree in both seasons: 83%.

* Agree in one season, disagree in another: 9%.

* Disagree in both seasons: 4%, including:

- Water always reported by SAR but not by GIEMS-D: 1%

- Water always reported by GIEMS-D but not by SAR: 3%

- Out of phase: 0%

Figure 13a–c compares the water occurrence obtained from GIEMS-D with that from Landsat/GSWO [20] and SAR [24]. The three datasets have similar main hydrology structures. However, the GIEMS-D still looks sharper than the other two. Small channels hidden in the deep forest appear faintly in GSWO. SAR data looks noisy in many places due to speckle noise and instabilities of the retrieval algorithm. The SAR detects water on single
pixels without closely following hydrology structures as it is done in the downscaling of GIEMS. However, many tiny channels are reported by SAR while they do not appear in GIEMS-D. This might be related to the underestimation of the original GIEMS in sparse water locations. In contrast, the overestimation of GIEMS is likely the cause of the inflated appearance of the main river in GIEMS-D compared to the other datasets.

<figure><img src="image_18.png" /><figcaption>**Figure 13.** Comparison of water occurrence from GIEMS-D a), GSWO b), and SAR c), over the Amazon (-8° to 0° in latitude; and -66° to -54° in longitude).</figcaption></figure>

**5. Conclusions and Perspectives**

A new floodability index was developed in [9] to include improvements such as less topography artifacts and better coherency with permanent water information from visible observation datasets. In that paper, it was demonstrated that such a floodability index is a general tool useful for instance for potential data fusions at different resolutions. We show here that the new floodability index helps downscaling low resolution surface water with a better *a priori* integration of the permanent water information. The quality of the downscaling is highly dependent on the quality of the floodability index, and in particular in the permanent surface water that is part of it. The fusion of permanent water information can help compensate LR data underestimation and constrain the downscaling to be more coherent with the permanent water databases.

The downscaling scheme itself is also improved. A smoothing parameter is adjusted to obtain an adequate smoothness of the downscaling maps while preserving the original LR information. A new method to extrapolate water from the inland toward coastal areas is proposed. Although imperfect, it is a reasonable solution to provide an estimate on coastal cells that are overly contaminated by ocean to provide reliable LR surface water estimations. The extrapolation over two LR cells is not ideal, and some developments in the future should concentrate on using more direct observations than the floodability index. (1) For instance, HR observations from SAR or visible data could be used to build an “empirical floodability index”. (2) The Surface Water and Ocean Topography (SWOT) french/american mission was launched by NASA/CNES in 15 December 2022 [30,31]. It will be providing, among others, surface water estimates at 100 m resolution (https://swot.jpl.nasa.gov/ accessed on 10 December 2024). This means that an empirical floodability index could be based on direct high spatial resolution. Of course, this is useful only if SWOT can provide surface water estimates below the vegetation. (3) Furthermore, GIEMS original algorithm
could attempt to use higher frequencies of its microwave data (at higher spatial resolution than the actual 25 km) to obtain LR estimates with less oceanic contamination.

When tested on GIEMS data, the new downscaling technique shows improved results compared to its previous version, as expected. Independent datasets were used to evaluate the new GIEMS-D, at the global scale and over the Amazon basin, with an overall effective performance of the downscaling. Overall, spatial patterns of GIEMS-D and GSW are in apparently strong agreement. However, locally, it can be seen that GIEMS-D detects more water below vegetation and that it has less vulnerability to cloud cover which is a huge problem for visible observations over several areas. Together, these attributes enhance temporally dynamic observations across areas. Actually, the floodability index could be used to improve the visible-based datasets below vegetation, and it could be used to post-process SAR data. This is currently attempted in our team on the SWOT data to reduce artifacts and errors. We expect to use the new GIEMS-D for some applications such as for the prediction of river discharge [32,33]. We would like to analyze the variability of the surface waters [34]. We expect to perform data fusion to exploit the synergy of multiple complementary satellite observations such as e.g., ref. [35–37].

Downscaling framework is based on a floodability index, so improving the floodability index is a natural way to improve the downscaling. Note that with the proposed downscaling method, different types of floodability index can be used or even combined. We can develop a better floodability index for regions where surface water does not occur naturally based on topography but with human control such as dams and dykes. In such places, it will be difficult to model human behavior but a floodability index based on observations could help us define the regions that are more frequently under water. In some natural environments where surface water is not mainly controlled by topography such as peatlands, the floodability index should also be based more on observation than on topography. For peatlands, a solution could be obtained by downscaling the peat maps at 10 km resolution of [38] using high-resolution reflectances. There is also a need to operationalize the downscaling framework so that new GIEMS versions such as in [3] can be processed in near real time. Finally, GIEMS-D data can be used as a reference to evaluate the data from the SWOT satellite, then it can be fused with SWOT data for a more comprehensive description of global surface water or used for temporal extension of SWOT data back into the past.

**Author Contributions:** Conceptualization, FA and THN; methodology, FA and THN; software, THN; validation, FA and THN; writing—original draft preparation, THN and FA; writing—review and editing, THN and FA; supervision, FA; project administration, FA; funding acquisition, FA.

**Funding:** The authors thank the Embassy of France in Vietnam for funding Hang’s PhD, and then extending this funding due to difficulties related to the COVID19 and some important personal reasons. The authors acknowledge support from the ESA CCI RECCAP2 project (ESRIN/4000123002/18/I-NB).

**Data Availability Statement:** Data access can be obtained by contacting Filipe AIRES at filipe.aires@obspm.fr.

**Acknowledgments:** The authors would like to thank Catherine Prigent for fruitfull conversations.

**Conflicts of Interest:** The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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