Accurate measurement of river discharge, the volumetric rate of water flow passing through a river's cross section, is essential to water supply planning and management, reservoir management and control, hydropower generation, flood prediction and control, understanding the global water cycle, and other hydrological applications. It is costly, labor intensive, and time consuming to directly measure river discharge because of the irregular geometry of river cross sections and the high variation of flow velocity in space and time. Most rivers require a series of measurements of flow velocity in each subsection of the cross section to achieve one accurate measurement of discharge. To save cost, labor, and time, river discharge is usually inferred from the measurement of river stage based on the stage-discharge rating (SDR) curve. The river stage is the height of water surface above a nearby reference point. Even if this technique is used, field surveys that measure the river discharge and stage simultaneously are still needed in order to construct the SDR curve at a particular cross section. Moreover, the stage-discharge relationship varies with time because the erosion and sediment deposition processes occurring in river channels and riverbanks constantly alter the geometry of channels. Therefore, a periodic check of the SDR curves against the direct measurements is needed. This is yet another reason why maintaining river gauging stations is cost-, labor-, and time-intensive.
Remote sensing of river stage and discharge from space provides us with a promising alternative approach for monitoring watersheds. Since the 1990s, significant progress has been made in remote sensing of discharge and river stage.1–4 One relatively simple approach is to estimate river stage and discharge based on satellite-measured inundation area. While it is simple, there are still three obstacles to be overcome to improve the effectiveness and applicability of this approach. First, is it possible to construct the inundation area – river stage relationship (IARSR) curves without ground-based measurements? Second, can the accuracy of the satellite-measured inundation area be improved? And third, how can we establish the river SDR curve at an ungauged site?
Recently, we demonstrated that digital elevation model data could be used to construct the IARSR curves.4, 5 Constructing the IARSR using a digital elevation model takes four steps. The first step is to define a polygon covering the river cross section where the IARSR is constructed. The width of the polygon should be wide enough to cover both riverbanks as well as a portion of the floodplain on both sides. The second step is to identify the minimum elevation (zo) inside the polygon. This minimum elevation actually represents the water surface elevation inside the polygon when the terrain survey was conducted, and data was collected for the digital elevation model data. All connected pixels with the same elevation as zo inside the polygon form the inundation area (Ao). On the inundation area – river stage plane, the point (Ao, zo) represents the lower limit of the IARSR curve that can be derived from the digital elevation model data. The third step is an iterative loop to obtain multiple points for constructing the IARSR curve, and these multiple points are all above the lower limit point (Ao, zo). To obtain points above (Ao, zo), we can ‘artificially’ raise the water level and use the hypothetical water level to determine the associated inundation area. The fourth step is to construct the IARSR curve using the smooth spline curve fitting method. The IARSR curve inside the pre-defined polygon near the US Geological Survey (USGS) gauging station on the Trinity River at Liberty in Texas is shown in Figure 1. We constructed it from the 10m resolution digital elevation model shown in Figure 2.
Figure 1. The inundation area – river stage relationship (IARSR) curve (red) constructed from multiple data points (dots) of inundation area versus water level derived from the 10m resolution digital elevation model (DEM) inside the predefined polygon near the US Geological Survey gauging station on the Trinity River at Liberty in Texas.
Figure 2. Elevation overlain by the predefined polygon (black box) and boundaries of inundation area (inside the polygon) associated with different water levels: 1.52m (white), 2.52m (yellow), 3.52m (red), 4.52m (orange), 5.52m (green), 6.52m (blue), and 7.52 (purple).
After the IARSR is obtained, it is straightforward to apply the constructed IARSR to estimate water level or river stage from the satellite-measured inundation area. First we estimate the inundation areas inside the pre-defined polygon from satellite images. Then we calculate the river stages with the constructed IARSR curve. To improve the accuracy of the satellite-measured inundation area, we proposed a dual-threshold method.4 The first threshold is the lower limit of pixel value for classifying water body pixels with a high certainty. The second threshold is the upper limit of pixel value for classifying potentially flooded pixels. All pixels adjacent to the classified water body pixels and with a pixel value between the first threshold and the second threshold may be partially flooded. Linear interpolation can be used to estimate the wet area of each partially flooded pixel. We used the constructed IARSR curve (see Figure 1) to estimate river stages based on the Landsat-measured inundation areas near the USGS gauging station at Liberty. The root mean square error of the estimated river stages compared to the observations is 0.38m.
There is one limitation in the constructed IARSR curves. They are only applicable as river stages above the minimum water surface elevation (zo) detected by the digital elevation model. Bathymetric information and a complete IARSR curve (starting from the stream bed) are necessary for stages below zo. We need to improve our ability to retrieve river bathymetry from satellite imagery or data.
Despite our success constructing IARSR curves and the accuracy of satellite-measured inundation areas, to measure river discharge from space we also need the SDR curve. This is often unavailable for ungauged rivers. The SDR curve depends on the morphometry of channel cross-section (e.g., channel cross sectional shape, channel width and depth, stream bed slope) and channel friction.6 Although the channel morphometric and frictional characteristics can be obtained through field surveys, the direct field survey approach is time consuming and labor intensive. Our next steps will work on improving our ability to construct the SDR curves using remotely sensed data.
University of North Texas
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