Flow Duration Curves from Surface Reflectance in the Near Infrared Band
<p>Geographical location of the Mississippi River, including spatial distribution of in-situ stations used in this study.</p> "> Figure 2
<p>River discharge hydrograph (<b>a</b>) and reflectance ratio C/M (<b>b</b>) for the selected in-situ gauged stations.</p> "> Figure 3
<p>Conceptual scheme of the procedure between ground-based and remote sensing data. (<b>a</b>) schematic representation of the relationship between Discharge Q and remote sensing data, C/M through their duration; duration curve in terms of remote sensing, C/M (<b>b</b>) and discharge Q (<b>c</b>).</p> "> Figure 4
<p>(<b>a</b>,<b>c</b>) show flow duration curves (FDCs) calculated for (i) the entire period (tot), from 2003 to 2019, (ii) for the selected calibration period (cal), from 2003 to 2015, and (iii) for the calibration period adopting an eight-day sampling interval for all the sites analyzed. (<b>b</b>,<b>d</b>) columns show differences in discharge between the FDCs built referring to the calibration and total period, and between the FDCs built in the calibration period, but in case of considering daily or eight-day sampling intervals.</p> "> Figure 5
<p>(<b>a</b>,<b>c</b>) show reflectance ratio duration curves (RDCs) calculated for (i) the entire period (tot), from 2003 to 2019, and (ii) for the selected calibration period (cal), from 2003 to 2015. (<b>b</b>,<b>d</b>) columns show differences in reflectance ratio C/M between the RDCs built considering the calibration and the total period, for all the sites analyzed.</p> "> Figure 6
<p>Calibration phase: Comparison between the observed and simulated discharges.</p> "> Figure 7
<p>Validation phase: Comparison between the observed and simulated discharges.</p> "> Figure 8
<p>Simulated and observed FDCs for the period of validation (2016–2019). For comparison, the FDC built on single years of the entire observation period, 2003–2019, are also represented.</p> "> Figure 9
<p>Errors between estimated and observed discharges in function of the duration.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Datasets
2.1.1. In Situ Dataset
2.1.2. Satellite Dataset
2.2. Methods
2.2.1. Estimation of the Reflectance Ratio
- Cut the MODIS images over a square of size proportional to the width of the river (the side ranges from 0.05 to 0.11 km) and centered on the selected site.
- Calculate the temporal coefficient of variation for every pixel of the box considering the set of available MODIS images.
- Calculate, for each image, the spatial average of the reflectance considering the pixels with the coefficient of variation lower than the 5th percentile; this represents the time series of dry pixel (C) at a given location.
- Select a buffer of 1 km around the river and calculate all possible C/M ratios by considering M values of the pixels within the buffer and the average C obtained at step (3).
- Compare every C/M time series against the discharge recorder by the ground monitoring network and calculate the coefficient of correlation.
- Identify the C/M combination and, hence, M pixel that maximizes the coefficient of correlation.
2.2.2. FDC Estimation
2.2.3. Data Consistency
2.3. Evaluation of the Results
- Root mean square error, RMSE, the second sample moment of the residuals (or differences) between predicted and observed values. It ranges from 0 (perfect fit) to +∞ (low performances).
- Relative RMSE, rRMSE, defined as:
- Normalized RMSE, NRMSE, defined as:
- The Nash–Sutcliffe efficiency [27], NSE, defined as:
3. Results
3.1. FDCs and RDCs Definition Based on Available Datasets
3.2. Comparison in Terms of River Discharge: Calibration Phase
3.3. Comparison in Terms of River Discharge: Validation Phase
3.4. FDCs in the Validation Phase: Evaluation of the Performances
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Station | USGS ID | Lat. | Lon. | Ab [km2] | Missing Data [%] | Qmax [m3/s] | Qmin [m3/s] | Qmean [m3/s] |
---|---|---|---|---|---|---|---|---|
St. Cloud | 5270700 | 45.547 | −94.147 | 34,498 | 0 | 10,333 | 277 | 2040 |
St. Paul | 5331000 | 44.945 | −93.084 | 95,311 | 0 | 35,052 | 622 | 5847 |
Prescott | 5344500 | 44.746 | −92.800 | 116,031 | 12.0 | 4049 | 108 | 705 |
Winona | 5378500 | 44.056 | −91.638 | 153,327 | 0.3 | 5040 | 173 | 1076 |
McGregor | 5389500 | 43.027 | −91.171 | 174,823 | 48.1 | 55,169 | 2213 | 12,333 |
Clinton | 5420500 | 41.781 | −90.252 | 221,702 | 0 | 6654 | 238 | 1771 |
Keokuk | 5474500 | 40.394 | −91.374 | 308,207 | 0 | 15,121 | 229 | 2635 |
Below Grafton | 5587455 | 38.951 | −90.373 | 443,663 | 10.2 | 159,106 | 4084 | 43,651 |
St. Louis | 7010000 | 38.628 | −90.181 | 1,805,213 | 0 | 283,769 | 16,459 | 74,299 |
Chester | 7020500 | 37.901 | −89.830 | 1,835,256 | 0 | 27,014 | 1620 | 7202 |
Thebes | 7022000 | 37.220 | −89.467 | 1,847,170 | 0 | 295,961 | 19,050 | 80,995 |
Memphis | 7032000 | 35.127 | −90.079 | 2,415,929 | 75.0 | 48,988 | 5097 | 20,250 |
Vicksburg | 7289000 | 32.315 | −90.906 | 2,964,227 | 35.3 | 65,412 | 5409 | 21,415 |
Station | Rp [-] | Rs [-] | RMSE [m3/s] | rRMSE [%] | NRMSE [%] | NSE [-] |
---|---|---|---|---|---|---|
St. Cloud | 0.29 | 0.37 | 1789 | 95.8 | 23.3 | −0.38 |
St. Paul | 0.37 | 0.36 | 5502 | 111.2 | 18.6 | −0.24 |
Prescott | 0.82 | 0.76 | 316 | 50.3 | 9.5 | 0.67 |
Winona | 0.66 | 0.62 | 571 | 61.3 | 14.1 | 0.36 |
McGregor | 0.78 | 0.71 | 5763 | 46.9 | 11.8 | 0.53 |
Clinton | 0.75 | 0.66 | 700 | 45.1 | 12.4 | 0.53 |
Keokuk | 0.46 | 0.49 | 1654 | 70.9 | 16.4 | −0.06 |
Below Grafton | 0.16 | 0.17 | 35,301 | 88.0 | 27.8 | −0.64 |
St. Louis | 0.73 | 0.83 | 31,574 | 46.5 | 15.4 | 0.46 |
Chester | 0.30 | 0.40 | 4880 | 74.2 | 23.4 | −0.38 |
Thebes | 0.85 | 0.88 | 25,535 | 34.4 | 12.7 | 0.69 |
Memphis | 0.90 | 0.90 | 3854 | 24.4 | 14.0 | 0.77 |
Vicksburg | 0.80 | 0.88 | 7059 | 35.7 | 12.3 | 0.55 |
Station | Rp [-] | Rs [-] | RMSE [m3/s] | rRMSE [%] | NRMSE [%] | NSE [-] |
---|---|---|---|---|---|---|
St. Cloud | 0.39 | 0.55 | 17,843 | 69.2 | 29.5 | −0.53 |
St. Paul | 0.14 | 0.31 | 83,784 | 96.5 | 27.2 | −1.20 |
Prescott | 0.85 | 0.90 | 3815 | 33.7 | 10.7 | 0.79 |
Winona | 0.73 | 0.74 | 6725 | 43.7 | 15.5 | 0.36 |
McGregor | - | - | - | - | - | - |
Clinton | 0.57 | 0.58 | 9768 | 39.7 | 18.3 | 0.32 |
Keokuk | 0.40 | 0.35 | 20,709 | 57.6 | 22.1 | −0.31 |
Below Grafton | 0.44 | 0.33 | 326,920 | 54.2 | 23.1 | −0.03 |
St. Louis | 0.57 | 0.74 | 489,400 | 51.7 | 19.6 | −0.03 |
Chester | 0.58 | 0.65 | 47,113 | 51.2 | 20.0 | −0.04 |
Thebes | 0.69 | 0.79 | 382,943 | 37.4 | 15.3 | 0.44 |
Memphis | 0.81 | 0.84 | 61,406 | 27.8 | 14.7 | 0.66 |
Vicksburg | 0.72 | 0.82 | 82,228 | 33.8 | 17.9 | 0.52 |
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Tarpanelli, A.; Domeneghetti, A. Flow Duration Curves from Surface Reflectance in the Near Infrared Band. Appl. Sci. 2021, 11, 3458. https://doi.org/10.3390/app11083458
Tarpanelli A, Domeneghetti A. Flow Duration Curves from Surface Reflectance in the Near Infrared Band. Applied Sciences. 2021; 11(8):3458. https://doi.org/10.3390/app11083458
Chicago/Turabian StyleTarpanelli, Angelica, and Alessio Domeneghetti. 2021. "Flow Duration Curves from Surface Reflectance in the Near Infrared Band" Applied Sciences 11, no. 8: 3458. https://doi.org/10.3390/app11083458