808
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

, &
Pages 101-113 | Received 08 Jul 2016, Accepted 23 Aug 2017, Published online: 14 Dec 2017

Figures & data

Figure 1. Framework for input uncertainty quantification in Stage 1 of optimization.

Figure 1. Framework for input uncertainty quantification in Stage 1 of optimization.

Figure 2. Plots of autocorrelation: (a) discharge; and cross-correlation of (b) discharge–rainfall and (c) discharge–evapotranspiration.

Figure 2. Plots of autocorrelation: (a) discharge; and cross-correlation of (b) discharge–rainfall and (c) discharge–evapotranspiration.

Figure 3. The final architecture of ANN identified for the Leaf River basin.

Figure 3. The final architecture of ANN identified for the Leaf River basin.

Figure 4. Histogram of rainfall multiplier sampled from the log-normal distribution (Leaf River).

Figure 4. Histogram of rainfall multiplier sampled from the log-normal distribution (Leaf River).

Figure 5. Two-dimensional scatter plots of observed rainfall vs corrected rainfall.

Figure 5. Two-dimensional scatter plots of observed rainfall vs corrected rainfall.

Figure 6. Convergence of objective function against number of generations.

Figure 6. Convergence of objective function against number of generations.

Table 1. Statistical properties of the ANN parameters optimized for Case I and Case II. SD: standard deviation.

Table 2. Summary statistics and model performance indices.

Figure 7. Case I: Variation of parameter range along the number of generations. W: weight parameter; B: bias parameter; I, H and O: input, hidden and output nodes, respectively; subscript i corresponds to the ith node in the respective layer, e.g. WI1H2 indicates a weight connection between 1st input and 2nd hidden node.

Figure 7. Case I: Variation of parameter range along the number of generations. W: weight parameter; B: bias parameter; I, H and O: input, hidden and output nodes, respectively; subscript i corresponds to the ith node in the respective layer, e.g. WI1H2 indicates a weight connection between 1st input and 2nd hidden node.

Figure 8. Case II: Variation of parameter range along the number of generations. See for explanation of notation.

Figure 8. Case II: Variation of parameter range along the number of generations. See Figure 7 for explanation of notation.

Figure 9. Pareto-optimal front of optimization during ensemble creation in the calibration period.

Figure 9. Pareto-optimal front of optimization during ensemble creation in the calibration period.

Table 3. Uncertainty indices estimated for Case I and Case II. POC: percentage of coverage; AW: average width.

Figure 10. Prediction interval corresponding to selected ensemble during the calibration period.

Figure 10. Prediction interval corresponding to selected ensemble during the calibration period.

Figure 11. Prediction interval corresponding to selected ensemble during the validation period.

Figure 11. Prediction interval corresponding to selected ensemble during the validation period.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.