# Using Deep Learning Algorithms for Intermittent Streamflow Prediction in the Headwaters of the Colorado River, Texas

^{*}

## Abstract

**:**

^{2}> 0.75, and r > 0.85), with better evaluation metrics than the ELM and CNN algorithm, and competitive performance to the SA–LSTM model, was identified as an appropriate, effective, and parsimonious streamflow prediction tool for the headwaters of the Colorado River in Texas.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data

#### 2.3. Methods

#### 2.3.1. Extreme Learning Machine

#### 2.3.2. Convolutional Neural Networks

#### 2.3.3. Long Short-Term Memory

#### 2.3.4. Attention-Based Long Short-Term Memory

#### 2.4. Model Evaluation Metrics

- The Mean Absolute Error (MAE) and Root Mean Square Error (RMSE):

- The Index of Agreement (d):

- The Pearson’s r (r):

- The Coefficient of Determination (R
^{2}):

- The Nash–Sutcliffe Efficiency (NSE):

- The Kling–Gupta Efficiency (KGE):

## 3. Results and Discussion

#### 3.1. Predictive Performance over the Entire Range of Flowrates

^{2}, the baseline ELM model was outperformed by the more complex deep learning counterparts during the testing period. According to the NSE scores, the deep learning models achieved “very good” levels of performance (NSE > 0.75) against the unsatisfactory performance of the ELM model (NSE < 0.5). All models achieved “skillful” predictions (KGE > −0.41); however, the deep learners, particularly LSTM-based models offered better estimations with lower biases and better variability ratios and, thus, considerably better KGE scores in comparison to the ELM.

#### 3.2. Predictive Performance for the No-Flow Events

^{3}/s) in comparison to the ELM model (MAE = 0.67 m

^{3}/s).

#### 3.3. Predictive Performance for the Extreme High Flow Events

## 4. Summary and Conclusions

- While all the investigated models offered skillful streamflow predictions (as measured by the KGE score above −0.41), overall, the deep learning models clearly outperformed the baseline ELM model with respect to all evaluation metrics. The more advanced models better captured the flow dynamics in the IRES setting and were found to be appropriate tools for streamflow prediction at the site of study.
- None of the investigated data-driven algorithms were able to capture absolute zero flowrates. However, deep learning models, more specifically LSTM and SA–LSTM, estimated closer values to zero and predicted considerably less unrealistic negative flowrates.
- Deep learners also offered more accurate predictions of the extreme high flows, with lower RMSE and MAE errors and higher correlations and KGE scores in comparison to the ELM.
- With respect to the principle of parsimony, the LSTM model is the most appropriate model among the considered alternatives as it outperformed the ELM and CNN models with considerable higher performance metrics and achieved relatively similar results to the SA–LSTM model, despite not having the attention unit and being a slightly simpler methodology.
- LSTM and SA–LSTM models outperformed their counterparts when challenged with the extrapolation problem for the unprecedented record-breaking flood events of 2014 and 2015.
- Despite its simplicity and fast speed, the ELM model was found to provide unreliable streamflow estimations, and its application is not recommended for the studied stream, particularly because it exhibited the most severe underestimation of the extreme high flows.
- The ELM model was found to be prone to overfitting and learning the noise in the training data, which yielded noticeably lower quality of performance during the independent testing period.
- The CNN model, while achieving better evaluation metrics than the baseline ELM model, predicted a large number of negative flowrates and failed to provide accurate estimates of the extreme high flows. Hence, the application of the CNN algorithm is not recommended for the stream of study.
- The SA–LSTM, as the cutting-edge alternative and the most complex tool among the investigated models, offered the best performance in capturing the extreme ends of the IRES streamflow spectrum: no-flow events and extreme floods.
- The pooling mechanism in CNNs and the dropout mechanism for the LSTM-based models were found to be effective in considerably lowering the extent of performance loss from training to testing and controlling overfitting.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Datry, T.; Singer, G.; Sauquet, E.; Capdevilla, D.J.; Von Schiller, D.; Subbington, R.; Magrand, C.; Paril, P.; Milisa, M.; Acuña, V. Science and management of intermittent rivers and ephemeral streams (SMIRES). Res. Ideas Outcomes
**2017**, 3, 23. [Google Scholar] [CrossRef] - Levick, L.R.; Goodrich, D.C.; Hernandez, M.; Fonseca, J.; Semmens, D.J.; Stromberg, J.C.; Tluczek, M.; Leidy, R.A.; Scianni, M.; Guertin, D.P. The Ecological and Hydrological Significance of Ephemeral and Intermittent Streams in the Arid and Semi-Arid American Southwest; US Environmental Protection Agency, Office of Research and Development: Washington, DC, USA, 2008. [Google Scholar]
- Eng, K.; Wolock, D.M.; Dettinger, M.D. Sensitivity of intermittent streams to climate variations in the USA. River Res. Appl.
**2016**, 32, 885–895. [Google Scholar] [CrossRef] - Gutiérrez-Jurado, K.Y.; Partington, D.; Batelaan, O.; Cook, P.; Shanafield, M. What triggers streamflow for intermittent rivers and ephemeral streams in low-gradient catchments in Mediterranean climates. Water Resour. Res.
**2019**, 55, 9926–9946. [Google Scholar] [CrossRef] - Leigh, C.; Boulton, A.J.; Courtwright, J.L.; Fritz, K.; May, C.L.; Walker, R.H.; Datry, T. Ecological research and management of -intermittent rivers: An historical review and future directions. Freshw. Biol.
**2016**, 61, 1181–1199. [Google Scholar] [CrossRef] - Jaeger, K.L.; Sutfin, N.A.; Tooth, S.; Michaelides, K.; Singer, M. Chapter 2.1—Geomorphology and Sediment Regimes of Intermittent Rivers and Ephemeral Streams. In Intermittent Rivers and Ephemeral Streams; Datry, T., Bonada, N., Boulton, A., Eds.; Academic Press: Cambridge, MA, USA, 2017; pp. 21–49. [Google Scholar] [CrossRef]
- Hill, M.J.; Milner, V.S. Ponding in intermittent streams: A refuge for lotic taxa and a habitat for newly colonising taxa? Sci. Total Environ.
**2018**, 628–629, 1308–1316. [Google Scholar] [CrossRef] - Tolonen, K.E.; Picazo, F.; Vilmi, A.; Datry, T.; Stubbington, R.; Pařil, P.; Rocha, M.P.; Heino, J. Parallels and contrasts between intermittently freezing and drying streams: From individual adaptations to biodiversity variation. Freshw. Biol.
**2019**, 64, 1679–1691. [Google Scholar] [CrossRef] - Catalán, N.; Casas-Ruiz, J.P.; von Schiller, D.; Proia, L.; Obrador, B.; Zwirnmann, E.; Marcé, R. Biodegradation kinetics of dissolved organic matter chromatographic fractions in an intermittent river. J. Geophys. Res. Biogeosci.
**2017**, 122, 131–144. [Google Scholar] [CrossRef] - Scordo, F.; Seitz, C.; Melo, W.D.; Piccolo, M.C.; Perillo, G.M.E. Natural and human impacts on the landscape evolution and hydrography of the Chico River basin (Argentinean Patagonia). Catena
**2020**, 195, 104783. [Google Scholar] [CrossRef] - Steward, D.R.; Yang, X.; Lauwo, S.Y.; Staggenborg, S.A.; Macpherson, G.L.; Welch, S.M. From precipitation to groundwater baseflow in a native prairie ecosystem: A regional study of the Konza LTER in the Flint Hills of Kansas, USA. Hydrol. Earth Syst. Sci.
**2011**, 15, 3181–3194. [Google Scholar] [CrossRef] [Green Version] - Courtwright, J.; May, C.L. Importance of terrestrial subsidies for native brook trout in Appalachian intermittent streams. Freshw. Biol.
**2013**, 58, 2423–2438. [Google Scholar] [CrossRef] - Datry, T.; Boulton, A.J.; Bonada, N.; Fritz, K.; Leigh, C.; Sauquet, E.; Tockner, K.; Hugueny, B.; Dahm, C.N. Flow intermittence and ecosystem services in rivers of the Anthropocene. J. Appl. Ecol.
**2018**, 55, 353–364. [Google Scholar] [CrossRef] - Karaouzas, I.; Smeti, E.; Vourka, A.; Vardakas, L.; Mentzafou, A.; Tornés, E.; Sabater, S.; Muñoz, I.; Skoulikidis, N.T.; Kalogianni, E. Assessing the ecological effects of water stress and pollution in a temporary river—Implications for water management. Sci. Total Environ.
**2018**, 618, 1591–1604. [Google Scholar] [CrossRef] [PubMed] - Vander Vorste, R.; Obedzinski, M.; Pierce, S.N.; Carlson, S.M.; Grantham, T.E. Refuges and ecological traps: Extreme drought threatens persistence of an endangered fish in intermittent streams. Glob. Chang. Biol.
**2020**, 26, 3834–3845. [Google Scholar] [CrossRef] [PubMed] - Grey, D.; Sadoff, C.W. Sink or Swim? Water security for growth and development. Water Policy
**2007**, 9, 545–571. [Google Scholar] [CrossRef] - Kampf, S.K.; Faulconer, J.; Shaw, J.R.; Lefsky, M.; Wagenbrenner, J.W.; Cooper, D.J. Rainfall thresholds for flow generation in desert ephemeral streams. Water Resour. Res.
**2018**, 54, 9935–9950. [Google Scholar] [CrossRef] - Azarnivand, A.; Camporese, M.; Alaghmand, S.; Daly, E. Simulated response of an intermittent stream to rainfall frequency patterns. Hydrol. Processes
**2020**, 34, 615–632. [Google Scholar] [CrossRef] - Sauquet, E.; Beaufort, A.; Sarremejane, R.; Thirel, G. Predicting flow intermittence in France under climate change. Hydrol. Sci. J.
**2021**, 66, 2046–2059. [Google Scholar] [CrossRef] - Tramblay, Y.; Rutkowska, A.; Sauquet, E.; Sefton, C.; Laaha, G.; Osuch, M.; Albuquerque, T.; Alves, M.H.; Banasik, K.; Beaufort, A.; et al. Trends in flow intermittence for European rivers. Hydrol. Sci. J.
**2021**, 66, 37–49. [Google Scholar] [CrossRef] - Zipper, S.C.; Hammond, J.C.; Shanafield, M.; Zimmer, M.; Datry, T.; Jones, C.N.; Kaiser, K.E.; Godsey, S.E.; Burrows, R.M.; Blaszczak, J.R.; et al. Pervasive changes in stream intermittency across the United States. Environ. Res. Lett.
**2021**, 16, 084033. [Google Scholar] [CrossRef] - Mix, K.; Groeger, A.W.; Lopes, V.L. Impacts of dam construction on streamflows during drought periods in the Upper Colorado River Basin, Texas. Lakes Reserv. Sci. Policy Manag. Sustain. Use
**2016**, 21, 329–337. [Google Scholar] [CrossRef] - Diffenbaugh, N.S.; Giorgi, F.; Pal, J.S. Climate change hotspots in the United States. Geophys. Res. Lett.
**2008**, 35, L16709. [Google Scholar] [CrossRef] - Datry, T.; Fritz, K.; Leigh, C. Challenges, developments and perspectives in intermittent river ecology. Freshw. Biol.
**2016**, 61, 1171–1180. [Google Scholar] [CrossRef] - Stubbington, R.; Paillex, A.; England, J.; Barthès, A.; Bouchez, A.; Rimet, F.; Sánchez-Montoya, M.M.; Westwood, C.G.; Datry, T. A comparison of biotic groups as dry-phase indicators of ecological quality in intermittent rivers and ephemeral streams. Ecol. Indic.
**2019**, 97, 165–174. [Google Scholar] [CrossRef] - Sazib, N.; Bolten, J.; Mladenova, I. Exploring spatiotemporal relations between soil moisture, precipitation, and streamflow for a large set of watersheds using Google Earth Engine. Water
**2020**, 12, 1371. [Google Scholar] [CrossRef] - Katz, G.L.; Denslow, M.W.; Stromberg, J.C. The Goldilocks Effect: Intermittent streams sustain more plant species than those with perennial or ephemeral flow. Freshw. Biol.
**2012**, 57, 467–480. [Google Scholar] [CrossRef] - Tooth, S.; Nanson, G.C. The role of vegetation in the formation of anabranching channels in an ephemeral river, Northern plains, arid central Australia. Hydrol. Process.
**2000**, 14, 3099–3117. [Google Scholar] [CrossRef] - Mehr, A.D. An improved gene expression programming model for streamflow forecasting in intermittent streams. J. Hydrol.
**2018**, 563, 669–678. [Google Scholar] [CrossRef] - Chebaane, M.; Salas, J.D.; Boes, D.C. Product periodic autoregressive processes for modeling intermittent monthly streamflows. Water Resour. Res.
**1995**, 31, 1513–1518. [Google Scholar] [CrossRef] - Aksoy, H.; Bayazit, M. A model for daily flows of intermittent streams. Hydrol. Process.
**2000**, 14, 1725–1744. [Google Scholar] [CrossRef] - Kişi, Ö. Neural networks and wavelet conjunction model for intermittent streamflow forecasting. J. Hydrol. Eng.
**2009**, 14, 773–782. [Google Scholar] [CrossRef] - Makwana, J.J.; Tiwari, M.K. Intermittent streamflow forecasting and extreme event modelling using wavelet based artificial neural networks. Water Resour. Manag.
**2014**, 28, 4857–4873. [Google Scholar] [CrossRef] - Badrzadeh, H.; Sarukkalige, R.; Jayawardena, A.W. Intermittent stream flow forecasting and modelling with hybrid wavelet neuro-fuzzy model. Hydrol. Res.
**2017**, 49, 27–40. [Google Scholar] [CrossRef] - Rahmani-Rezaeieh, A.; Mohammadi, M.; Danandeh Mehr, A. Ensemble gene expression programming: A new approach for evolution of parsimonious streamflow forecasting model. Theor. Appl. Climatol.
**2020**, 139, 549–564. [Google Scholar] [CrossRef] - Mehr, A.D.; Gandomi, A.H. MSGP-LASSO: An improved multi-stage genetic programming model for streamflow prediction. Inf. Sci.
**2021**, 561, 181–195. [Google Scholar] [CrossRef] - Kisi, O.; Alizamir, M.; Shiri, J. Conjunction Model Design for Intermittent Streamflow Forecasts: Extreme Learning Machine with Discrete Wavelet Transform. In Intelligent Data Analytics for Decision-Support Systems in Hazard Mitigation; Springer: Berlin/Heidelberg, Germany, 2021; pp. 171–181. [Google Scholar]
- Li, M.; Robertson, D.E.; Wang, Q.J.; Bennett, J.C.; Perraud, J.-M. Reliable hourly streamflow forecasting with emphasis on ephemeral rivers. J. Hydrol.
**2021**, 598, 125739. [Google Scholar] [CrossRef] - Alizadeh, B.; Bafti, A.G.; Kamangir, H.; Zhang, Y.; Wright, D.B.; Franz, K.J. A novel attention-based LSTM cell post-processor coupled with bayesian optimization for streamflow prediction. J. Hydrol.
**2021**, 601, 126526. [Google Scholar] [CrossRef] - Uhlenbrook, S.; Seibert, J.A.N.; Leibundgut, C.; Rodhe, A. Prediction uncertainty of conceptual rainfall-runoff models caused by problems in identifying model parameters and structure. Hydrol. Sci. J.
**1999**, 44, 779–797. [Google Scholar] [CrossRef] - Hapuarachchi, H.; Bari, M.; Kabir, A.; Hasan, M.; Woldemeskel, F.; Gamage, N.; Sunter, P.; Zhang, X.; Robertson, D.; Bennett, J.; et al. Development of a national 7-day ensemble streamflow forecasting service for Australia. Hydrol. Earth Syst. Sci. Discuss.
**2022**, 2022, 1–35. [Google Scholar] [CrossRef] - Sneed, E.D.; Folk, R.L. Pebbles in the lower Colorado River, Texas a study in particle morphogenesis. J. Geol.
**1958**, 66, 114–150. [Google Scholar] [CrossRef] - Clay, C.; Kleiner, D.J. Colorado River—The Handbook of Texas Online. 2017. Available online: https://www.tshaonline.org/handbook/entries/colorado-river (accessed on 10 July 2022).
- Samady, M.K. Continuous Hydrologic Modeling for Analyzing the Effects of Drought on the Lower Colorado River in Texas; Michigan Technological University: Houghton, MI, USA, 2017. [Google Scholar]
- Nielsen-Gammon, J.W. The changing climate of Texas. Impact Glob. Warm. Tex.
**2011**, 39, 86. [Google Scholar] - Griffith, G.E.; Bryce, S.; Omernik, J.; Rogers, A. Ecoregions of Texas; US Geological Survey: Reston, VA, USA, 2004. [Google Scholar]
- US Environmental Protection Agency. Available online: https://www.epa.gov/ (accessed on 10 July 2022).
- U.S. Geological Survey. Available online: https://www.usgs.gov (accessed on 15 July 2022).
- Moritz, S.; Sardá, A.; Bartz-Beielstein, T.; Zaefferer, M.; Stork, J. Comparison of different methods for univariate time series imputation in R. arXiv
**2015**, arXiv:1510.03924. [Google Scholar] - Welch, G.; Bishop, G. An Introduction to the Kalman Filter; Department of Computer Science, University of North Carolina at Chapel Hill: Chapel Hill, NC, USA, 1995. [Google Scholar]
- Godsey, S.E.; Kirchner, J.W. Dynamic, discontinuous stream networks: Hydrologically driven variations in active drainage density, flowing channels and stream order. Hydrol. Process.
**2014**, 28, 5791–5803. [Google Scholar] [CrossRef] - Durighetto, N.; Vingiani, F.; Bertassello, L.E.; Camporese, M.; Botter, G. Intraseasonal drainage network dynamics in a headwater catchment of the Italian alps. Water Resour. Res.
**2020**, 56, e2019WR025563. [Google Scholar] [CrossRef] - Botter, G.; Durighetto, N. The Stream Length Duration Curve: A Tool for Characterizing the Time Variability of the Flowing Stream Length. Water Resour. Res.
**2020**, 56, e2020WR027282. [Google Scholar] [CrossRef] [PubMed] - Botter, G.; Vingiani, F.; Senatore, A.; Jensen, C.; Weiler, M.; McGuire, K.; Mendicino, G.; Durighetto, N. Hierarchical climate-driven dynamics of the active channel length in temporary streams. Sci. Rep.
**2021**, 11, 21503. [Google Scholar] [CrossRef] - PRISM Climate Group, Oregon State University. Available online: https://prism.oregonstate.edu (accessed on 1 June 2022).
- Thornthwaite, C.W. An approach toward a rational classification of climate. Geogr. Rev.
**1948**, 38, 55–94. [Google Scholar] [CrossRef] - Montgomery, D.C.; Jennings, C.L.; Kulahci, M. Introduction to Time Series Analysis and Forecasting; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Huang, G.-B.; Zhu, Q.-Y.; Siew, C.-K. Extreme learning machine: Theory and applications. Neurocomputing
**2006**, 70, 489–501. [Google Scholar] [CrossRef] - Huang, G.-B.; Chen, L.; Siew, C.K. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans. Neural Netw.
**2006**, 17, 879–892. [Google Scholar] [CrossRef] - Kisi, O.; Alizamir, M. Modelling reference evapotranspiration using a new wavelet conjunction heuristic method: Wavelet extreme learning machine vs. wavelet neural networks. Agric. For. Meteorol.
**2018**, 263, 41–48. [Google Scholar] [CrossRef] - Zhu, S.; Heddam, S.; Wu, S.; Dai, J.; Jia, B. Extreme learning machine-based prediction of daily water temperature for rivers. Environ. Earth Sci.
**2019**, 78, 202. [Google Scholar] [CrossRef] - Atiquzzaman, M.; Kandasamy, J. Prediction of hydrological time-series using extreme learning machine. J. Hydroinform.
**2015**, 18, 345–353. [Google Scholar] [CrossRef] - Yin, Z.; Feng, Q.; Yang, L.; Deo, R.C.; Wen, X.; Si, J.; Xiao, S. Future projection with an extreme-learning machine and support vector regression of reference evapotranspiration in a mountainous inland watershed in North-West China. Water
**2017**, 9, 880. [Google Scholar] [CrossRef] - Niu, W.-J.; Feng, Z.-K.; Zeng, M.; Feng, B.-F.; Min, Y.-W.; Cheng, C.-T.; Zhou, J.-Z. Forecasting reservoir monthly runoff via ensemble empirical mode decomposition and extreme learning machine optimized by an improved gravitational search algorithm. Appl. Soft Comput.
**2019**, 82, 105589. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Faris, H.; Al-Ansari, N. Hybridized extreme learning machine model with Salp swarm algorithm: A novel predictive model for hydrological application. Complexity
**2020**, 2020, 8206245. [Google Scholar] [CrossRef] - Feng, B.-F.; Xu, Y.-S.; Zhang, T.; Zhang, X. Hydrological time series prediction by extreme learning machine and sparrow search algorithm. Water Supply
**2021**, 22, 3143–3157. [Google Scholar] [CrossRef] - Khoi, D.N.; Quan, N.T.; Linh, D.Q.; Nhi, P.T.T.; Thuy, N.T.D. Using machine learning models for predicting the water quality index in the La Buong River, Vietnam. Water
**2022**, 14, 1552. [Google Scholar] [CrossRef] - Deo, R.C.; Şahin, M. An extreme learning machine model for the simulation of monthly mean streamflow water level in Eastern Queensland. Environ. Monit. Assess.
**2016**, 188, 90. [Google Scholar] [CrossRef] - Mosavi, A.; Ozturk, P.; Chau, K.-W. Flood prediction using machine learning models: Literature review. Water
**2018**, 10, 1536. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Sulaiman, S.O.; Deo, R.C.; Chau, K.-W. An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. J. Hydrol.
**2019**, 569, 387–408. [Google Scholar] [CrossRef] - Boucher, M.-A.; Quilty, J.; Adamowski, J. Data assimilation for streamflow forecasting using extreme learning machines and multilayer perceptrons. Water Resour. Res.
**2020**, 56, e2019WR026226. [Google Scholar] [CrossRef] - Belotti, J.; Mendes, J.J.; Leme, M.; Trojan, F.; Stevan, S.L.; Siqueira, H. Comparative study of forecasting approaches in monthly streamflow series from Brazilian hydroelectric plants using Extreme Learning Machines and Box & Jenkins models. J. Hydrol. Hydromech.
**2021**, 69, 180–195. [Google Scholar] [CrossRef] - Abda, Z.; Zerouali, B.; Chettih, M.; Santos, C.A.G.; de Farias, C.A.S.; Elbeltagi, A. Assessing machine learning models for streamflow estimation: A case study in Oued Sebaou watershed (Northern Algeria). Hydrol. Sci. J.
**2022**, 67, 1328–1341. [Google Scholar] [CrossRef] - Huang, G.; Huang, G.-B.; Song, S.; You, K. Trends in extreme learning machines: A review. Neural Netw.
**2015**, 61, 32–48. [Google Scholar] [CrossRef] [PubMed] - Huang, G.-B.; Chen, L. Enhanced random search based incremental extreme learning machine. Neurocomputing
**2008**, 71, 3460–3468. [Google Scholar] [CrossRef] - Zhao, W.; Jiao, L.; Ma, W.; Zhao, J.; Zhao, J.; Liu, H.; Cao, X.; Yang, S. Superpixel-based multiple local CNN for panchromatic and multispectral image classification. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 4141–4156. [Google Scholar] [CrossRef] - Canizo, M.; Triguero, I.; Conde, A.; Onieva, E. Multi-head CNN–RNN for multi-time series anomaly detection: An industrial case study. Neurocomputing
**2019**, 363, 246–260. [Google Scholar] [CrossRef] - Shu, X.; Peng, Y.; Ding, W.; Wang, Z.; Wu, J. Multi-step-ahead monthly streamflow forecasting using convolutional neural networks. Water Resour. Manag.
**2022**, 36, 3949–3964. [Google Scholar] [CrossRef] - Ghimire, S.; Yaseen, Z.M.; Farooque, A.A.; Deo, R.C.; Zhang, J.; Tao, X. Streamflow prediction using an integrated methodology based on convolutional neural network and long short-term memory networks. Sci. Rep.
**2021**, 11, 17497. [Google Scholar] [CrossRef] - Mozo, A.; Ordozgoiti, B.; Gómez-Canaval, S. Forecasting short-term data center network traffic load with convolutional neural networks. PLoS ONE
**2018**, 13, e0191939. [Google Scholar] [CrossRef] - Barzegar, R.; Aalami, M.T.; Adamowski, J. Short-term water quality variable prediction using a hybrid CNN–LSTM deep learning model. Stoch. Environ. Res. Risk Assess.
**2020**, 34, 415–433. [Google Scholar] [CrossRef] - Baek, S.-S.; Pyo, J.; Chun, J.A. Prediction of water level and water quality using a CNN-LSTM combined deep learning approach. Water
**2020**, 12, 3399. [Google Scholar] [CrossRef] - Duan, S.; Ullrich, P.; Shu, L. Using convolutional neural networks for streamflow projection in California. Front. Water
**2020**, 2. [Google Scholar] [CrossRef] - Le, X.H.; Nguyen, D.H.; Jung, S.; Yeon, M.; Lee, G. Comparison of deep learning techniques for river streamflow forecasting. IEEE Access
**2021**, 9, 71805–71820. [Google Scholar] [CrossRef] - Xu, W.; Chen, J.; Zhang, X.J. Scale effects of the monthly streamflow prediction using a state-of-the-art deep learning model. Water Resour. Manag.
**2022**, 36, 3609–3625. [Google Scholar] [CrossRef] - Li, P.; Zhang, J.; Krebs, P. Prediction of flow based on a CNN-LSTM combined deep learning approach. Water
**2022**, 14, 993. [Google Scholar] [CrossRef] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Kratzert, F.; Klotz, D.; Brenner, C.; Schulz, K.; Herrnegger, M. Rainfall–runoff modelling using Long Short-Term Memory (LSTM) networks. Hydrol. Earth Syst. Sci.
**2018**, 22, 6005–6022. [Google Scholar] [CrossRef] - Sudriani, Y.; Ridwansyah, I.; Rustini, H.A. Long short term memory (LSTM) recurrent neural network (RNN) for discharge level prediction and forecast in Cimandiri River, Indonesia. IOP Conf. Ser. Earth Environ. Sci.
**2019**, 299, 012037. [Google Scholar] [CrossRef] - Wu, Q.; Lin, H. Daily urban air quality index forecasting based on variational mode decomposition, sample entropy and LSTM neural network. Sustain. Cities Soc.
**2019**, 50, 101657. [Google Scholar] [CrossRef] - Liu, W.; Liu, W.D.; Gu, J. Forecasting oil production using ensemble empirical model decomposition based long short-term memory neural network. J. Pet. Sci. Eng.
**2020**, 189, 107013. [Google Scholar] [CrossRef] - Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R. Dropout: A simple way to prevent neural networks from overfitting. J. Mach. Learn. Res.
**2014**, 15, 1929–1958. [Google Scholar] - Liang, C.; Li, H.; Lei, M.; Du, Q. Dongting lake water level forecast and its relationship with the three gorges dam based on a long short-term memory network. Water
**2018**, 10, 1389. [Google Scholar] [CrossRef] [Green Version] - Bowes, B.D.; Sadler, J.M.; Morsy, M.M.; Behl, M.; Goodall, J.L. Forecasting groundwater table in a flood prone coastal city with long short-term memory and recurrent neural networks. Water
**2019**, 11, 1098. [Google Scholar] [CrossRef] - Miao, Q.; Pan, B.; Wang, H.; Hsu, K.; Sorooshian, S. Improving monsoon precipitation prediction using combined convolutional and long short term memory neural network. Water
**2019**, 11, 977. [Google Scholar] [CrossRef] - Lees, T.; Reece, S.; Kratzert, F.; Klotz, D.; Gauch, M.; De Bruijn, J.; Kumar Sahu, R.; Greve, P.; Slater, L.; Dadson, S.J. Hydrological concept formation inside long short-term memory (LSTM) networks. Hydrol. Earth Syst. Sci.
**2022**, 26, 3079–3101. [Google Scholar] [CrossRef] - Hu, C.; Wu, Q.; Li, H.; Jian, S.; Li, N.; Lou, Z. Deep learning with a long short-term memory networks approach for rainfall-runoff simulation. Water
**2018**, 10, 1543. [Google Scholar] [CrossRef] - Apaydin, H.; Feizi, H.; Sattari, M.T.; Colak, M.S.; Shamshirband, S.; Chau, K.-W. Comparative analysis of recurrent neural network architectures for reservoir inflow forecasting. Water
**2020**, 12, 1500. [Google Scholar] [CrossRef] - Thapa, S.; Zhao, Z.; Li, B.; Lu, L.; Fu, D.; Shi, X.; Tang, B.; Qi, H. Snowmelt-driven streamflow prediction using machine learning techniques (LSTM, NARX, GPR, and SVR). Water
**2020**, 12, 1734. [Google Scholar] [CrossRef] - Rahimzad, M.; Nia, A.M.; Zolfonoon, H.; Soltani, J.; Mehr, A.D.; Kwon, H.-H. Performance comparison of an LSTM-based deep learning model versus conventional machine learning algorithms for streamflow forecasting. Water Resour. Manag.
**2021**, 35, 4167–4187. [Google Scholar] [CrossRef] - Hunt, K.M.R.; Matthews, G.R.; Pappenberger, F.; Prudhomme, C. Using a long short-term memory (LSTM) neural network to boost river streamflow forecasts over the western United States. Hydrol. Earth Syst. Sci. Discuss.
**2022**, 2022, 1–30. [Google Scholar] [CrossRef] - Nogueira Filho, F.J.M.; Souza Filho, F.d.A.; Porto, V.C.; Rocha, R.V.; Sousa Estácio, Á.B.; Martins, E.S.P.R. Deep learning for streamflow regionalization for ungauged basins: Application of long-short-term-memory cells in Semiarid regions. Water
**2022**, 14, 1318. [Google Scholar] [CrossRef] - Wang, Y.; Huang, M.; Zhu, X.; Zhao, L. Attention-Based LSTM for Aspect-Level Sentiment Classification. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, Austin, TX, USA, 1–5 November 2016; pp. 606–615. [Google Scholar]
- Katrompas, A.; Metsis, V. Enhancing LSTM Models with Self-attention and Stateful Training. In Proceedings of the SAI Intelligent Systems Conference, Amsterdam, The Netherlands, 1–2 September 2022; pp. 217–235. [Google Scholar]
- Jing, R. A self-attention based LSTM network for text classification. J. Phys. Conf. Ser.
**2019**, 1207, 012008. [Google Scholar] [CrossRef] - Chen, B.; Li, T.; Ding, W. Detecting deepfake videos based on spatiotemporal attention and convolutional LSTM. Inf. Sci.
**2022**, 601, 58–70. [Google Scholar] [CrossRef] - Pei, W.; Baltrusaitis, T.; Tax, D.M.; Morency, L.-P. Temporal attention-gated model for robust sequence classification. IEEE Conf. Comput. Vis. Pattern Recognit.
**2016**, 1, 6730–6739. [Google Scholar] - Girihagama, L.; Khaliq, M.N.; Lamontagne, P.; Perdikaris, J.; Roy, R.; Sushama, L.; Elshorbagy, A. Streamflow modelling and forecasting for Canadian watersheds using LSTM networks with attention mechanism. Neural Comput. Appl.
**2022**. [Google Scholar] [CrossRef] - Yan, L.; Chen, C.; Hang, T.; Hu, Y. A stream prediction model based on attention-LSTM. Earth Sci. Inform.
**2021**, 14, 723–733. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2022; Available online: https://www.R-project.org/ (accessed on 1 June 2022).
- Van Rossum, G.; Drake, F.L. Python 3 Reference Manual; CreateSpace: Scotts Valley, CA, USA, 2009. [Google Scholar]
- Kling, H.; Fuchs, M.; Paulin, M. Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. J. Hydrol.
**2012**, 424–425, 264–277. [Google Scholar] [CrossRef] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Willmott, C.J. On the validation of models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef] - Legates, D.R.; McCabe, G.J., Jr. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Pearson, K., IV. Contributions to the mathematical theory of evolution. III. Regression, heredity, and panmixia. Proc. R. Soc. Lond.
**1896**, 59, 69–71. [Google Scholar] [CrossRef] - Galton, A. English Prose: From Maundevile to Thackeray; W. Scott: London, UK; Gage: Toronto, WJ, Canada, 1888; Volume 35. [Google Scholar]
- Lee Rodgers, J.; Nicewander, W.A. Thirteen ways to look at the correlation coefficient. Am. Stat.
**1988**, 42, 59–66. [Google Scholar] [CrossRef] - Asuero, A.G.; Sayago, A.; González, A.G. The correlation coefficient: An overview. Crit. Rev. Anal. Chem.
**2006**, 36, 41–59. [Google Scholar] [CrossRef] - Schober, P.; Boer, C.; Schwarte, L.A. Correlation coefficients: Appropriate use and interpretation. Anesth. Analg.
**2018**, 126, 1763–1768. [Google Scholar] [CrossRef] [PubMed] - Draper, N.R.; Smith, H. Applied Regression Analysis; John Wiley & Sons: Hoboken, NJ, USA, 1998; Volume 326. [Google Scholar]
- Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - McCuen, R.H.; Knight, Z.; Cutter, A.G. Evaluation of the Nash–Sutcliffe Efficiency Index. J. Hydrol. Eng.
**2006**, 11, 597–602. [Google Scholar] [CrossRef] - Lin, F.; Chen, X.; Yao, H. Evaluating the use of Nash-Sutcliffe Efficiency coefficient in goodness-of-fit measures for daily runoff simulation with SWAT. J. Hydrol. Eng.
**2017**, 22, 05017023. [Google Scholar] [CrossRef] - Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol.
**2009**, 377, 80–91. [Google Scholar] [CrossRef] - Milella, P.; Bisantino, T.; Gentile, F.; Iacobellis, V.; Liuzzi, G.T. Diagnostic analysis of distributed input and parameter datasets in Mediterranean basin streamflow modeling. J. Hydrol.
**2012**, 472–473, 262–276. [Google Scholar] [CrossRef] - Zajac, Z.; Revilla-Romero, B.; Salamon, P.; Burek, P.; Hirpa, F.A.; Beck, H. The impact of lake and reservoir parameterization on global streamflow simulation. J. Hydrol.
**2017**, 548, 552–568. [Google Scholar] [CrossRef] - Paul, M.; Negahban-Azar, M. Sensitivity and uncertainty analysis for streamflow prediction using multiple optimization algorithms and objective functions: San Joaquin Watershed, California. Modeling Earth Syst. Environ.
**2018**, 4, 1509–1525. [Google Scholar] [CrossRef] - Alfieri, L.; Lorini, V.; Hirpa, F.A.; Harrigan, S.; Zsoter, E.; Prudhomme, C.; Salamon, P. A global streamflow reanalysis for 1980–2018. J. Hydrol. X
**2020**, 6, 100049. [Google Scholar] [CrossRef] [PubMed] - Hallouin, T.; Bruen, M.; O’Loughlin, F.E. Calibration of hydrological models for ecologically relevant streamflow predictions: A trade-off between fitting well to data and estimating consistent parameter sets? Hydrol. Earth Syst. Sci.
**2020**, 24, 1031–1054. [Google Scholar] [CrossRef] [Green Version] - Knoben, W.J.M.; Freer, J.E.; Woods, R.A. Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores. Hydrol. Earth Syst. Sci.
**2019**, 23, 4323–4331. [Google Scholar] [CrossRef] - Zagoruyko, S.; Komodakis, N. Wide residual networks. arXiv
**2016**, arXiv:1605.07146. [Google Scholar] - Salman, S.; Liu, X. Overfitting mechanism and avoidance in deep neural networks. arXiv
**2019**, arXiv:1901.06566. [Google Scholar] - Hawkins, D.M. The problem of overfitting. J. Chem. Inf. Comput. Sci.
**2004**, 44, 1–12. [Google Scholar] [CrossRef] - Dietterich, T. Overfitting and undercomputing in machine learning. ACM Comput. Surv. CSUR
**1995**, 27, 326–327. [Google Scholar] [CrossRef] - Deng, W.-Y.; Zheng, Q.-H.; Chen, L.; Xu, X.-B. Research on extreme learning of neural networks. Chin. J. Comput.
**2010**, 33, 279–287. [Google Scholar] - Ding, S.; Zhao, H.; Zhang, Y.; Xu, X.; Nie, R. Extreme learning machine: Algorithm, theory and applications. Artif. Intell. Rev.
**2015**, 44, 103–115. [Google Scholar] [CrossRef] - Ashiquzzaman, A.; Tushar, A.K.; Islam, M.; Shon, D.; Im, K.; Park, J.-H.; Lim, D.-S.; Kim, J. Reduction of Overfitting in Diabetes Prediction Using Deep Learning Neural Network. In IT Convergence and Security 2017; Springer: Berlin/Heidelberg, Germany, 2018; pp. 35–43. [Google Scholar]
- Sheela, K.G.; Deepa, S.N. Review on methods to fix number of hidden neurons in neural networks. Math. Probl. Eng.
**2013**, 2013, 425740. [Google Scholar] [CrossRef] - Nair, V.; Hinton, G.E. Rectified Linear Units Improve Restricted Boltzmann Machines. In Proceedings of the 27th International Conference on International Conference on Machine Learning, Haifa, Israel, 21–24 June 2010. [Google Scholar]
- Liu, Z.P.; Castagna, J.P. Avoiding Overfitting Caused by Noise Using a Uniform Training Mode. In Proceedings of the IJCNN’99 International Joint Conference on Neural Networks (Cat. No.99CH36339), Washington, DC, USA, 10–16 July 1999; Volume 1783, pp. 1788–1793. [Google Scholar]
- Martín-Félez, R.; Xiang, T. Uncooperative gait recognition by learning to rank. Pattern Recognit.
**2014**, 47, 3793–3806. [Google Scholar] [CrossRef] - Qian, L.; Hu, L.; Zhao, L.; Wang, T.; Jiang, R. Sequence-dropout block for reducing overfitting problem in image classification. IEEE Access
**2020**, 8, 62830–62840. [Google Scholar] [CrossRef] - Bejani, M.M.; Ghatee, M. A systematic review on overfitting control in shallow and deep neural networks. Artif. Intell. Rev.
**2021**, 54, 6391–6438. [Google Scholar] [CrossRef] - Uddameri, V.; Singaraju, S.; Karim, A.; Gowda, P.; Bailey, R.; Schipanski, M. Understanding climate-hydrologic-human interactions to guide groundwater model development for southern high plains. J. Contemp. Water Res. Educ.
**2017**, 162, 79–99. [Google Scholar] [CrossRef] - De Girolamo, A.M.; Bouraoui, F.; Buffagni, A.; Pappagallo, G.; Lo Porto, A. Hydrology under climate change in a temporary river system: Potential impact on water balance and flow regime. River Res. Appl.
**2017**, 33, 1219–1232. [Google Scholar] [CrossRef] - Reichstein, M.; Camps-Valls, G.; Stevens, B.; Jung, M.; Denzler, J.; Carvalhais, N.; Prabhat. Deep learning and process understanding for data-driven Earth system science. Nature
**2019**, 566, 195–204. [Google Scholar] [CrossRef] - Meredig, B.; Antono, E.; Church, C.; Hutchinson, M.; Ling, J.; Paradiso, S.; Blaiszik, B.; Foster, I.; Gibbons, B.; Hattrick-Simpers, J. Can machine learning identify the next high-temperature superconductor? Examining extrapolation performance for materials discovery. Mol. Syst. Des. Eng.
**2018**, 3, 819–825. [Google Scholar] [CrossRef] - Reyes, K.G.; Maruyama, B. The machine learning revolution in materials? MRS Bull.
**2019**, 44, 530–537. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**a**) Map of the study area and the relative location of the streamflow monitoring station, (

**b**) Average precipitation, and (

**c**) Digital elevation map of the Colorado River watershed in Texas.

**Figure 3.**Correlation coefficients between the climate variables, Precipitation at each month (P), Precipitation of the last month (P-Lag1), Precipitation of the second last month (P-Lag2), Evapotranspiration at each month (ET), Evapotranspiration of the last month (ET-Lag1), Evapotranspiration of the second last month (ET-Lag2), and the streamflow data.

**Figure 6.**Observed vs. simulated flowrates for the no-flow events by the investigated models during the testing period.

**Figure 7.**Evaluation of the predictive performance of the models with respect to capturing the extreme high flows during the testing period.

Minimum | Median | Mean | Maximum | |
---|---|---|---|---|

Flowrate (m^{3}/s) | 0 | 0.013 | 0.377 | 20.102 |

Precipitation (mm) | 0 | 29.8 | 42.0 | 251.2 |

ET (mm) | 2.1 | 64.8 | 80.6 | 221.33 |

ELM | CNN | LSTM | SA–LSTM | |
---|---|---|---|---|

MAE (m^{3}/s) | 0 | 0.02 | 0.04 | 0.04 |

RMSE (m^{3}/s) | 0 | 0.04 | 0.07 | 0.07 |

d | 1 | 1 | 1 | 1 |

r | 1 | 1 | 1 | 1 |

R^{2} | 1 | 1 | 0.99 | 0.99 |

NSE | 1 | 1 | 0.99 | 0.99 |

KGE | 1 | 0.98 | 0.99 | 0.99 |

**Table 3.**Summary of model evaluation metrics during the testing period (the best performing model is highlighted with respect to each metric).

ELM | CNN | LSTM | SA–LSTM | |
---|---|---|---|---|

MAE (m^{3}/s) | 1.15 | 0.51 | 0.49 | 0.47 |

RMSE (m^{3}/s) | 1.85 | 1.28 | 1.26 | 1.24 |

d | 0.81 | 0.9 | 0.92 | 0.92 |

r | 0.7 | 0.9 | 0.88 | 0.88 |

R^{2} | 0.49 | 0.82 | 0.78 | 0.77 |

NSE | 0.47 | 0.75 | 0.76 | 0.76 |

KGE | 0.48 | 0.63 | 0.7 | 0.73 |

**Table 4.**Summary of the percentage of negative flowrate estimations by each model during the testing period.

ELM | CNN | LSTM | SA–LSTM | |
---|---|---|---|---|

% of negative flowrates | 36% | 45% | 30% | 21% |

**Table 5.**Summary of estimation errors for each model for the three highest flowrates during the testing period.

Error in Flood Estimation% | ELM | CNN | LSTM | SA–LSTM |
---|---|---|---|---|

September 2014 | −47% | −37% | −39% | −39% |

May 2015 | −42% | −43% | −29% | −24% |

June 2021 | −56% | −25% | +6% | +6% |

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**MDPI and ACS Style**

Forghanparast, F.; Mohammadi, G.
Using Deep Learning Algorithms for Intermittent Streamflow Prediction in the Headwaters of the Colorado River, Texas. *Water* **2022**, *14*, 2972.
https://doi.org/10.3390/w14192972

**AMA Style**

Forghanparast F, Mohammadi G.
Using Deep Learning Algorithms for Intermittent Streamflow Prediction in the Headwaters of the Colorado River, Texas. *Water*. 2022; 14(19):2972.
https://doi.org/10.3390/w14192972

**Chicago/Turabian Style**

Forghanparast, Farhang, and Ghazal Mohammadi.
2022. "Using Deep Learning Algorithms for Intermittent Streamflow Prediction in the Headwaters of the Colorado River, Texas" *Water* 14, no. 19: 2972.
https://doi.org/10.3390/w14192972