Abstract
Precise and reliable irrigation water use (IWU) prediction is beneficial for irrigation district reservoirs interaction and water resources management. However, existing methods face the challenges of high prediction errors at extreme points and accumulative error problem. Meanwhile, ignoring the effects of spurious relationships are among the driving factors on prediction results. This study introduces the Peter and Clark Momentary Conditional Independence (PCMCI) causal inference method to analyze driving factors. The causal inference results of PCMCI are taken as input to the IWU prediction model. This investigation constructs six IWU forecasting models, including the Informer neural network, long short-term memory (LSTM) neural network, attention-based LSTM network, the Prophet model, random forest model, and seasonal autoregressive integrated moving average (SARIMA). The performance of these six models and their variants are evaluated and compared by the long-term month IWU data series of the Zhanghe irrigation area of China. The results show that the Informer model based on self-attention mechanism is more advantageous than others. The PCMCI method can overcome the spurious relationships, and contribute to a clearer understanding of physical mechanisms, as compared to the correlation analysis. Combined with the dynamic time warping barycenter averaging (DBA) data augmentation method, the proposed DBA-PCMCI-Informer method can reduce the prediction errors at extreme points, and improve the IWU forecasting accuracy. This approach alleviates the accumulative error problem, enabling high accuracy even in multistep prediction.
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Data Availability
Available from the corresponding authors upon reasonable request.
Abbreviations
- \(A_t\) :
-
Actual value
- \(D_O\) :
-
Original dataset
- \(D_{OE}\) :
-
Test dataset
- \(D_{OT}\) :
-
Original training set
- \(D_T\) :
-
Training dataset MAMP
- \(F_t\) :
-
Forecast value
- X :
-
Variable X in the dataset
- \(\bar{X}\) :
-
Mean value of variable X in the data set
- Y :
-
Variable Y in the dataset
- \(X_t\) :
-
Potential time-relevant system
- \(P(X_t^j)\) :
-
The parents of causality of \(X_t\)
- \(\hat{P}(X_t^j)\) :
-
The preliminary parents
- S :
-
The strongest p parents in the \(\hat{P}(X_t^j)\) (a superset)
- \(\eta _t^j\) :
-
The mutually independent dynamical noise
- \(\tau\) :
-
The time delays
- \(\not \! \perp \!\!\! \perp\) :
-
Conditions not independent
- \(\perp \!\!\! \perp\) :
-
Condition independent
- \(\rightarrow\) :
-
The causal link pointers
- Adam:
-
Adaptive Moment Estimation optimizer
- AIC:
-
Akaike Information Criterion
- AP:
-
Atmospheric Pressure
- CA:
-
Canola Area
- CMR:
-
Cumulative Monthly Rainfall
- CMSH:
-
Cumulative Monthly Sunshine Hours
- CP:
-
Canola Price
- CRP:
-
Crop Production
- CY:
-
Canola Yield
- DBA:
-
Dynamic time warping Barycenter Averaging
- DL:
-
Deep Learning
- ELU:
-
Exponential Linear Unit
- GP:
-
Grain Prices
- HUM:
-
Humidity
- IWU:
-
Irrigation Water Use
- LSTM:
-
Long-Short Term Memory
- LSTMa:
-
LSTM with Attention Mechanism
- MAE:
-
Mean Absolute Error
- MAMP:
-
Maximum Monthly Pressure
- MARH:
-
Monthly Average Relative Humidity
- MAT:
-
Monthly Average Temperature
- MCI:
-
Momentary Conditional Independence
- MIMP:
-
Minimum Monthly Pressure
- ML:
-
Machine Learning
- MMAT:
-
Monthly Maximum Temperature
- MMH:
-
Monthly Minimum Humidity
- MMIT:
-
Monthly Minimum Temperature
- MMP:
-
Monthly Mean air Pressure
- MSE:
-
Mean Square Error
- PCMCI:
-
Peter and Clark Momentary Conditional Independence
- PLS:
-
Planting Structure
- PRE:
-
Precipitation
- NSE:
-
Nash-Sutcliffe Efficiency
- RA:
-
Rice Area
- ReLU:
-
Rectified Linear Unit
- RF:
-
Random Forest
- RMSE:
-
Root Mean Square Error
- RNN:
-
Recurrent Neural Network
- RP:
-
Rice Price
- RY:
-
Rice Yield
- SARIMA:
-
Seasonal Autoregressive Integrated Moving Average
- SH:
-
Sunshine Hours
- sMAPE:
-
symmetric Mean Absolute Percentage Error
- TEM:
-
Temperature
- WA:
-
Wheat Area
- WP:
-
Wheat Price
- WY:
-
Wheat Yield
- ZID:
-
Zhanghe Irrigation District
References
Abbasimehr H, Shabani M, Yousefi M (2020) An optimized model using LSTM network for demand forecasting. Comput Ind Eng 143:106435. https://doi.org/10.1016/j.cie.2020.106435
Allen RG, Pereira LS, Raes D, Smith M et al (1998) Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome 300(9):D05109
Almorox J, Hontoria C (2004) Global solar radiation estimation using sunshine duration in Spain. Energy Convers Manage 45(9–10):1529–1535. https://doi.org/10.1016/j.enconman.2003.08.022
Babel M, Gupta AD, Pradhan P (2007) A multivariate econometric approach for domestic water demand modeling: an application to Kathmandu. Nepal. Water Resour Manage 21(3):573–589. https://doi.org/10.1007/s11269-006-9030-6
Bakay MS, Ağbulut Ü (2021) Electricity production based forecasting of greenhouse gas emissions in turkey with deep learning, support vector machine and artificial neural network algorithms. J Cleaner Prod 285:125324. https://doi.org/10.1016/j.jclepro.2020.125324
Barnett L, Barrett AB, Seth AK (2009) Granger causality and transfer entropy are equivalent for gaussian variables. Phys Rev Lett 103(23):238701. https://doi.org/10.1103/PhysRevLett.103.238701
Barrios-Perez C, Okada K, Varón GG, Ramirez-Villegas J, Rebolledo MC, Prager SD (2021) How does El Niño Southern Oscillation affect rice-producing environments in central Colombia? Agric For Meteorol 306:108443. https://doi.org/10.1016/j.agrformet.2021.108443
Boretti A, Rosa L (2019) Reassessing the projections of the world water development report. NPJ Clean Water 2(1):1–6. https://doi.org/10.1038/s41545-019-0039-9
Brentan BM, Luvizotto E Jr, Herrera M, Izquierdo J, Pérez-García R (2017) Hybrid regression model for near real-time urban water demand forecasting. J Comput Appl Math 309:532–541. https://doi.org/10.1016/j.cam.2016.02.009
Briët J, Harremoës P (2009) Properties of classical and quantum Jensen-Shannon divergence. Phys Rev A 79(5):052311. https://doi.org/10.1103/PhysRevA.79.052311
Caiado J, etal. (2010) Performance of combined double seasonal univariate time series models for forecasting water demand. J Hydrol Eng 15(3):215. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000182
Cholewa T, Siuta-Olcha A, Smolarz A, Muryjas P, Wolszczak P, Guz Ł, Balaras CA (2021) On the short term forecasting of heat power for heating of building. J Cleaner Prod 307:127232. https://doi.org/10.1016/j.jclepro.2021.127232
Cutler DR, Edwards TC Jr, Beard KH, Cutler A, Hess KT, Gibson J, Lawler JJ (2007) Random forests for classification in ecology. Ecology 88(11):2783–2792
Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30
Deo RC, Wen X, Qi F (2016) A wavelet-coupled support vector machine model for forecasting global incident solar radiation using limited meteorological dataset. Appl Energy 168:568–593. https://doi.org/10.1016/j.apenergy.2016.01.130
Donkor EA, Mazzuchi TA, Soyer R, Alan Roberson J (2014) Urban water demand forecasting: review of methods and models. J Water Resour Plann Manage 140(2):146–159. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000314
Endres D, Schindelin J (2003) A new metric for probability distributions. IEEE Trans Inform Theory 49(7):1858–1860. https://doi.org/10.1109/TIT.2003.813506
Forestier G, Petitjean F, Dau HA, Webb GI, Keogh E (2017) Generating synthetic time series to augment sparse datasets. In: IEEE international conference on data mining, pp 865–870
Foster T, Mieno T, Brozović N (2020) Satellite-based monitoring of irrigation water use: Assessing measurement errors and their implications for agricultural water management policy. Water Resour Res 56(11):e2020WR028378. https://doi.org/10.1029/2020WR028378
Gao F, Chi H, Shao X (2021) Forecasting residential electricity consumption using a hybrid machine learning model with online search data. Appl Energy 300:117393. https://doi.org/10.1016/j.apenergy.2021.117393
García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Inform Sciences 180(10):2044–2064. https://doi.org/10.1016/j.ins.2009.12.010
Guo G, Liu S, Wu Y, Li J, Zhou R, Zhu X (2018) Short-term water demand forecast based on deep learning method. J Water Resour Plann Manage 144(12):04018076. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000992
Hlinka J, Hartman D, Vejmelka M, Runge J, Marwan N, Kurths J, Paluš M (2013) Reliability of inference of directed climate networks using conditional mutual information. Entropy 15(6):2023–2045. https://doi.org/10.3390/e15062023
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Kim TY, Cho SB (2019) Predicting residential energy consumption using CNN-LSTM neural networks. Energy 182:72–81. https://doi.org/10.1016/j.energy.2019.05.230
Kisi O (2016) Modeling reference evapotranspiration using three different heuristic regression approaches. Agric Water Manage 169:162–172. https://doi.org/10.1016/j.agwat.2016.02.026
Kratzert F, Klotz D, Brenner C, Schulz K, Herrnegger M (2018) Rainfall-runoff modelling using long short-term memory (lstm) networks. Hydrol Earth Syst Sci 22(11):6005–6022. https://doi.org/10.5194/hess-22-6005-2018
Kretschmer M, Coumou D, Donges JF, Runge J (2016) Using causal effect networks to analyze different Arctic drivers of midlatitude winter circulation. J Clim 29(11):4069–4081. https://doi.org/10.1175/JCLI-D-15-0654.1
Kretschmer M, Cohen J, Matthias V, Runge J, Coumou D (2018) The different stratospheric influence on cold-extremes in Eurasia and North America. NPJ Clim Atmos Sci 1(1):1–10. https://doi.org/10.1038/s41612-018-0054-4
Krich C, Runge J, Miralles DG, Migliavacca M, Perez-Priego O, El-Madany T, Carrara A, Mahecha MD (2020) Estimating causal networks in biosphere-atmosphere interaction with the PCMCI approach. Biogeosciences 17(4):1033–1061. https://doi.org/10.5194/bg-17-1033-2020
Krich C, Mahecha MD, Migliavacca M, DeKauwe MG, Griebel A, Runge J, Miralles DG (2022) Decoupling between ecosystem photosynthesis and transpiration: a last resort against overheating. Environ Res Lett 17(4):044013. https://doi.org/10.1088/1748-9326/ac583e
LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444. https://doi.org/10.1038/nature14539
Leenhardt D, Trouvat JL, Gonzalès G, Pérarnaud V, Prats S, Bergez JE (2004) Estimating irrigation demand for water management on a regional scale: I. ADEAUMIS, a simulation platform based on bio-decisional modelling and spatial information. Agric Water Manage 68(3):207–232. https://doi.org/10.1016/J.AGWAT.2004.04.004
Li S, Jin X, Xuan Y, Zhou X, Chen W, Wang YX, Yan X (2019) Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting. In: NeurIPS
Luo B, Liu X, Zhang F, Guo P (2021) Optimal management of cultivated land coupling remote sensing-based expected irrigation water forecasting. J Cleaner Prod 308:127370. https://doi.org/10.1016/j.jclepro.2021.127370
Majtey AP, Lamberti PW, Prato DP (2005) Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states. Phys Rev A 72(5):1–6. https://doi.org/10.1103/PhysRevA.72.052310
Masia S, Trabucco A, Spano D, Snyder RL, Sušnik J, Marras S (2021) A modelling platform for climate change impact on local and regional crop water requirements. Agric Water Manage 255:107005. https://doi.org/10.1016/j.agwat.2021.107005
Meng XL, Rosenthal R, Rubin DB (1992) Comparing correlated correlation coefficients. Psychol Bull 111(1):172
Mohammadi B, Mehdizadeh S (2020) Modeling daily reference evapotranspiration via a novel approach based on support vector regression coupled with whale optimization algorithm. Agric Water Manage 237:106145. https://doi.org/10.1016/j.agwat.2020.106145
Mojid MA, Mainuddin M, Murad KFI, MacKirby J (2021) Water usage trends under intensive groundwater-irrigated agricultural development in a changing climate–Evidence from Bangladesh. Agric Water Manage 251:106873. https://doi.org/10.1016/j.agwat.2021.106873
Mouatadid S, Adamowski JF, Tiwari MK, Quilty JM (2019) Coupling the maximum overlap discrete wavelet transform and long short-term memory networks for irrigation flow forecasting. Agric Water Manage 219:72–85. https://doi.org/10.1016/j.agwat.2019.03.045
Ni L, Wang D, Singh VP, Wu J, Wang Y, Tao Y, Zhang J (2020) Streamflow and rainfall forecasting by two long short-term memory-based models. J Hydrol 583:124296. https://doi.org/10.1016/j.jhydrol.2019.124296
Papagiannopoulou C, Miralles DG, Decubber S, Demuzere M, Verhoest NE, Dorigo WA, Waegeman W (2017) A non-linear Granger-causality framework to investigate climate-vegetation dynamics. Geosci Model Dev 10(5):1945–1960. https://doi.org/10.5194/gmd-10-1945-2017
Pearl J (2009) Causality. Cambridge University Press
Pearl J (2013) Linear models: A useful “microscope” for causal analysis. J Causal Inference 1(1):155–170. https://doi.org/10.1515/jci-2013-0003
Pearl J, Mackenzie D (2018) The book of why: the new science of cause and effect. Basic books
Peng Y, Xiao Y, Fu Z, Dong Y, Zheng Y, Yan H, Li X (2019) Precision irrigation perspectives on the sustainable water-saving of field crop production in China: Water demand prediction and irrigation scheme optimization. J Cleaner Prod 230:365–377. https://doi.org/10.1016/j.jclepro.2019.04.347
Perea RG, Poyato EC, Montesinos P, Díaz JA (2015) Irrigation Demand Forecasting Using Artificial Neuro-Genetic Networks. Water Resour Manage 29(15):5551–5567. https://doi.org/10.1007/s11269-015-1134-4
Petitjean F, Ketterlin A, Gançarski P (2011) A global averaging method for dynamic time warping, with applications to clustering. Pattern Recognit 44(3):678–693. https://doi.org/10.1016/j.patcog.2010.09.013
Petitjean F, Forestier G, Webb GI, Nicholson AE, Chen Y, Keogh E (2014) Dynamic time warping averaging of time series allows faster and more accurate classification. In: IEEE international conference on data mining, pp 470–479
Pulido-Calvo I, Montesinos P, Roldán J, Ruiz-Navarro F (2007) Linear regressions and neural approaches to water demand forecasting in irrigation districts with telemetry systems. Biosystems Eng 97(2):283–293. https://doi.org/10.1016/j.biosystemseng.2007.03.003
Rawls E, Kummerfeld E, Zilverstand A (2021) An integrated multimodal model of alcohol use disorder generated by data-driven causal discovery analysis. Commun Biol 4(1):1–12. https://doi.org/10.1038/s42003-021-01955-z
Rezaali M, Quilty J, Karimi A (2021) Probabilistic urban water demand forecasting using wavelet-based machine learning models. J Hydrol 600:126358. https://doi.org/10.1016/j.jhydrol.2021.126358
Rubin DB (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66(5):688–701
Runge J, Petoukhov V, Donges JF, Hlinka J, Jajcay N, Vejmelka M, Hartman D, Marwan N, Paluš M, Kurths J (2015) Identifying causal gateways and mediators in complex spatio-temporal systems. Nat Commun 6(1):1–10. https://doi.org/10.1038/ncomms9502
Runge J, Bathiany S, Bollt E, Camps-Valls G, Coumou D, Deyle E, Glymour C, Kretschmer M, Mahecha MD, Muñoz-Marí J et al (2019a) Inferring causation from time series in Earth system sciences. Nat Commun 10(1):1–13. https://doi.org/10.1038/s41467-019-10105-3
Runge J, Nowack P, Kretschmer M, Flaxman S, Sejdinovic D (2019b) Detecting and quantifying causal associations in large nonlinear time series datasets. Sci Adv 5(11):eaau4996. https://doi.org/10.1126/sciadv.aau4996
Saggi MK, Jain S (2020) Application of fuzzy-genetic and regularization random forest (FG-RRF): estimation of crop evapotranspiration (ETc) for maize and wheat crops. Agric Water Manage 229:105907. https://doi.org/10.1016/j.agwat.2019.105907
Salloom T, Kaynak O, He W (2021) A novel deep neural network architecture for real-time water demand forecasting. J Hydrol 599:126353. https://doi.org/10.1016/j.jhydrol.2021.126353
Saruwatari N, Yomota A (1995) Forecasting system of irrigation water on paddy field by fuzzy theory. Agric Water Manage 28(2):163–178. https://doi.org/10.1016/0378-3774(95)92338-F
Shu X, Peng Y, Ding W, Wang Z, Wu J (2022) Multi-step-ahead monthly streamflow forecasting using convolutional neural networks. Water Resour Manage 36(11):3949–3964. https://doi.org/10.1007/s11269-022-03165-6
Smith JA (1988) A model of daily municipal water use for short-term forecasting. Water Resour Res 24(2):201–206
Smith R, Steiner J, Meyer W, Erskine D (1985) Influence of season to season variability in weather on irrigation scheduling of wheat: a simulation study. Irrigation Sci 6(4):241–251
Spirtes P, Glymour C (1991) An algorithm for fast recovery of sparse causal graphs. Soc Sci Comput Rev 9(1):62–72
Sugihara G, May R, Ye H, Hsieh Ch, Deyle E, Fogarty M, Munch S (2012) Detecting causality in complex ecosystems. Science 338(6106):496–500. https://doi.org/10.1126/science.1227079
Tang Y, Zhang F, Wang S, Zhang X, Guo S, Guo P (2019) A distributed interval nonlinear multiobjective programming approach for optimal irrigation water management in an arid area. Agric Water Manage 220:13–26. https://doi.org/10.1016/j.agwat.2019.03.052
Tao F, Yokozawa M, Hayashi Y, Lin E (2003) Future climate change, the agricultural water cycle, and agricultural production in China. Agric Ecosyst Environ 95(1):203–215. https://doi.org/10.1016/S0167-8809(02)00093-2
Taylor SJ, Letham B (2018) Forecasting at scale. Am Stat 72(1):37–45. https://doi.org/10.7287/peerj.preprints.3190v2
Tong F, Guo P (2013) Forecast method of irrigation water use considering uncertain runoff. Trans Chin Soc Agric Eng 29(7):66–75. https://doi.org/10.3969/j.issn.1002-6819.2013.07.009
Van Aelst P, Ragab R, Feyen J, Raes D (1988) Improving irrigation management by modelling the irrigation schedule. Agric Water Manag 13(2–4):113–125
Wang Y, Huang M, Zhu X, Zhao L (2016) Attention-based LSTM for aspect-level sentiment classification. In: EMNLP, pp 606–615
Wang Z, Si Y, Chu H (2022) Daily streamflow prediction and uncertainty using a long short-term memory (LSTM) network coupled with bootstrap. Water Resour Manage 36(12):4575–4590. https://doi.org/10.1007/s11269-022-03264-4
Wu N, Green B, Ben X, O’Banion S (2020) Deep transformer models for time series forecasting: The influenza prevalence case. arXiv preprint arXiv:2001.08317
Xu H, Tian Z, He X, Wang J, Sun L, Fischer G, Fan D, Zhong H, Wu W, Pope E et al (2019) Future increases in irrigation water requirement challenge the water-food nexus in the northeast farming region of China. Agric Water Manage 213:594–604. https://doi.org/10.1016/j.agwat.2018.10.045
Xu Z, Lv Z, Li J, Shi A (2022) A novel approach for predicting water demand with complex patterns based on ensemble learning. Water Resour Manage 36(11):4293–4312. https://doi.org/10.1007/s11269-022-03255-5
Yan R, Liao J, Yang J, Sun W, Nong M, Li F (2021) Multi-hour and multi-site air quality index forecasting in Beijing using CNN, LSTM, CNN-LSTM, and spatiotemporal clustering. Expert Syst Appl 169:114513. https://doi.org/10.1016/j.eswa.2020.114513
Yin J, Medellín-Azuara J, Escriva-Bou A, Liu Z (2021) Bayesian machine learning ensemble approach to quantify model uncertainty in predicting groundwater storage change. Sci Total Environ 769:144715. https://doi.org/10.1016/j.scitotenv.2020.144715
Zang H, Xu R, Cheng L, Ding T, Liu L, Wei Z, Sun G (2021) Residential load forecasting based on LSTM fusing self-attention mechanism with pooling. Energy 229:120682. https://doi.org/10.1016/j.energy.2021.120682
Zhang C, Long D (2021) Estimating spatially explicit irrigation water use based on remotely sensed evapotranspiration and modeled root zone soil moisture. Water Resour Res 57(12):e2021WR031382. https://doi.org/10.1029/2021WR031382
Zhang J, Li Y, Zhao Y, Hong Y (2017) Wavelet-cointegration prediction of irrigation water in the irrigation district. J Hydrol 544:343–351. https://doi.org/10.1016/j.jhydrol.2016.11.040
Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2020) Informer: Beyond efficient transformer for long sequence time-series forecasting. arXiv preprint arXiv:2012.07436
Acknowledgements
The authors would like to thank the reviewers and the editors for their valuable suggestions and contributions, which significantly helped to improve this article. The authors would like to thank Jakob Runge for sharing their PCMCI code at https://github.com/jakobrunge/ tigra mite, and Haoyi Zhou for sharing their Informer code at https://github.com/zhouha oyi/Informer2020.
Funding
The research project was financially supported by the Natural Science Foundation of China (No. U21A20156) and the Natural Science Foundation of China (52279042).
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Liangfeng Zou: conceptualization, methodology, software, formal analysis, resources, writing of the original draft; Yuanyuan Zha: conceptualization, funding acquisition, reviewing and editing; Yuqing Diao: software, formal analysis; Chi Tang: data curation; Wenquan Gu: reviewing and editing; Dongguo Shao: resources, supervision, funding acquisition, reviewing and editing.
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Highlights
• Introducing the Peter and Clark Momentary Conditional Independence (PCMCI) to analyze driving factors.
• Building Informer networks to forecast irrigation water use (IWU).
• Proposing a novel IWU forecast method and proving its validity by a real case.
• The proposed approach can improve accuracy by 17.6%-72.1%.
• The PCMCI method can eliminate spurious relationships effectively.
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Zou, L., Zha, Y., Diao, Y. et al. Coupling the Causal Inference and Informer Networks for Short-term Forecasting in Irrigation Water Usage. Water Resour Manage 37, 427–449 (2023). https://doi.org/10.1007/s11269-022-03381-0
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DOI: https://doi.org/10.1007/s11269-022-03381-0