Stochastic periodic autoregressive to anything (SPARTA): Modelling and simulation of cyclostationary processes with arbitrary marginal distributions

I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Stochastic periodic autoregressive to anything (SPARTA): Modelling and simulation of cyclostationary processes with arbitrary marginal distributions, Water Resources Research, 54 (1), 161–185, WRCR23047, doi:10.1002/2017WR021394, 2018.



Stochastic models in hydrology traditionally aim at reproducing the empirically derived statistical characteristics of the observed data rather than any specific distribution model that attempts to describe the usually non-Gaussian statistical behavior of the associated processes. SPARTA (Stochastic Periodic AutoRegressive To Anything) offers an alternative and novel approach which allows the explicit representation of each process of interest with any distribution model, while simultaneously establishes dependence patterns that cannot be fully captured by the typical linear stochastic schemes. Cornerstone of the proposed approach is the Nataf joint-distribution model, which is related with the Gaussian copula, combined with Gaussian periodic autoregressive processes. In order to obtain the target stochastic structure, we have also developed a computationally simple and efficient algorithm, based on a hybrid Monte-Carlo procedure that is used to approximate the required equivalent correlation coefficients. Theoretical and practical benefits of the proposed method, contrasted to outcomes from widely used stochastic models, are demonstrated by means of real-world as well as hypothetical monthly simulation examples involving both univariate and multivariate time series.

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Our works referenced by this work:

1. D. Koutsoyiannis, and A. Manetas, Simple disaggregation by accurate adjusting procedures, Water Resources Research, 32 (7), 2105–2117, doi:10.1029/96WR00488, 1996.
2. D. Koutsoyiannis, Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology, Water Resources Research, 35 (4), 1219–1229, doi:10.1029/1998WR900093, 1999.
3. D. Koutsoyiannis, A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, doi:10.1029/2000WR900044, 2000.
4. D. Koutsoyiannis, G. Karavokiros, A. Efstratiadis, N. Mamassis, A. Koukouvinos, and A. Christofides, A decision support system for the management of the water resource system of Athens, Physics and Chemistry of the Earth, 28 (14-15), 599–609, doi:10.1016/S1474-7065(03)00106-2, 2003.
5. D. Koutsoyiannis, Uncertainty, entropy, scaling and hydrological stochastics, 1, Marginal distributional properties of hydrological processes and state scaling, Hydrological Sciences Journal, 50 (3), 381–404, doi:10.1623/hysj.50.3.381.65031, 2005.
6. D. Koutsoyiannis, H. Yao, and A. Georgakakos, Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods, Hydrological Sciences Journal, 53 (1), 142–164, doi:10.1623/hysj.53.1.142, 2008.
7. S.M. Papalexiou, D. Koutsoyiannis, and A. Montanari, Can a simple stochastic model generate rich patterns of rainfall events?, Journal of Hydrology, 411 (3-4), 279–289, 2011.
8. S.M. Papalexiou, and D. Koutsoyiannis, Entropy based derivation of probability distributions: A case study to daily rainfall, Advances in Water Resources, 45, 51–57, doi:10.1016/j.advwatres.2011.11.007, 2012.
9. A. Efstratiadis, Y. Dialynas, S. Kozanis, and D. Koutsoyiannis, A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence, Environmental Modelling and Software, 62, 139–152, doi:10.1016/j.envsoft.2014.08.017, 2014.
10. P. Kossieris, C. Makropoulos, C. Onof, and D. Koutsoyiannis, A rainfall disaggregation scheme for sub-hourly time scales: Coupling a Bartlett-Lewis based model with adjusting procedures, Journal of Hydrology, 556, 980–992, doi:10.1016/j.jhydrol.2016.07.015, 2018.

Our works that reference this work:

1. I. Tsoukalas, C. Makropoulos, and A. Efstratiadis, Stochastic simulation of periodic processes with arbitrary marginal distributions, 15th International Conference on Environmental Science and Technology (CEST2017), Rhodes, Global Network on Environmental Science and Technology, 2017.
2. P. Dimitriadis, and D. Koutsoyiannis, Stochastic synthesis approximating any process dependence and distribution, Stochastic Environmental Research & Risk Assessment, 32 (6), 1493–1515, doi:10.1007/s00477-018-1540-2, 2018.
3. I. Tsoukalas, S.M. Papalexiou, A. Efstratiadis, and C. Makropoulos, A cautionary note on the reproduction of dependencies through linear stochastic models with non-Gaussian white noise, Water, 10 (6), 771, doi:10.3390/w10060771, 2018.
4. I. Tsoukalas, C. Makropoulos, and D. Koutsoyiannis, Simulation of stochastic processes exhibiting any-range dependence and arbitrary marginal distributions, Water Resources Research, 54 (11), 9484–9513, doi:10.1029/2017WR022462, 2018.
5. P. Kossieris, and C. Makropoulos, Exploring the statistical and distributional properties of residential water demand at fine time scales, Water, 10 (10), 1481, doi:10.3390/w10101481, 2018.
6. C. Rebolho, V. Andréassian, I. Tsoukalas, et A. Efstratiadis, La crue du Loing de Juin 2016 était-elle exceptionnelle?, De la prévision des crues à la gestion de crise, Avignon, Société Hydrotechnique de France, 2018.
7. I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure, Journal of Hydrology, 575, 354–380, doi:10.1016/j.jhydrol.2019.05.017, 2019.
8. P. Kossieris, I. Tsoukalas, C. Makropoulos, and D. Savic, Simulating marginal and dependence behaviour of water demand processes at any fine time scale, Water, 11 (5), 885, doi:10.3390/w11050885, 2019.
9. C. Makropoulos, and D. Savic, Urban hydroinformatics: past, present and future, Water, 11 (10), 1959, doi:10.3390/w11101959, 2019.
10. D. Nikolopoulos, G. Moraitis, D. Bouziotas, A. Lykou, G. Karavokiros, and C. Makropoulos, Cyber-physical stress-testing platform for water distribution networks, Journal of Environmental Engineering, 146 (7), 04020061, doi:10.1061/(ASCE)EE.1943-7870.0001722, 2020.
11. I. Tsoukalas, P. Kossieris, and C. Makropoulos, Simulation of non-Gaussian correlated random variables, stochastic processes and random fields: Introducing the anySim R-Package for environmental applications and beyond, Water, 12 (6), 1645, doi:10.3390/w12061645, 2020.
12. H. Elsayed, S. Djordjević, D. Savic, I. Tsoukalas, and C. Makropoulos, The Nile water-food-energy nexus under uncertainty: Impacts of the Grand Ethiopian Renaissance Dam, Journal of Water Resources Planning and Management - ASCE, 146 (11), 04020085, doi:10.1061/(ASCE)WR.1943-5452.0001285, 2020.
13. A. Efstratiadis, I. Tsoukalas, and D. Koutsoyiannis, Generalized storage-reliability-yield framework for hydroelectric reservoirs, Hydrological Sciences Journal, 66 (4), 580–599, doi:10.1080/02626667.2021.1886299, 2021.
14. P. Kossieris, I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Generic framework for downscaling statistical quantities at fine time-scales and its perspectives towards cost-effective enrichment of water demand records, Water, 13 (23), 3429, doi:10.3390/w13233429, 2021.
15. K.-K. Drakaki, G.-K. Sakki, I. Tsoukalas, P. Kossieris, and A. Efstratiadis, Day-ahead energy production in small hydropower plants: uncertainty-aware forecasts through effective coupling of knowledge and data, Advances in Geosciences, 56, 155–162, doi:10.5194/adgeo-56-155-2022, 2022.
16. G.-K. Sakki, I. Tsoukalas, P. Kossieris, C. Makropoulos, and A. Efstratiadis, Stochastic simulation-optimisation framework for the design and assessment of renewable energy systems under uncertainty, Renewable and Sustainable Energy Reviews, 168, 112886, doi:10.1016/j.rser.2022.112886, 2022.
17. G. Moraitis, G.-K. Sakki, G. Karavokiros, D. Nikolopoulos, P. Kossieris, I. Tsoukalas, and C. Makropoulos, Exploring the cyber-physical threat landscape of water systems: A socio-technical modelling approach, Water, 15 (9), 1687, doi:10.3390/w15091687, 2023.
18. A. Efstratiadis, I. Tsoukalas, and P. Kossieris, Improving hydrological model identifiability by driving calibration with stochastic inputs, Advances in Hydroinformatics: Machine Learning and Optimization for Water Resources, edited by G. A. Corzo Perez and D. P. Solomatine, doi:10.1002/9781119639268.ch2, American Geophysical Union, 2024.

Other works that reference this work (this list might be obsolete):

1. Papalexiou, S. M., Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency, Advances in Water Resources, 115, 234-252, doi:10.1016/j.advwatres.2018.02.013, 2018.
2. Brunner, M. I., A. Bárdossy, and R. Furrer, Technical note: Stochastic simulation of streamflow time series using phase randomization, Hydrology and Earth System Sciences, 23, 3175-3187, doi:10.5194/hess-23-3175-2019, 2019.
3. Marković, D., S. Ilić, D. Pavlović, J. Plavšić, and N. Ilich, Multivariate and multi-scale generator based on non-parametric stochastic algorithms, Journal of Hydroinformatics, 21(6), 1102-1117, doi:10.2166/hydro.2019.071, 2019.
4. #Elsayed, H., S. Djordjević, and D. Savić, The Nile water, food and energy nexus – A system dynamics model, 7th International Computing & Control for the Water Industry Conference, Exeter, United Kingdom, 2019.
5. Nazemi, A., M. Zaerpour, and E. Hassanzadeh, Uncertainty in bottom-up vulnerability assessments of water supply systems due to regional streamflow generation under changing conditions, Journal of Water Resources Planning and Management, 146(2), doi:10.1061/(ASCE)WR.1943-5452.0001149, 2020.
6. Barber, C., J. R. Lamontagne, and R. M. Vogel, Improved estimators of correlation and R2 for skewed hydrologic data, Hydrological Sciences Journal, 65(1), 87-101, doi:10.1080/02626667.2019.1686639, 2020.
7. Dutta, R., and R. Maity, Temporal networks based approach for non‐stationary hydroclimatic modelling and its demonstration with streamflow prediction, Water Resources Research, 56(8), e2020WR027086, doi:10.1029/2020WR027086, 2020.
8. Demetriou, E., G. Mallouppas, and C.Hadjistassou, Embracing carbon neutral electricity and transportation sectors in Cyprus, Energy, doi:10.1016/, 2021.
9. Pouliasis, G., G. A. Torres-Alves, and O. Morales-Napoles, Stochastic modeling of hydroclimatic processes using vine copulas, Water, 13(16), 2156, doi:10.3390/w13162156, 2021.
10. Zang, N., J. Zhu, X. Wang, Y. Liao, G. Cao, C. Li, Q. Liu, and Z. Yang, Eutrophication risk assessment considering joint effects of water quality and water quantity for a receiving reservoir in the South-to-North Water Transfer Project, China, Journal of Cleaner Production, 331, 129966, doi:10.1016/j.jclepro.2021.129966, 2021.
11. Vanem, E., Analysing multivariate extreme conditions using environmental contours and accounting for serial dependence, Renewable Energy, doi:10.1016/j.renene.2022.11.033, 2022.
12. Chadwick, C., F. Babonneau, T. Homem-de-Mello, and A. Letelier, Synthetic simulation of spatially-correlated streamflows: Weighted-modified Fractional Gaussian Noise, Water Resources Research, 60(2), e2023WR035371, doi:10.1029/2023WR035371, 2024.

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