swxg: A Python Library for Generalized Multivariate, Multisite, Copula-Based Stochastic Weather Generation
References
- Wilks DS, Wilby RL. The weather generation game: A review of stochastic weather models. Progress in Physical Geography. 1999;23(3):329–357. DOI: 10.1177/030913339902300302
- Lorenz EN. Deterministic nonperiodic flow. Journal of Atmospheric Sciences. 1963;20:130–141. DOI: 10.1175/1520-0469(1963)020<;0130:DNF>2.0.CO;2
- Berner J, Achatz U, Batté L, Bengtsson L, Cámara ADL, Christensen HM, Colangeli M, Coleman DRB, Crommelin D, Dolaptchiev SI, Franzke CLE, Friederichs P, Imkeller P, Järvinen H, Juricke S, Kitsios V, Lott F, Lucarini V, Mahajan S, Palmer TN, Penland C, Sakradzija M, Von Storch J-S, Weisheimer A, Weniger M, Williams PD, Yano JI. Stochastic parameterization: Toward a new view of weather and climate models. Bulletin of the American Meteorological Society. 2017;98(3):565–588. DOI: 10.1175/BAMS-D-15-00268.1
- Hasselmann K. Stochastic climate models: Part I. Theory. Tellus A: Dynamic Meteorology and Oceanography. 1976;28(6):
473 . DOI: 10.3402/tellusa.v28i6.11316 - Walker WE, Harremoës P, Rotmans J, Van Der Sluijs JP, Van Asselt MBA, Janssen P, Krayer Von Krauss M. Defining uncertainty: A conceptual basis for uncertainty management in model-based decision support. Integrated Assessment. 2003;4(1):5–17. DOI: 10.1076/iaij.4.1.5.16466
- Li W, Wang Q, Zhu H, Tang Z. Influence of internal variability on future changes in extreme wind speed over North America. Global and Planetary Change. 2022;218:
103968 . DOI: 10.1016/j.gloplacha.2022.103968 - Palmer TN. Towards the probabilistic Earth-system simulator: A vision for the future of climate and weather prediction. Quarterly Journal of the Royal Meteorological Society. 2012;138(665):841–861. DOI: 10.1002/qj.1923
- Lempert RJ, Collins MT. Managing the risk of uncertain threshold responses: Comparison of robust, optimum, and precautionary approaches. Risk Analysis. 2007;27(4):1009–1026. DOI: 10.1111/j.1539-6924.2007.00940.x
- Kwakkel JH, Walker WE, Marchau VA. Classifying and communicating uncertainties in model-based policy analysis. International Journal of Technology, Policy and Management. 2010;10(4):299–315. DOI: 10.1504/IJTPM.2010.036918
- Brown C, Boltz F, Freeman S, Tront J, Rodriguez D. Resilience by design: A deep uncertainty approach for water systems in a changing world. Water Security. 2020;9:
100051 . DOI: 10.1016/j.wasec.2019.100051 - Bankes S. Exploratory modeling for policy analysis. Operations Research. 1993;41(3):435–449. DOI: 10.1287/opre.41.3.435
- Moallemi EA, Kwakkel J, De Haan FJ, Bryan BA. Exploratory modeling for analyzing coupled human-natural systems under uncertainty. Global Environmental Change. 2020;65:
102186 . DOI: 10.1016/j.gloenvcha.2020.102186 - Bankes S, Walker WE, Kwakkel JH. Exploratory modeling and analysis. Encyclopedia of Operations Research and Management Science. 2013;532–537. DOI: 10.1007/978-1-4419-1153-7_314
- Gelfert A.
Probing possibilities: Toy models, minimal models, and exploratory models . In: Nepomuceno-Fernández A, Magnani L, Salguero-Lamillar FJ, Barés-Gómez C, Fontaine M (Eds.) Model-Based Reasoning in Science and Technology, vol. 49. Cham: Springer International Publishing; 2019. pp. 3–19. DOI: 10.1007/978-3-030-32722-4_1 - Hadjimichael A, Quinn J, Wilson E, Reed P, Basdekas L, Yates D, Garrison M. Defining robustness, vulnerabilities, and consequential scenarios for diverse stakeholder interests in institutionally complex river basins. Earth’s Future. 2020;8(7):
e2020EF001503 . DOI: 10.1029/2020EF001503 - Hadjimichael A, Quinn J, Reed P. Advancing diagnostic model evaluation to better understand water shortage mechanisms in institutionally complex river basins. Water Resources Research. 2020;56(10):
e2020WR028079 . DOI: 10.1029/2020WR028079 - Quinn JD, Hadjimichael A, Reed PM, Steinschneider S. Can exploratory modeling of water scarcity vulnerabilities and robustness be scenario neutral? Earth’s Future. 2020;8(11):
e2020EF001650 . DOI: 10.1029/2020EF001650 - Gabriel K, Neumann JA. Markov chain model for daily rainfall occurrence at Tel Aviv. Quarterly Journal of the Royal Meteorological Society. 1962;88(375):90–95. DOI: 10.1002/qj.49708837511
- Richardson CW. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research. 1981;17(1):182–190. DOI: 10.1029/WR017i001p00182
- Ailliot P, Allard D, Monbet V, Naveau P. Stochastic weather generators: An overview of weather type models. Journal de la société française de statistique. 2015;156(1):101–113.
- Van Wart J, Grassini P, Yang H, Claessens L, Jarvis A, Cassman KG. Creating long-term weather data from thin air for crop simulation modeling. Agricultural and Forest Meteorology. 2015;209-210:49–58. DOI: 10.1016/j.agrformet.2015.02.020
- Li X, Babovic V. A new scheme for multivariate, multisite weather generator with inter-variable, inter-site dependence and inter-annual variability based on empirical copula approach. Climate Dynamics. 2019;52(3-4):2247– 2267. DOI: 10.1007/s00382-018-4249-5
- Cong RG, Brady M. The interdependence between rainfall and temperature: Copula analyses. The Scientific World Journal. 2012;2012:1–11. DOI: 10.1100/2012/405675
- Rana A, Moradkhani H, Qin Y. Understanding the joint behavior of temperature and precipitation for climate change impact studies. Theoretical and Applied Climatology. 2017;129(1-2):321–339. DOI: 10.1007/s00704-016-1774-1
- Pandey PK, Das L, Jhajharia D, Pandey V. Modelling of interdependence between rainfall and temperature using copula. Modeling Earth Systems and Environment. 2018;4(2):867–879. DOI: 10.1007/s40808-018-0454-9
- Mesbahzadeh T, Miglietta MM, Mirakbari M, Soleimani Sardoo F, Abdolhoseini M. Joint modeling of precipitation and temperature using copula theory for current and future prediction under climate change scenarios in arid lands (case study, Kerman Province, Iran). Advances in Meteorology. 2019;2019:1–15. DOI: 10.1155/2019/6848049
- Wazneh H, Arain MA, Coulibaly P, Gachon P. Evaluating the dependence between temperature and precipitation to better estimate the risks of concurrent extreme weather events. Advances in Meteorology. 2020;2020:1–16. DOI: 10.1155/2020/8763631
- Rupp DE, Li S, Mote PW, Shell KM, Massey N, Sparrow SN, Wallom DCH, Allen MR. Seasonal spatial patterns of projected anthropogenic warming in complex terrain: A modeling study of the Western US. Climate Dynamics. 2017;48(7–8):2191–2213. DOI: 10.1007/s00382-016-3200-x
- Henn B, Newman AJ, Livneh B, Daly C, Lundquist JD. An assessment of differences in gridded precipitation datasets in complex terrain. Journal of Hydrology. 2018;556:1205–1219. DOI: 10.1016/j.jhydrol.2017.03.008
- Steinschneider S, Ray P, Rahat SH, Kucharski J. A weather-regime-based stochastic weather generator for climate vulnerability assessments of water systems in the Western United States. Water Resources Research. 2019;55(8):6923–6945. DOI: 10.1029/2018WR024446
- Chen J, Li X, Xu CY, Zhang XJ, Xiong L, Guo Q. Postprocessing ensemble weather forecasts for introducing multisite and multivariable correlations using rank shuffle and copula theory. Monthly Weather Review. 2022;150(3):551–565. DOI: 10.1175/MWR-D-21-0100.1
- Gupta RS, Steinschneider S, Reed PM. Understanding contributions of paleo-informed natural variability and climate changes on hydroclimate extremes in the central valley region of California; 2023. Available from:
https://essopenarchive.org/users/540265/articles/629110-understanding-contributions-of-paleo-informed-natural-variability-and-climate-changes-on-hydroclimate-extremes-in-the-central-valley-region-of-california?commit=c03d1581c1ba8337f8f570e42963f0e8c4e839c6 - Van de Velde J, Demuzere M, De Baets B, Verhoest N. Future multivariate weather generation by combining Bartlett-Lewis and vine copula models. Hydrological Sciences Journal. 2023;68(1):1–15. DOI: 10.1080/02626667.2022.2144322
- Najibi N, Perez AJ, Arnold W, Schwarz A, Maendly R, Steinschneider S. A statewide, weather-regime based stochastic weather generator for process-based bottom-up climate risk assessments in California – Part I: Model evaluation. Climate Services. 2024;34:
100489 . DOI: 10.1016/j.cliser.2024.100489 - Zaniolo M, Fletcher S, Mauter M. FIND: A synthetic weather generator to control drought frequency, intensity, and duration. Environmental Modelling & Software. 2024;172:
105927 . DOI: 10.1016/j.envsoft.2023.105927 - Richardson CW, Wright DA. WGEN: A model for generating daily weather variables. Report ARS-8 August 1984 83 p, 3 Fig, 12 Tab, 13 Ref, 4 App. 1984.
- Meyer CR, Renschler CS, Vining RC. Implementing quality control on a random number stream to improve a stochastic weather generator. Hydrological Processes. 2008;22(8):1069–1079. DOI: 10.1002/hyp.6668
- Chen J, Brissette FP, Leconte R. WeaGETS – A MATLAB-based daily scale weather generator for generating precipitation and temperature. Procedia Environmental Sciences. 2012;13:2222–2235. DOI: 10.1016/j.proenv.2012.01.211
- Sommer PS, Kaplan JO. A globally calibrated scheme for generating daily meteorology from monthly statistics: Global-WGEN (GWGEN) v1.0. Geoscientific Model Development. 2017;10(10):3771–3791. DOI: 10.5194/gmd-10-3771-2017
- Woodson D, Gangopadhyay S, Bearup L, Verdin A, Shamir E, Halper E, McGuire M. wxgenR: An R package for stochastic weather generation with seasonality. SoftwareX. 2025;31:
102209 . DOI: 10.1016/j.softx.2025.102209 - Semenov MA, Barrow EM. use of a stochastic weather generator in the development of climate change scenarios. Climatic Change. 1997;35(4):397–414. DOI: 10.1023/A:1005342632279
- Cordano E, Eccel E, Luedeling E. RMAWGEN: Multi-site auto-regressive weather generator. Available from:
https://cran.r-project.org/web/packages/RMAWGEN/index.html - Wilks D. Multisite generalization of a daily stochastic precipitation generation model. Journal of Hydrology. 1998;210(1–4):178–191. DOI: 10.1016/S0022-1694(98)00186-3
- Wilks DS. A gridded multisite weather generator and synchronization to observed weather data. Water Resources Research. 2009;45(10):
2009WR007902 . DOI: 10.1029/2009WR007902 - Pandas development team. pandas-dev/pandas: Pandas. Zenodo. Available from:
https://zenodo.org/doi/10.5281/zenodo.3509134 - Bracken C, Rajagopalan B, Zagona E. A hidden Markov model combined with climate indices for multidecadal streamflow simulation. Water Resources Research. 2014;50(10):7836–7846. DOI: 10.1002/2014WR015567
- Gold DF, Gupta RS, Reed PM. Exploring the spatially compounding multi-sectoral drought vulnerabilities in Colorado’s west slope river basins. Earth’s Future. 2024;12(11):
e2024EF004841 . DOI: 10.1029/2024EF004841 - Franzen SE, Farahani MA, Goodwell AE. Information flows: characterizing precipitation-streamflow dependencies in the Colorado headwaters with an information theory approach. Water Resources Research. 2020;56(10):
e2019WR026133 . DOI: 10.1029/2019WR026133 - Lebedev S. hmmlearn. GitHub. Available from:
https://hmmlearn.readthedocs.io/ - Stoica P, Selen Y. Model-order selection. IEEE Signal Processing Magazine. 2004;21(4):36–47. DOI: 10.1109/MSP.2004.1311138
- Tootoonchi F, Sadegh M, Haerter JO, Räty O, Grabs T, Teutschbein C. Copulas for hydroclimatic analysis: A practice-oriented overview. WIREs Water. 2022;9(2):
e1579 . DOI: 10.1002/wat2.1579 - Box GEP, Jenkins GM, Reinsel GC, Ljung GM. Time Series Analysis: Forecasting and Control. 5th ed. Wiley Series in Probability and Statistics. Hoboken, New Jersey: Wiley; 2016.
- MacKinnon JG. Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business & Economic Statistics. 1994;12(2):167–176. DOI: 10.1080/07350015.1994.10510005
- Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics. 1992;54 (1-3):159–178. DOI: 10.1016/0304-4076(92)90104-Y
- Genest C, Boies JC. Detecting dependence with Kendall plots. The American Statistician. 2003;57(4):275–284. DOI: 10.1198/0003130032431
- Cramér H. On the composition of elementary errors: First paper: Mathematical deductions. Scandinavian Actuarial Journal. 1928;1928(1):13–74. DOI: 10.1080/03461238.1928.10416862
- Kolmogorov A. Sulla determinazione empirica di una legge didistribuzione. Giorn Dell’inst Ital Degli Att. 1933;4:89–91.
- Smirnov N. Table for estimating the goodness of fit of empirical distributions. The Annals of Mathematical Statistics. 1948;19(2):279–281. DOI: 10.1214/aoms/1177730256
- Apipattanavis S, Podestá G, Rajagopalan B, Katz RW. A semiparametric multivariate and multisite weather generator. Water Resources Research. 2007;43(11):
W11401 . DOI: 10.1029/2006WR005714 - Nowak K, Prairie J, Rajagopalan B, Lall U. A nonparametric stochastic approach for multisite disaggregation of annual to daily streamflow. Water Resources Research. 2010;46(8):
2009WR008530 . DOI: 10.1029/2009WR008530 - Thames AB, Hadjimichael A, Quinn JD.: Climate sensitivity of agricultural water demand depends on control over growing season: implications for producers in the upper Colorado river basin; 2026. Available from:
https://essopenarchive.org/users/1013018/articles/1378421-climate-sensitivity-of-agricultural-water-demand-depends-on-control-over-growing-season-implications-for-producers-in-the-upper-colorado-river-basin?commit=9f851bfc29430fe7089205921060b7612705ae42 - Stephens MA. EDF statistics for goodness of fit and some comparisons. Journal of the American statistical Association. 1974;69(347):730–737. DOI: 10.1080/01621459.1974.10480196
- Myung IJ. Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology. 2003;47(1):90–100. DOI: 10.1016/S0022-2496(02)00028-7
- Burnham KP, Anderson DR, Burnham KP. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. New York: Springer; 2002.
- Kuha J. AIC and BIC: Comparisons of assumptions and performance. Sociological Methods & Research. 2004;33(2):188–229. DOI: 10.1177/0049124103262065
- Genest C, Rémillard B, Beaudoin D. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics. 2009;44(2):199–213. DOI: 10.1016/j.insmatheco.2007.10.005
- Arnold TW. Uninformative parameters and model selection using Akaike’s information criterion. Journal of Wildlife Management. 2010;74(6):1175–1178. DOI: 10.2193/2009-367
- Mann HB, Whitney DR. On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics. 1947;18(1):50–60. DOI: 10.1214/aoms/1177730491
- Levene H.
Robust tests for equality of variances . In: Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford Studies in Mathematics and Statistics. Redwood City, CA: Stanford University Press; 1960. pp. 278–292. Available from:https://books.google.com/books?id=ZUSsAAAAIAAJ - Thrasher B, Wang W, Michaelis A, Melton F, Lee T, Nemani R. NASA global daily downscaled projections, CMIP6. Scientific Data. 2022;9(1):
262 . DOI: 10.1038/s41597-022-01393-4 - Kao SC, Ghimire GR, Gangrade S.
CMIP6-based multi-model streamflow projections over the conterminousUS . Oak Ridge, TN: Oak Ridge National Laboratory (ORNL); 2023. Available from:https://www.osti.gov/servlets/purl/2007926/ - Dhawan P, Dalla Torre D, Niazkar M, Kaffas K, Larcher M, Righetti M, et al. A comprehensive comparison of bias correction methods in climate model simulations: Application on ERA5-Land across different temporal resolutions. Heliyon. 2024;10(23):
e40352 . DOI: 10.1016/j.heliyon.2024.e40352 - McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 1979;21(2):
239 . DOI: 10.2307/1268522 - Tang B. Orthogonal array-based latin hypercubes. Journal of the American Statistical Association. 1993;88(424):1392–1397. DOI: 10.1080/01621459.1993.10476423
- Reed PM, Hadjimichael A, Malek K, Karimi T, Vernon CR, Srikrishnan V, Gupta RS, Gold DF, Lee B, Keller K, Thurber TB, Rice JS. Addressing Uncertainty in Multisector Dynamics Research. Zenodo; 2025. Available from:
https://zenodo.org/doi/10.5281/zenodo.6110623 - Song X, Zhang J, Zhan C, Xuan Y, Ye M, Xu C. Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications. Journal of Hydrology. 2015;523:739–757. DOI: 10.1016/j.jhydrol.2015.02.013
- Pianosi F, Beven K, Freer J, Hall JW, Rougier J, Stephenson DB, et al. Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modelling & Software. 2016;79:214–232. DOI: 10.1016/j.envsoft.2016.02.008
- Saltelli A, Aleksankina K, Becker W, Fennell P, Ferretti F, Holst N, Li S, Wu Q. Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices. Environmental Modelling & Software. 2019;114:29–39. DOI: 10.1016/j.envsoft.2019.01.012
- Alhija F.
Factor Analysis: An overview and some contemporary advances . In International Encyclopedia of Education. Oxford, UK: Elsevier; 2010. pp. 162–170. DOI: 10.1016/B978-0-08-044894-7.01328-2 - Maydeu-Olivares A, García-Forero C.
Goodness-of-fit testing . In International Encyclopedia of Education. Oxford, UK: Elsevier; 2010. pp. 190–196. DOI: 10.1016/B978-0-08-044894-7.01333-6
DOI: https://doi.org/10.5334/jors.651 | Journal eISSN: 2049-9647
Language: English
Page range: 47 - 47
Submitted on: Dec 1, 2025
Accepted on: May 26, 2026
Published on: Jun 19, 2026
Published by: Ubiquity Press
In partnership with: Paradigm Publishing Services
Keywords:
© 2026 Alexander B. Thames, Antonia Hadjimichael, Julianne D. Quinn, published by Ubiquity Press
This work is licensed under the Creative Commons Attribution 4.0 License.