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Algorithms

SynHydro's generators are classified into three bins by the mathematical character of their generative mechanism. The classification follows the parametric / non-parametric distinction set out by Studnicka and Panu (2025), with the third "hybrid" bin reserved for methods whose synthesis path combines both parametric and non-parametric components.

Generator classification

Parametric

Fit a probability model (AR, MAR, ARFIMA, PAR, SMA, HMM) to the historical record, then synthesize new flows by drawing random innovations from the fitted model. The generative step samples from a fitted distribution. Parametric generators are interpretable and data-efficient, but bound by the assumed model structure.

Algorithm Resolution Sites
Thomas-Fiering AR(1) Monthly Univariate
Matalas MAR(1) Monthly Multisite
ARFIMA Monthly/Annual Univariate
SPARTA Monthly Multisite
SMARTA Annual Multisite
Multi-Site HMM Annual Multisite

Hybrid

Combine a parametric structure (standardization, marginal distributions, regime states, AR-per-band) with a non-parametric resampling step (bootstrap, k-NN, phase shuffle, wavelet decomposition). The parametric layer enforces statistical properties such as monthly moments, intra-annual correlation, or marginal shape; the non-parametric layer preserves empirical detail the parametric layer would smooth away.

Algorithm Parametric component Non-parametric component Resolution Sites
Kirsch Bootstrap Per-period mean/std, intra-annual Cholesky correlation Bootstrap of standardized residuals Weekly/Monthly Multisite
WARM AR(p) per spectral band Continuous wavelet decomposition Annual Univariate
Phase Randomization Four-parameter kappa marginal per day-of-year FFT phase shuffle Daily Univariate
Multisite Phase Randomization Per-site kappa marginals per day-of-year Wavelet CWT phase shuffle (shared across sites) Daily Multisite

Non-parametric

Generate new flows by direct resampling of the historical record with no fitted probability distribution. The generative step is empirical. Non-parametric generators preserve the empirical distribution and complex nonlinear dependence structures by construction; the trade-off is that they cannot extrapolate beyond observed values and need an adequate historical record.

Algorithm Resolution Sites
KNN Bootstrap Monthly/Annual Univariate/Multisite

Disaggregation Methods

Algorithm Type Resolution
Nowak KNN Non-parametric {Annual, Monthly, Weekly} to
Valencia-Schaake Parametric Annual to Monthly

Key Properties Preserved

Property Thomas-Fiering Matalas ARFIMA SMARTA SPARTA MS-HMM Kirsch WARM Phase Random KNN-Bootstrap
Monthly means/stds x x x - x - x - - x
Temporal correlation x x x x x x x x x x
Spatial correlation - x - x x x x - - x
Long-range persistence - - x x - - - x - -
Non-stationarity - - - - - - - x - -
Drought states - - - - - x - - - -
Power spectrum - - x - - - - x x -
Arbitrary marginals - - - x x - - - x -
Empirical distribution - - - - - - x - - x

Reference

Studnicka, S. and Panu, U.S. (2025). Techniques and Developments in Stochastic Streamflow Synthesis: A Comprehensive Review. Encyclopedia, 5, 198. https://doi.org/10.3390/encyclopedia5040198