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