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Thomas-Fiering (1962) with Stedinger-Taylor Normalization
Type Parametric
Resolution Monthly
Sites Univariate
Class ThomasFieringGenerator

Overview

The Thomas-Fiering method generates synthetic monthly streamflow using a seasonal AR(1) model with month-specific parameters. The Stedinger-Taylor (1982) normalization applies a lower-bound adjustment before log transformation, reducing skewness and improving the normality assumption. The method preserves monthly means, standard deviations, and lag-1 serial correlations.

Algorithm

Preprocessing

  1. Resample to monthly if input is daily or sub-monthly (sum within each month).
  2. Univariate enforcement - use first column if multi-site DataFrame is provided.
  3. Stedinger-Taylor normalization - for each month m:
  4. Estimate lower bound: 
    tau_m = (Q_max * Q_min - Q_median^2) / (Q_max + Q_min - 2 * Q_median)
tau_m = max(tau_m, 0)
  5. Transform: X_m = log(Q_m - tau_m)

Fitting

  1. Monthly statistics - for each month m, compute from transformed flows X:
  2. Mean: mu_m
  3. Standard deviation: sigma_m
  4. Lag-1 serial correlations - for each transition m to m+1:
  5. rho_m = corr(X_m, X_{m+1}) (Dec-Jan wraps across year boundary)
  6. Store parameters - 48 total (12 months x 4: mu, sigma, rho, tau).

Generation

  1. Initialize first month: X_1 = mu_1 + epsilon * sigma_1 where epsilon ~ N(0,1).
  2. AR(1) recursion for each subsequent month: 
    X_m = mu_m + rho_m * (sigma_m / sigma_{m-1}) * (X_{m-1} - mu_{m-1})
      + sqrt(1 - rho_m^2) * sigma_m * epsilon
  3. Inverse transform: Q_m = exp(X_m) + tau_m
  4. Non-negativity: clip to observed monthly minimum.

Parameters

Parameter Type Default Description
Q_obs pd.Series or pd.DataFrame - Observed streamflow with DatetimeIndex
name Optional[str] None Optional name identifier for this generator instance
debug bool False Enable debug logging

Properties Preserved

  • Monthly means and standard deviations (in transformed space)
  • Lag-1 serial correlation (month-to-month)
  • Seasonal flow patterns (via month-specific parameters)

Not preserved: - Higher-order autocorrelation (lag > 1) - Spatial correlations (univariate method) - Exact marginal distributions (normality imposed via transformation)

Limitations

  • Univariate only - no spatial correlation modeling
  • First-order memory - misses multi-month drought persistence
  • Requires at least 2 complete years; 10+ recommended
  • Assumes stationarity (no trends or regime shifts)

References

Primary: Thomas, H.A., and Fiering, M.B. (1962). Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In Design of Water Resource Systems (eds. Maass et al.), pp. 459-493. Harvard University Press.

See also: - Stedinger, J.R., and Taylor, M.R. (1982). Synthetic streamflow generation: 1. Model verification and validation. Water Resources Research, 18(4), 909-918. https://doi.org/10.1029/WR018i004p00909

Implementation: src/synhydro/methods/generation/parametric/thomas_fiering.py Tests: tests/test_thomas_fiering_generator.py