Synthetic hydrology based on regional statistical parameters

Abstract

The generation of a long series of hydrologic events by use of the statistical parameters based on a short sample has come to be known as synthetic hydrology. In present practice, there are two major deficiencies in the method. There are large errors due to the sampling errors of the original sample, and there is no way to generate a series for an ungaged location. The authors propose a method to correct for these deficiencies.

An empirical‐stochastic, event‐based program for simulating inflow from a tributary network: Framework and application to the Sacramento River basin, California

“…Its methods later became more formalized using statistical theories to develop autoregressive models for monthly rainfall data [Hannan, 1955]. Since that time, stochastic statistical theory has been applied to empirical streamflow simulation primarily to synthetically extend the historical record of annual maximum series at a particular gauging point [e.g., Stedinger and Taylor, 1982] and to generate synthetic series for ungauged basins using regional parameters [e.g., Benson and Matalas, 1967].…”

Theoretical predictions of observed to expected ratios in RIVPACS-type predictive model assessments of stream biological condition

“…Originally, physical models were calibrated with data from all gauged catchments in a region, and then model parameters were statistically related to catchment attributes, such as climate, topography, land use, geology, soils, or composites of these variables (Sefton and Howarth 1998). These attributes could then be measured at an ungauged site and the statistical relationships could be used to estimate the parameters for the model at the ungauged site (Benson and Matalas 1967, Ross 1970, Heerdegen and Reich 1974, Jarboe and Haan 1974, NERC 1975. Various physical models have been used; these models range from the simple lumped conceptual rainfall-runoff models IHACRES (Sefton et al 1995) and SYMHID (Peel et al 2000) to the more complex spatially distributed Stanford Watershed (Ross 1970), HBV (Seibert 1999), and SWAT models (Heuvelmans et al 2006).…”

Estimating peak flow characteristics at ungaged sites by ridge regression

“…Regional analysis of streamflow characteristics with a multiple linear regression of flow characteristics on basin characteristics has been used by hydrologists to predict flow characteristics at ungaged sites (Thomas and Benson, 1970) and to improve predictions of flow characteristics at gaged sites (Benson and Matalas, 1967). In addition, some applications of regression analysis rely on individual parameter estimates to infer causeeffect relationships between basin characteristics and flow characteristics (Espey and Winslow, 1974).…”

“…Substituting these known values into the equation above This is equivalent to assuming a log normal distribution (Johnson and Kotz, 1970, p. 170). Therefore, a multi-variate streamflow generator (Matalas, 1967) was used to synthesize the common logarithms of a sequence of n observed annual peaks; z, .3 2 ? .3 z~ .., ... 3 z ; at -"--> 3 ^j 3 -^ j 3 fly o 20 stations in a simulation region while preserving the following assumptions: 1) the random variable Z. is normally and independently 3 distributed in time with mean u. and standard deviation a., and 2) the 3 3 cross correlation between logarithms of annual peaks for any pair of stations (p ) is a constant for all pairs of stations.…”