Conceptual‐stochastic modeling of seasonal runoff using autoregressive moving average models and different scales of aggregation

Abstract

"The statistical and phenomenological aspects of the runoff process observed on different scales of aggregation are taken as a priori information for the conceptually based stochastic modeling of seasonal runoff. Runoff is considered as the sum of two groundwater components, with over-year and subannual response lag, and of a purely random component representing the direct runoff. This scheme is equivalent to a linear system, with two parallel linear reservoirs plus a zero lag linear channel. The system output is the runoff, and the input is the effective rainfall, considered proportional to the direct runoff. Assuming the effective rainfall as a non-Gaussian periodic independent process and considering nonseasonal groundwater parameters, this conceptualization leads to an autoregressive and moving average (2, 2) stochastic process with periodic independent residual. Stochastic model parameters are directly related to the linear system coefficients, and the effective rainfall structure can be determined from the estimated model residual. In order to obtain parameter estimates consistent with the conceptual constraints, two estimation stages, on an annual and a seasonal basis, and an iterative procedure are needed. The model was applied to a number of time series of monthly streamflows in the Apennine regions of Italy with promising results.

An Introduction to Probability, Statistics, and Uncertainty

“…ARMA(p, q) models have been extended to describe seasonal flow series by having their coefficients depend upon the season-these are called periodic Autoregressive-Moving average models, or PARMA. Salas and Obeysekera (1992), Salas and Fernandez (1993), and Claps et al (1993) discuss the conceptual basis of such stochastic streamflow models. For example, Salas and Obeysekera (1992) found that low-order PARMA models, such as a PARMA(2,1), arise from reasonable conceptual representations of persistence in rainfall, runoff, and groundwater recharge and release.…”

“…For example, Salas and Obeysekera (1992) found that low-order PARMA models, such as a PARMA(2,1), arise from reasonable conceptual representations of persistence in rainfall, runoff, and groundwater recharge and release. Claps et al (1993Claps et al ( , p. 2553 observe that the PARMA(2, 2) model which may be needed if one wants to preserve year-to-year correlation poses a parameter estimation challenge (see also Rasmussen et al 1996). The PARMA (1, 1) model is more practical and easy to extend to the multivariate case (Hirsch 1979;Stedinger et al 1985;Rasmussen et al 1996).…”

Water Resources Assessment for Karst Aquifer Conditioned River Basins: Conceptual Balance Model Results and Comparison with Experimental Environmental Tracers Evidences

“…For this reason and taking advantage of the dense monitoring campaign, a semi-distributed formulation, accounting for each sub-basin particular characteristics, seems to be more appropriate. When dealing with the monthly time scale, each sub-basin can be described (figure 8) as two linear reservoirs in parallel, representing the groundwater flow and the deep subsurface flow, whereas the rainfall contributes, which are characterized by delay times smaller than a month, are supposed to reach the outlet through a linear channel (Claps et al, 1993). The scheme is also supported by the conceptual hydro-geological model described in the previous paragraph.…”

Multi-year drought frequency analysis at multiple sites by operational hydrology – A comparison of methods

“…Their applications in hydrology at all time scales are countless and it would be impossible to report them. Their underlying conceptual basis at yearly scale has been investigated, among the others, by Salas and Obeysekera (1992) and by Claps et al (1993). In particular, Claps et al (1993) consider runoff as generated by a linear system featuring two parallel linear reservoirs (one for the groundwater component with over-year response lag and one for the subannual component) and a zero-lag linear channel.…”

“…Model selection according to traditional analysis is based on the study of the empirical autocorrelogram and on the empirical partial autocorrelogram of the series to which a model is to be fitted (e.g. Salas et al, 1980), whereas the conceptual framework proposed by Claps et al (1993) restricts the choice of a model for flows at annual scale either to a white noise for ephemeral streams or to an ARMA(1, 1) process for streams with a significant groundwater component. For springs, a third choice, namely an AR(1) process, is compatible with the conceptual scheme proposed by Claps et al (1993).…”