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# 128 Rainfall-Runoff Modeling: Transfer Function Models

Part 11. Rainfall-Runoff Modeling

1. Peter C Young1,2

Published Online: 15 APR 2006

DOI: 10.1002/0470848944.hsa141a

## Encyclopedia of Hydrological Sciences

#### How to Cite

Young, P. C. 2006. Rainfall-Runoff Modeling: Transfer Function Models. Encyclopedia of Hydrological Sciences. 11:128.

#### Author Information

1. 1

Lancaster University, Centre for Research on Environmental Systems & Statistics (CRES), Lancaster, UK

2. 2

Australian National University, Centre for Resource & Environmental Studies Institute of Advanced Studies, Canberra ACT 2020, Australia

#### Publication History

1. Published Online: 15 APR 2006

## SEARCH

### Abstract

This article discusses continuous and discrete-time transfer function (TF) models within the context of the Data-Based Mechanistic (DBM) modeling of hydrological systems. Although, at a superficial level, TF models simply provide a convenient and concise way of presenting differential or difference equations in an input-output form, they are much more than this. In particular, they allow for the consideration of linear dynamic systems in simple algebraic terms and for their analysis within a dynamic systems and control context. This is useful in various ways, particularly where a higher order TF model is identified and estimated directly from hydrological data. Often, this data-based model can then be decomposed into serial, parallel, and feedback connections of first-order systems that can be interpreted in hydrologically meaningful terms, thereby facilitating the model's use in hydrological systems analysis. The article also shows that TF models can be considered in time-variable and state-dependent parameter (SDP) form, so allowing for them to describe nonstationary and nonlinear systems. And, since it is straightforward to consider all TF models in stochastic terms, they provide a powerful vehicle for uncertainty, forecasting, and risk analysis. The practical utility and power of DBM TF models is illustrated by two real hydrological examples.

### Keywords:

• transfer functions;
• differential equations;
• continuous time;
• discrete time;
• transfer function decomposition;
• data-based mechanistic models