## 1. Introduction

[2] Artificial neural network (ANN) methods have found increasing utility in a variety of hydrological applications [*Maier and Dandy*, 2000; *ASCE Task Committee on the Application of Artificial Neural Networks in Hydrology*, 2000]. Among the most widely used network structures are the Multilayer Feedforward Network (MFN), the recurrent neural network (RNN), and the radial basis function (RBF) network. In previous work [*Hsu et al.*, 1995, 1997a, 1997b, 1999; *Sorooshian et al.*, 2000], the applicability of ANN methods for hydrologic applications such as streamflow forecasting and estimation of spatial precipitation fields was investigated. Relevant to this paper, *Hsu et al.* [1995] showed that a 3-layer MFN (Figure 1a) provides excellent one step ahead predictions of streamflow, including both flood peaks and recessions. *Hsu et al.* [1997a] explored the RNN extension of the MFN structure (Figure 1b) which adds time-delayed feedback loops to simulate the “storage capacity” of a dynamical hydrologic system.

[3] However, the existence of multiple local optima and extensive regions of parameter insensitivity complicates the identification and training of MFN and RFN networks, which significantly limits their widespread application [*Gupta et al.*, 1997]. Therefore it is important to resolve the network identification problem while maintaining high standards of network performance and accuracy. This paper presents a multivariate ANN procedure, entitled self-organizing linear output map (SOLO), whose structure has been designed for rapid, precise, and inexpensive estimation of network structure/parameters and system outputs, as well as estimates of their uncertainty. More important, SOLO provides additional insight into the underlying input-output processes, thereby extending its usefulness beyond forecast applications. The scope of this paper is organized as follows. The architecture of the SOLO model and an illustrative application to a streamflow prediction problem are described in sections 2 and 3, respectively. In addition, the performance of SOLO is evaluated in comparison with multilayer feedforward ANNs, a linear time series model, and a conceptual rainfall-runoff model. Section 4 discusses how the analysis of intermediate products generated by the network can facilitate insight into the underlying structure of the input-output process. Technical issues including identification of network size, stability of the parameter estimates, principal component analysis, the relationship to linear input-output modeling, and “overfitting” are discussed in section 5. Issues of model prediction uncertainty are presented in section 6.