Identification-based Diagnosis of Rainfall  Stream Flow Data: the Tinderry Catchment Karel J. Keesman 1,2 , Peter C. Young 2,3 and Anthony J. Jakeman 2 1 Systems and Control Group, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, The Netherlands 2 Fenner School of Environment and Society and National Centre for Groundwater Research and Training, The Australian National University, Canberra ACT 0200 3 Lancaster Environment Centre, Lancaster University, Lancaster, LA1 5BL Abstract System identification tools, such as transfer function (TF) model structure identification, recursive estimation, time-varying parameter (TVP) estimation and assessment of data information, are used to evaluate the quality of rainfall-stream flow data from the Tinderry catchment (ACT, Australia) and the time- varying behaviour of the rainfall-stream flow dynamics. For the catchment, given the wide range and the abrupt changes of the single input-single output transfer functions describing different periods or events, we conclude that further investigation of (i) local rainfall effects, (ii) time-varying time delays (travelling time), (iii) time-varying residence times related to the base flow and (iv) occurrence of negative residues is needed. Periods with high and low data information content, for further use in effective parameter estimation procedures, are clearly indicated by the analysis. Keywords Diagnosis, rainfall-stream flow data, system identification, recursive parameter estimation INTRODUCTION Usually relatively long data records of rainfall and stream flow are available: e.g. 20 years of daily measurements from rainfall and stream flow gauges. This even holds for remote catchments due to the wide availability of wireless communication techniques. However, these data are not always of good quality and the question arises: what can be said about the quality of these long data records?. Instead of statistical, model-free data analysis, we analyse the data using (dynamic) transfer function (TF) model identification. In particular, we introduce system identification tools, such as structure/order identification (model selection), recursive and time-varying parameter estimation and the assessment of data information content (Young, 1984, Norton, 1986; Keesman, 2011), to diagnose the data quality. These tools allow us not only to investigate the data quality, but also to interpret the results in a hydrological context. The goal of the paper is to show how such diagnostic tools can be used in the case of the Tinderry catchment (near Canberra, ACT, Australia). BACKGROUND Dynamic, linear, time-invariant (LTI) systems can be represented by a transfer function (TF) model. In short hand notation, a noise-free TF model, relating the input u k , at the discrete time instant t k , to the resulting output y k , with k the time index, is presented as 1 1 ( ) ( ) k k k n Bq y u Aq (1) where y k is the stream flow, u k the effective (excess) rainfall, which is usually calculated from a non-linear module that accounts for evapotranspiration and soil moisture, and n k is a pure time delay of n k samples, introduced to allow for any delay that occurs between the occurrence of rainfall and its first effect on flow. The polynomials A(q 1 ) and B(q 1 ) are given by A( q 1 ) 1 a 1 q 1 a 2 q 2 ... a n a q n a B( q 1 ) b 0 b 1 q 1 b 2 q 2 ... b n b q n b (2) where A(q 1 ) is chosen to be monic to avoid structural identifiability problems. In these polynomials, q 1 is the backward-shift operator (sometimes denoted by z 1 ). Consequently, the input-output relationship can also be written in terms of a difference equation, that is _______________________________________________________________________________ 8th IWA Symposium on Systems Analysis and Integrated Assessment _______________________________________________________________________________ 412 Watermatex 2011: Conference Proceedings