The hydrology of areas of low precipitation - L'hydrologie des régions à faibles précipitations (Proceedings of the Canberra Symposium, December 1979; Actes du Colloque de Canberra, décembre 1979): IAHS-AISH Publ. no. 128. Assessment of some streamflow simulation models used in an irrigation scheme design study I. SIMMERS University of Waikato, HamUton, New Zealand Abstract. This paper investigates streamflow data requirements for irrigation scheme design in the low rainfall Maniototo Plains area of Central Otago, New Zealand. The data collection network is theoretically acceptable for most purposes, but the measured discharge values do not allow estimation of all the needed basin and sub-basin parameters at the required precision level. Record synthesis is necessary in order to increase the amount of information contained in the present streamflow data series. Techniques chosen for time series extension and spatial extrapolation are linear, curvilinear and multiple regression, water balance, and conceptual models. Discussed are: theoretical aspects which concern precision of population parameter estimates from blended data; standard errors of prediction for synthetic records; and the relative simulation and prediction abilities of models chosen. The analyses showed that increased information could be obtained from the blended records, though the study objective was not fully realized. In some instances, record extension resulted in a decrease of statistical information. For design of an irrigation scheme to proceed now, the chosen error criterion is judged too stringent for the data. If the calculated errors cannot be accepted, all streamflow records from the area will require extension by additional observations. Evaluation de quelques modèles d'écoulement simulé utilisés dans une étude pour le projet d'un système d'irrigation Résumé. Cette communication étudie les besoins en données d'écoulement pour le projet d'un système d'irrigation dans les plaines de Maniototo de l'Otago Central en Nouvelle-Zélande, où les précipitations sont peu abondantes. Le réseau qui collecte les données est acceptable en théorie pour la plupart des cas, mais les valeurs de débits observées ne permettent pas d'apprécier avec la précision nécessaire tous les paramètres du bassin total et des bassins partiels. La synthèse des relevés est essentielle pour augmenter le volume d'information contenu dans la série actuelle des données d'écoulement. Nous avons choisi pour l'extension des séries dans le temps et l'espace les techniques suivantes: régressions linéaires, curvilignes, multiples, le bilan hydrique, et les modèles conceptuels. Nous discutons: les aspects théoriques qui concernent la précision des calculs des paramètres de populations basés sur les données reconstituées; les écarts-types des prédictions basées sur les relevés reconstitués et les capacités relatives des modèles choisis pour la simulation et la prédiction. Les analyses ont montré qu'on pouvait obtenir une augmentation de renseigne­ ments à partir des relevés reconstitués bien que l'étude n'ait pas atteint tous ses objectifs. Dans certains cas, l'extrapolation des relevés a eu pour résultat une diminution de l'information statis­ tique. Nous jugeons que le critère d'erreur-type choisi est trop rigoureux pour les données, pour que l'on puisse procéder actuellement à l'exécution du projet d'un système d'irrigation. Si les erreurs calculées sont inacceptables, il faudra majorer le volume des relevés d'écoulement de la région au moyen d'observations supplémentaires. WATER RESOURCE ASSESSMENT TECHNIQUES Data precision requirements To plan a data collection or synthesis programme it is vital to first establish clearly the purpose for which the data are to be used, and the degree of precision of the infor­ mation at a particular confidence level that will be adequate. Purpose will determine the required data precision. Precision requirements will in turn dictate the minimum record lengths of each variable necessary to estimate population parameters at a point, and for climatological data, the network density needed for parameter estimation over an area. Determination of these areal mean values also requires a statement on whether the requirements are for daily, monthly, or long-term data. 169 170 I. Simmers It is necessary to understand the relationship between precision and the data required to obtain it if a sampling programme is to be established at a point or over an area on a sound scientific basis. The relationships are well established for normal and lognormal distributions, and are outlined by Montgomery and Hart (1971). A numerical statement as to what data precision is required for water resource system design may be different for each parameter, and may refer to any number of variables over whatever time period. Parameters commonly chosen are the mean, sample standard deviation, coefficient of variation and extreme values. The suggested approach for any study is to use the existing data to establish statistically the network design and period of sampling which would be needed to estimate parameters of the population with stated precision at a stated level of confidence. This will determine the need for additional measured or synthesized information. Determination of yield parameters in ungauged areas The translation of streamflow parameters from one basin to another is a prediction problem, and is usually based on relationships between flow characteristics and several variables which describe basin and climatic characteristics. Several techniques are in common use for spatial extrapolation of hydrological data, and for time series exten­ sion either when records are missing or when measured information is insufficiently precise. These are linear, curvilinear and multiple regression, water balance and con­ ceptual models. A necessary condition for sound prediction is good model fit. However, the ultimate value of any model is determined not only by goodness of fit, but also by the degree of precision with which flow parameters are estimated in other basins, irrespective of the number of physiographic and climatic variables chosen. If the estimates do not accord with some previously stated allowable error criteria, determined by the purpose for which the data are required, then they must be considered to have little value. Precision of new parameter estimates Theoretical aspects of whether increased information in the statistical sense is added by time extension and spatial extrapolation of records are described in detail by Matalas and Langbein (1962), Fiering (1963) and by Frost and Clarke (1973). How­ ever, to summarize, statistical techniques may be used to examine the validity of using linear correlation analysis to augment data for any variable, when concurrent and additional data are available at a nearby station. Results from the theory of sampling give the variance of the first two statistical moments for a record of length m, taken to include only measured data. If correlation estimates are used to provide n2 addi­ tional values, the result is a combined record of nx measured values and n2 estimated values. If the variance of a parameter computed from this blended record exceeds that computed from the record of size nx alone, the combined record provides a less precise estimate of the parameter. However, if the variance is less than that computed from the original record alone, the correlation technique has provided a more precise estimate. A method to calculate the effective or net period of a combined short-term and extended record is given by Clark and Bruce (1966). Regression theory also affords a general solution for correlation of either similar or dissimilar variables (e.g. precipitation versus discharge), with application to linear, curvilinear, or multiple regression models. The estimated standard error in prediction by linear regression of the population mean j', given x, is shown by Snedecor and Cochran (1969) to be 1 1/2 2 Sixt_x=Sy.x -+C„(x-(x» (1) in Assessment of some streamflow simulation models 171 with (n — 2) degrees of freedom. Sy. x is the standard error of estimate from regres­ 2 sion; n is the number of items used in the correlation; Cn is l/(« — 1) (Sx) , where Sx is the standard deviation of the x values. For x = <x), Sju*.*2 is given by (Sy. x)2/n. Hence, a weighted average variance of the population mean for blended data may be 2 2 calculated ifS^x for n2 regression estimates is added to ay jn, given by nx measured values. Similar logic may be applied to estimate the precision of n$ <x) for curvilinear and multiple regression models. However, for second and third order polynomials and multiple regression, equation (1) becomes respectively, in matrix notation, Qi C12 x -<x) ni/2 Sii$. = Sy.x, x2 l(x - <x),x2 - <x2)) x 2 2 + (2) C21 C22 X (x )i -J with (n — 3) degrees of freedom, 2 3 Sn*x=Sy.x,x , x Ql ^12 C13" X — (x)~ a/2 2 2 3 3 2 2 x{(x-(x),x -<x ),x (x )) Çîl C22 C 3 x - (x ) (3) 2 n 3 3 p31 C32 C33_ x - (x ) with (n — 4) degrees of freedom, and 1 a/2 s =s x V*.xhx2 y- n*2 (*i-<*i>,*2-<*2>)) + - (4) -Ql ^22- -x2 ' -ix2)- n The degrees of freedom are (n — 3) for xh x2 only in equation (4). For 95 per cent confidence limits, equations (1) to (4) must be multiplied by the appropriate value of t005 given in standard statistical tables. In equations (1) to (3) for 2 3 first, second and third order polynomials, Sy.x, x , x is given by SbiJJCn, where Sbx is the standard error of the by coefficient. EXAMPLE FROM THE UPPER TAIERI RIVER, OTAGO Basin description A surface water resources analysis completed by Simmers (1975a) for the Upper Taieri River, affords a practical example of the theoretical principles discussed here. The area studied is outlined in Fig. 1, covers 738 km2 and lies 64 km northwest of Dunedin.