Journal of Hydrology ELSEVIER Journal of Hydrology 195 (1997) 160-171 On the interpolation of hydrologic variables: formal equivalence of multiquadratic surface fitting and kriging Marco Borga*, Andrea Vizzaccaro Dipartimento Territorio e SisteraiAgro-Forestali, Agripolis, Universit~ di Padova, 35020 Legnaro, Padova, Italy Received 3 November 1995; revised 27 March 1996; accepted 1 August 1996 Abstract The paper focuses on the ties of kriging with a deterministic interpolation procedure, known as multiquadratic surface fitting. The two methods are compared, first from a theoretical point of view, then using a practical example. It is shown that kriging equations with a linear variogram model are identical in form to equations of multiquadratic surface fitting with cone surfaces. The issue of the accuracy of both estimators is discussed through a case study where hourly rainfall maps of real storm events collected by radar provided the reference rainfall. Random point sampling of the accumulation pattern simulated gauge returns. Eight sampling densities were used and for each density rainfall spatial distributions were estimated for a large number of realisations. It is shown that kriging performs better at lower gauge density, while at higher gauge density the accuracy of both estimators is similar. 1. Introduction The quantitative evaluation of the amount and spatial distribution of precipitation is required for a number of applications in hydrology and water resources management and many techniques have been proposed for mapping rainfall patterns and for evaluating the mean areal rainfall over a watershed by making proper use of existing data points. Methods for precipitation interpolation from ground-based point data have ranged from techniques based on Thiessen polygons (Thiessen, 1911) and simple trend surface analysis (Edwards, 1973; Hughes, 1982), inverse distance weighting (Shepard, 1968), multi- quadratic surface fitting (Hardy, 1971; Shaw, 1994), and Daulaney triangulations (Akima, 1978) through to more sophisticated statistical methods. When a statistical * Corresponding author 0022-1694/97/$17.00 O 1997- Elsevier Science B.V. All fights rescrvcd PIi S0022-1694(96)03250-7