SEPTEMBER 2005 T A I T A N D TURNER 1315 Generating Multiyear Gridded Daily Rainfall over New Zealand ANDREW TAIT AND RICHARD TURNER National Institute of Water and Atmospheric Research, Kilbirnie, Wellington, New Zealand (Manuscript received 14 June 2004, in final form 2 March 2005) ABSTRACT Daily rainfall totals are a key input for hydrological models that are designed to simulate water and pollutant flow through both soil and waterways. Within New Zealand there are large areas and many river catchments where no long-term rainfall observations exist. A method for estimating daily rainfall over the whole of New Zealand on a 5-km grid is described and tested over a period from January 1985 to April 2002. Improvement over a spatial interpolation method was gained by scaling high-elevation rainfall estimates using simulated mesoscale model rainfall surfaces that are generated for short periods in 1994 and 1996. This method is judged to produce reasonable and useful estimates of daily rainfall. 1. Introduction This study examines a method for estimating daily rainfall on a regular 5-km grid, covering all of New In recent years, hydrological models such as the Spa- Zealand for the period of 1985–2002, for the purpose of tially Referenced Regressions on Watershed Attributes input into and testing of hydrological models. The ap- (SPARROW; Brakebill and Preston 2003) have been proach combines daily rainfalls that are interpolated used to provide information about the effects of land- from climate station sites with short-period-simulated use change on water quality in rivers. In New Zealand, mesoscale model rainfall surfaces. The paper is struc- such information has increasingly been used to decide tured in the following way: section 2 describes the the fate of resource consent applications where the deg- spatial interpolation procedure that is used—a thin- radation of waterways is an issue. Given the sensitive plate smoothing spline—and section 3 describes the and important nature of such decisions, it is critical that preferred rainfall estimation method that uses Regional the hydrological models—and their key inputs—are as Atmospheric Modeling System (RAMS) model out- accurate as possible. put to scale the spline-interpolated rainfalls at high el- The New Zealand catchments over which hydrologi- evations. The unscaled and scaled rainfall estimates cal models are applied, and for which daily rainfall to- are also validated in sections 2 and 3, using indepen- tals are needed, commonly vary in size from 10 000 to dent datasets. Discussion and conclusions follow in sec- 2 25 km . Over larger and/or more populated catchments tion 4. sufficient daily rainfall observations generally exist, so that obtaining the rainfall input into the hydrological models is not a problem. However, within New Zealand 2. Spatial interpolation using a thin-plate there are large areas (mainly mountainous) and many smoothing spline river catchments where no long-term (i.e., 1 yr or Hutchinson (1995) describes the method of thin-plate longer) rainfall observations exist (Fig. 1). Hydrological (or Laplacian) smoothing spline interpolation, and its models for these catchments are forced to rely on rain- application to the interpolation of rainfall data. fall data from outside of the catchment area, which A thin-plate smoothing spline works by fitting a sur- introduces additional uncertainty into the calculations. face to the data with some error allowed at each data point, so the surface can be smoother than if the data were fitted exactly. A single parameter controls the Corresponding author address: Dr. Andrew Tait, National In- stitute of Water and Atmospheric Research, Private Bag 14-901, smoothing and is normally chosen to minimize the Kilbirnie, Wellington, New Zealand. mean square error between the actual value at the sta- E-mail: [email protected] tions and their values that are predicted by all the other © 2005 American Meteorological Society Unauthenticated | Downloaded 09/26/21 11:23 PM UTC JAM2279 1316 JOURNAL OF APPLIED METEOROLOGY VOLUME 44 FIG. 1. Map of the terrain of New Zealand and the locations of gauges with daily rainfall records covering the period of 1985–2002 (black dots). Land above 1000 m above sea level is shaded dark gray. The four boxes labeled upper North Island, lower North Island, upper South Island, and lower South Island are the boundaries of the inner nested RAMS version- 4.3 domains that are used in this study. The six climatologically similar regions from Mullan (1998) are delineated by thick black lines, and Lewis Pass and Lake Ramsay (mentioned in the text) are also shown. stations. That is, each station is omitted, in turn, from for this Australian study, calculated within the spline the estimation of the fitted surface, and the mean error program, was 10%–15%. The inclusion of a continuous is found. This is repeated for a range of values of the spatially varying dependence on elevation significantly smoothing parameter, and then the value that mini- reduced the error, in comparison with no elevation de- mizes the mean error is taken to give the optimum pendence. This result has also been shown by Phillips smoothing. This is called the method of generalized et al. (1992), using a cokriging interpolation scheme, cross validation (GCV). which, when the variogram is well chosen, tends to pro- Hutchinson (1989) used a trivariate (latitude, longi- duce results that are similar to those achieved by thin- tude, and elevation) thin-plate smoothing spline, mini- plate splines (Seaman and Hutchinson 1985; Laslett et mizing the GCV, to interpolate several meteorological al. 1987). variables, including rainfall, across Australia. The ap- Trivariate (latitude, longitude, and elevation) thin- proximate standard error for the rainfall interpolation plate smoothing spline interpolation of cube root– Unauthenticated | Downloaded 09/26/21 11:23 PM UTC SEPTEMBER 2005 T A I T A N D TURNER 1317 transformed rainfall data at climate stations throughout Validation of the spline-interpolated daily rainfall New Zealand for every day between January 1985 and estimates April 2002 was performed for this study. The data were Comparison of the 18-yr daily time series of spline- transformed to reduce the degree of skewness. Other interpolated rainfall with climate station rainfall data transformations were experimented with, but did not showed very good correspondence. This was expected improve the results when they were validated against because all of the available station data were used in independent datasets. the derivation of the interpolated surfaces and the 4:1 Rather than using the GCV to determine the degree signal-to-noise ratio that was used forces the interpola- of smoothing, the daily rainfall surfaces were all fitted with a signal-to-error ratio of 4:1 to maintain a consis- tions to closely fit the observations. Hence, an addi- tency between the fitted surfaces and to force the in- tional comparison of rainfall at some high-elevation terpolated surface to more closely fit the actual rainfall sites was made using a short-term (1 month) dataset at the stations. This approach has been shown by Zheng compiled during the Southern Alps Experiment and Basher (1995) to produce rainfall surfaces derived (SALPEX) in October and November 1996 (Wratt et from sparse and noisy datasets that are not unrealisti- al. 1996). These rain gauge data were not included in cally smooth, as can sometimes result from minimizing the spline interpolations. Comparisons at 20 sites with the GCV. Visual inspection of the daily rainfall surfaces elevations above 600 m above sea level showed that for this study showed the rainfall patterns to be physi- while at some locations the spline interpolation was cally realistic. reasonable, many sites showed significant underestima- The rain gauge data used for the spline interpolation tion, and one site showed a large overestimation (Table were also weighted by the elevation of the station 1). Figure 2 shows the data from Lake Ramsay (eleva- above mean sea level, with higher stations receiving tion 945 m above sea level, see Fig. 1 for location), more weight in the interpolation. This was done be- where, while the timing of the rainfall events was well cause there are much fewer stations in high-elevation represented, the total spline-estimated rainfall over the areas as compared with low-lying coastal areas, so their 33-day period of observation was only 40% of the ac- relative contributions to the interpolation needed to be tual total. enhanced. The model that was used was the Australian As an additional form of validation, an indepen- National University (ANU) spline (Hutchinson 1989, dently derived map of the mean annual rainfall for the 1995), and the spatial resolution of the interpolation period of 1988–92 for the lower North Island, produced was 5 km. through the analysis of rainfall break-point data (San- TABLE 1. Percent of observed rainfall over the period of 5 Oct–10 Nov 1996, captured by the spline interpolation and by the scaled spline method at 20 high-elevation (greater than 600 m above sea level) locations. Spline method percent Scaled spline method percent Name Lon (°E) Lat (°S) Elev (m) of actual rainfall of actual rainfall Arthur’s Pass 171.56 42.94 760 76.15 80.03 Bull Creek 171.97 42.90 745 102.89 84.93 Tuke 170.89 43.09 975 27.36 79.36 Lake Ramsay 170.92 43.28 945 40.00 78.15 Panorama Ridge 170.48 43.49 1609 48.88 59.23 Mistake Flat 170.69 43.45 790 48.72 47.75 Eade Hut 170.48 43.52 979 54.02 49.81 The Hermitage 170.09 43.73 765 112.95 96.18 Ball Hut Road Bridge 170.13 43.74 759 123.61 87.76 Skifield 170.66 43.83 1364 249.09 93.33 Cabot 171.27 43.05 1430 28.40 58.24 Griffiths 171.31 43.05 700 59.05 76.44 Carrington 171.55 43.05 823 38.24 42.34 Waterfall 170.95 43.08 975 28.61 66.50 NZDSA Mathias 171.13 43.19 670 53.89 63.68 Dry Acheron 171.66 43.40 655 101.98 98.19 Nigger Hill 172.05 42.99 790 80.31 126.69 Boanerges Ridge 169.79 43.99 1447 75.67 72.48 Elcho Flats 169.84 43.92 739 62.38 73.29 Cassinia Moraine 169.67 44.12 980 164.47 79.65 Unauthenticated | Downloaded 09/26/21 11:23 PM UTC 1318 JOURNAL OF APPLIED METEOROLOGY VOLUME 44 FIG.