Agricultural and Forest Meteorology 101 2000 81–94
A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data
David T. Price
a,∗
, Daniel W. McKenney
b,1
, Ian A. Nalder
c,2
, Michael F. Hutchinson
d,3
, Jennifer L. Kesteven
d,3
a
Canadian Forest Service, Northern Forestry Centre, 5320-122 Street, Edmonton, Alta., Canada T6H 3S5
b
Canadian Forest Service, Great Lakes Forestry Centre, 1219 Queen Street East, Sault Ste. Marie, Ont., Canada P6A 5M7
c
Department of Renewable Resources, Faculty of Agriculture, Forestry and Economics, University of Alberta, Edmonton, Alta., Canada T6G 2E3
d
Centre for Resource and Environmental Studies, The Australian National University, Canberra ACT 0200, Australia Received 11 August 1999; received in revised form 8 December 1999; accepted 9 December 1999
Abstract
Two methods for elevation-dependent spatial interpolation of climatic data from sparse weather station networks were compared. Thirty-year monthly mean minimum and maximum temperature and precipitation data from regions in western and
eastern Canada were interpolated using thin-plate smoothing splines ANUSPLIN and a statistical method termed ‘Gradient plus Inverse-Distance-Squared’ GIDS. Data were withheld from approximately 50 stations in each region and both methods
were then used to predict the monthly mean values for each climatic variable at those locations. The comparison revealed lower root mean square error RMSE for ANUSPLIN in 70 out of 72 months three variables for 12 months for both regions.
Higher RMSE for GIDS was caused by more frequent occurrence of extreme errors. This result had important implications for surfaces generated using the two methods. Both interpolators performed best in the eastern OntarioQuébec region where
topographic and climatic gradients are smoother, whereas predicting precipitation in the west British ColumbiaAlberta was most difficult. In the latter case, ANUSPLIN clearly produced better results for most months. GIDS has certain advantages
in being easy to implement and understand, hence providing a useful baseline to compare with more sophisticated methods. The significance of the errors for any method should be considered in light of the planned applications e.g., in extensive,
uniform terrain with low relief, differences may not be important. ©2000 Elsevier Science B.V. All rights reserved.
Keywords: Climate; Temperature; Precipitation; Spatial interpolation; Topographic dependence; Canada; Thin-plate smoothing spline;
ANUSPLIN; GIDS
∗
Corresponding author. Tel.: +1-780-435-7249; fax: +1-780-435-7359.
E-mail addresses: dpricenrcan.gc.ca D.T. Price,
dmckennenrcan.gc.ca D.W. McKenney, inaldergpu.srv.ualberta.ca I.A. Nalder,
hutchcres.anu.edu.au M.F. Hutchinson, jenny.kestevangreenhouse.gov.au J.L. Kesteven.
1
Tel.: +1-705-759-5740; fax: +1-705-759-5700.
2
Currently resident in Australia. Tel.: +61-2-6254-3322.
3
Tel.: +61-2-6249-4783; Fax: +61-2-6249-0757.
1. Introduction
The development of methods to interpolate climatic data from sparse networks of stations has been a fo-
cus of research for much of this century Thiessen, 1911; Shepard, 1968; Hughes, 1982; Hutchinson and
Bischof, 1983; Phillips et al., 1992; Daly, 1994. Re- cent events, including the IPCC Second Assessment
0168-192300 – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 9 9 0 0 1 6 9 - 0
82 D.T. Price et al. Agricultural and Forest Meteorology 101 2000 81–94
Report on climate change Houghton et al., 1996 and the Kyoto Protocol of late 1997, have sparked
additional interest in climate data interpolation. Pre- diction of the impacts of a changing climate on the
distribution and functioning of terrestrial ecosystems requires as a first step, the development of reliable,
spatially-explicit models of current climate. For many of the areas of greatest concern, such as the boreal
forest and tundra biomes of central and northern Canada, station coverage is often very sparse, and
the long-term records often incomplete. In addition, many researchers attempt to predict future ecosys-
tem responses to climatic change using output from general circulation models GCMs and regional
climate models RCMs Boer et al., 1992; Caya et al., 1995. Although there are undoubtedly many
conceptual problems and practical limitations to us- ing coarse-scale climate model output for predicting
ecosystem responses, any attempt to do this will gen- erally require an unbiased method for interpolation to
the scale of operation of most ecosystem models. Im- proved methods of climate interpolation will enhance
our ability both to quantify effects of climate and cli- mate variability on natural and managed ecosystems,
including forests, wetlands and agroecosystems, and to forecast the possible impacts of climate change.
In most cases, simulation of ecosystem responses to climate does not require an exact representation of
reality, so interpolation from sparse or incomplete records is quite acceptable. However, because many
natural vegetation types occur in mountainous re- gions, it is reasonable to suppose that elevation is
a key factor influencing the climate experienced by these ecosystems. Hence it is generally necessary to
include elevation as an independent variable in the interpolation method.
In some instances, it may be preferable to use a simple method applied to the region of interest
than to use a more sophisticated approach which could be marginally more accurate, but requires
considerably more time and money to implement. In this paper, therefore, two elevation-dependent
climate interpolators are compared. One of these, ANUSPLIN Hutchinson, 1995a, 1999, has been
developed and tested over several years and is now widely used. The other interpolator, Gradient plus
Inverse-Distance-Squared GIDS Nalder and Wein, 1998, is less well known but attractively simple
and appears to give results adequate for modelling forest ecosystem responses to climate — at least in
relatively flat terrain. Recently, Price et al. 1998 generated national-scale
gridded climate surfaces for Canada using the GIDS weighting method of Nalder and Wein 1998.
Nalder and Wein 2000, in press developed GIDS as a straightforward method for interpolating cli-
mate data obtained from a sparse regional net- work of stations in northwestern Canada to the
positions of a large number of survey plots lo- cated in boreal forest stands. Using multiple lin-
ear regression to estimate regional gradients in temperature and precipitation with latitude, longi-
tude and elevation, GIDS was found to compare very favourably with several other interpolation
methods, including universal kriging, while having the benefit of straightforward implementation and
operation.
McKenney et al. 2000, submitted for publication have also developed national climatic grids, expand-
ing on previous work in Ontario and the Great Lakes Mackey et al., 1996 using the ANUSPLIN soft-
ware of Hutchinson 1999 see also Hutchinson, 1991, 1995a; Hutchinson and Gessler, 1994. ANUS-
PLIN is based on smoothing splines as described by Wahba 1990, Hutchinson 1984 and Wahba and
Wendelberger 1980. Additional FORTRAN pro- grams in the ANUSPLIN modeling package can be
used to generate interpolated grids and, hence, dig- ital climate maps. In this paper, we compare GIDS
with ANUSPLIN through a data-withholding pro- cess and attempt to identify the ‘better’ approach to
generating digital grids of monthly mean climate for Canada.
Both methods of climate interpolation have already been used in spatial modelling of forest ecosystems.
ANUSPLIN has been used to generate climatolo- gies in Ontario to determine the risk of infection of
pine forest by Sceleroderris disease and to assess climatic effects on the distributions of breeding birds
Venier et al., 1998a, 1998b. The GIDS methods was developed and used in a study of productivity
and succession in the western boreal forests of cen- tral Canada Nalder and Wein, 1998; Nalder et al.,
2000, submitted for publication. GIDS was also re- cently applied to a study of forest vegetation effects
on the climate of North America E.H. Hogg, per-
D.T. Price et al. Agricultural and Forest Meteorology 101 2000 81–94 83
sonal communication, 1999, Canadian Forest Service, Edmonton.
2. Methods
