Institute of Hydrology, Slovak Academy of Sciences, Ondrasovecka 16, 03105 Liptovsky Mikulas,
Slovakia, email: parajka@svslm.sk, fax + 421 849 5522522
The analyses of spatial variability of hydrological processes in general and precipitation processes in particular have been of interest to water resources planners and managers for quite some time
(Tabios, Salas, 1985). Such analyses have applications in such studies as determination of water budget at different spatial and temporal scales, validation of different hydrological models and recently climate change impact studies.
Number of techniques for the spatial interpolation of long-term mean precipitation for the whole territory of Slovakia have been tested with acceptable results (Parajka, 1999). In this paper, the performance of various interpolation techniques for the spatial interpretation of mean annual precipitation (MAP) for the territory of Western Tatra Mountains is tested. Main goals of the study are:
 to test the accuracy of various interpolation techniques using jack-knife technique;
 to compute and compare average basin MAP for selected mountain basins using GIS tools and environment.
We tested applicability of various methods used to compute areal precipitation in the mountain region of the Western Tatra Mountains (area 314 km 2 , elevation range 570-2248 m.a.s.l.). MAP data for ten years period 1989-98 were obtained at 23 measurement sites (Fig. 1). Inverse distance, nearest neighborhood, linear triangulation, linear and polynomial regressions, two-dimensional spline with tension and kriging methods were used to produce grid precipitation maps of MAP in the region. GIS map algebra operations were used to compute average basin precipitation for eight basins (Fig. 1), for each year and interpolation technique. The efficiency of interpolation methods was tested against stations data using jack-knife technique (Papamichail, Metaxa, 1996) by evaluating sample variance statistics.
0 3
[km]
6 9 12 elevation
[m.a.s.l.]
2400 precipitation measurement
2200
2000
1800
1600
1400
1200
1000
800
600
BASINS:
1- Jalovecka; 2 - Ziarska; 3 - Jamnicka; 4 - Bystra; 5 - Ticha; 6 - Koprova; 7 - Podbanske; 8 - Rohacska
Fig. 1 Digital elevation model of Western Tatra Mountains, location of precipitation stations and selected basins.

We compared the automated procedures to the measured data quantitatively. Differences between estimated and measured MAP values for each method were summarised using cross-validation statistics. Sample variance was used as the main criteria to evaluate the accuracy against station data. Sum of sample variance for ten years period (1989-98) for each interpolation method is presented in Fig. 2.
1200000
1000000
800000
600000
400000
200000
0
Fig. 2 Sum (10 years) of sample variances of interpolation methods calculated using jack-knife technique.
Results from jack-knife cross-validation show, that quadratic regression method gives the best results for selected 10 years time period. The greatest sum of variances was calculated for nearest neighbor interpolation method.
Results from computation of basin averages of MAP for selected basins indicate that the basin averages differ from year to year and from basin to basin. Fig. 2 shows sample variances of basin averages of MAP computed using different interpolation methods for 10 years period.
R o h a c s k a
P o d b a n s k e
K o p r o va
T i c h a
B y s t r a
J a m n i c k a
Z i a r s k a
J a l o ve c k a
0 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 v a r i a n c e
Fig. 3 Sample variance of basin MAP averages for eight basins computed using different interpolation methods for 10 years period.
From Fig. 2 could be concluded, that all interpolation methods give for Jalovecka basin practically the same basin average. On the other hand, different interpolation methods produce different basin average for Koprova basin.

Examples from statistical comparison of basin averages are presented in Fig. 4 and Fig. 5.
Frequencies of interpolation methods, which produce the minimum basin average, are shown in Fig. 4.
Histogram in Fig. 4 shows that linear triangulation method gives for majority of basins minimum basin average of MAP. Frequencies of interpolation techniques, which give maximum basin averages of
MAP, are presented in Fig. 5. Results in Fig. 5 indicate that maximum basin average is mostly produced by linear regression method, but this is not a case for Rohacska basin, where different interpolation method produce maximum basin average of MAP.
Rohacska
Podbanske
Koprova
Ticha
Bystra
Jamnicka
Ziarska
Jalovecka inv. dist.
kriging nearest neigh.
triangulation linear regr.
quadr. regr.
tps2d
0 1 2 3 4 5 6 7 8 9 10 number of years
Fig. 4 Frequencies of interpolation methods, which give the minimum basin averages for each year and basin.
Rohacska
Podbanske
Koprova
Ticha
Bystra
Jamnicka
Ziarska
Jalovecka inv. dist.
kriging nearest neigh.
triangulation linear regr.
quadr. regr.
tps2d
0 1 2 3 4 5 6 7 8 9 10 number of years
Fig. 5 Frequencies of interpolation methods, which give the maximum basin averages for each year and basin.
In this paper, the performance of various interpolation techniques for the computation of basin averages of MAP for the territory of Western Tatra Mountains is evaluated. The comparison of interpolation methods used in this study was based on jack-knife technique, as well as on statistical analysis of basin averages of MAP. Results indicate that all tested interpolation methods give for
Jalovecka, Jamnicka and Rohacska basins similar MAP basin averages for selected time period 1989-
98. On the other hand, different interpolation methods produce absolutely different basin average for
Koprova basin. These findings are probably caused by spatial arrangement and localization of precipitation measurement sites. New dimension in evaluation of the performance of various interpolation methods in the future will bring cross-validation within the framework of hydrological balance.

Papamichail, D. M. & Metaxa, I. G. (1996) Geostatistical Analysis of Spatial Variability of Rainfall and
Optimal Design of a Rain Gauge Network. Water Resources Management, 10.
Parajka, J. (1999) Mapping long-term mean annual precipitation in Slovakia using geostatistical procedures. In: Problems in Fluid Mechanics and Hydrology, Institute of Hydrodynamics
AS CR, Prague.
Tabios, G. Q. & Salas, J. D. (1985) A comparative analysis of techniques for spatial interpolation of precipitation. Water Resources Bulletin, No. 3.