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Estimation of Average Basin Precipitationfor Mountain Basins In Western Tatra Mountains

Juraj Parajka

Institute of Hydrology, Slovak Academy of Sciences, Ondrasovecka 16, 03105 Liptovsky Mikulas,Slovakia, email: parajka@svslm.sk, fax + 421 849 5522522

IntroductionThe analyses of spatial variability of hydrological processes in general and precipitation processes inparticular 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 waterbudget at different spatial and temporal scales, validation of different hydrological models and recentlyclimate change impact studies.Number of techniques for the spatial interpolation of long-term mean precipitation for the wholeterritory of Slovakia have been tested with acceptable results (Parajka, 1999). In this paper, theperformance of various interpolation techniques for the spatial interpretation of mean annualprecipitation (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 andenvironment.

Data and methodsWe tested applicability of various methods used to compute areal precipitation in the mountain regionof the Western Tatra Mountains (area 314 km2, elevation range 570-2248 m.a.s.l.). MAP data for tenyears period 1989-98 were obtained at 23 measurement sites (Fig. 1). Inverse distance, nearestneighborhood, linear triangulation, linear and polynomial regressions, two-dimensional spline withtension and kriging methods were used to produce grid precipitation maps of MAP in the region. GISmap algebra operations were used to compute average basin precipitation for eight basins (Fig. 1), foreach year and interpolation technique. The efficiency of interpolation methods was tested against

stations data using jack-knife technique (Papamichail, Metaxa, 1996) by evaluating sample variancestatistics.

6 0

8 0

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

e l e v[ m . a

0 3 6 9 1 2

[ k m ]

p r e c i p i t a t i o n m e a s u

B A S I N S :1 - J a l o v e c k a ; 2 - Z i a r s k a ; 3 - J a m n i c k a ; 4 - B y s

Fig. 1 Digital elevation model of Western Tatra Mountains, location of precipitation stations andselected basins.

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ResultsWe compared the automated procedures to the measured data quantitatively. Differences betweenestimated and measured MAP values for each method were summarised using cross-validationstatistics. Sample variance was used as the main criteria to evaluate the accuracy against stationdata. Sum of sample variance for ten years period (1989-98) for each interpolation method ispresented in Fig. 2.

0

200000

400000

600000

800000

1000000

1200000

in

v.

distance

tp

s2d

linear

regr.

qu

adr.

re

gr.

kri

ging

nea

rest

ne

igh.

varianc

Fig. 2 Sum (10 years) of sample variances of interpolation methods calculated using jack-knifetechnique.

Results from jack-knife cross-validation show, that quadratic regression method gives the best resultsfor selected 10 years time period. The greatest sum of variances was calculated for nearest neighborinterpolation method.Results from computation of basin averages of MAP for selected basins indicate that the basinaverages 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.

0 100000 200000 300000 400000

Jalovecka

Ziarska

Jamnicka

Bystra

Ticha

Koprova

Podbanske

Rohacska

basi

variance

Fig. 3 Sample variance of basin MAP averages for eight basins computed using different interpolationmethods 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 basinaverage for Koprova basin.

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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 basinaverage of MAP. Frequencies of interpolation techniques, which give maximum basin averages ofMAP, are presented in Fig. 5. Results in Fig. 5 indicate that maximum basin average is mostlyproduced by linear regression method, but this is not a case for Rohacska basin, where differentinterpolation method produce maximum basin average of MAP.

0 1 2 3 4 5 6 7 8 9 10

Jalovecka

Ziarska

Jamnicka

Bystra

Ticha

Koprova

Podbanske

Rohacska

basi

number of years

inv. dist.

kriging

nearest neigh.

triangulation

linear regr.

quadr. regr.

tps2d

Fig. 4 Frequencies of interpolation methods, which give the minimum basin averages for each yearand basin.

0 1 2 3 4 5 6 7 8 9 10

Jalovecka

Ziarska

Jamnicka

Bystra

Ticha

Koprova

Podbanske

Rohacska

basi

number of years

inv. dist.

kriging

nearest neigh.

triangulation

linear regr.

quadr. regr.

tps2d

Fig. 5 Frequencies of interpolation methods, which give the maximum basin averages for each yearand basin.

In this paper, the performance of various interpolation techniques for the computation of basinaverages of MAP for the territory of Western Tatra Mountains is evaluated. The comparison ofinterpolation methods used in this study was based on jack-knife technique, as well as on statisticalanalysis of basin averages of MAP. Results indicate that all tested interpolation methods give forJalovecka, 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 forKoprova basin. These findings are probably caused by spatial arrangement and localization ofprecipitation measurement sites. New dimension in evaluation of the performance of variousinterpolation methods in the future will bring cross-validation within the framework of hydrological

balance.

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ReferencesPapamichail, D. M. & Metaxa, I. G. (1996) Geostatistical Analysis of Spatial Variability of Rainfall andOptimal Design of a Rain Gauge Network. Water Resources Management, 10.Parajka, J. (1999) Mapping long-term mean annual precipitation in Slovakia using geostatisticalprocedures. In: Problems in Fluid Mechanics and Hydrology, Institute of HydrodynamicsAS CR, Prague.Tabios, G. Q. & Salas, J. D. (1985) A comparative analysis of techniques for spatial interpolation of

precipitation. Water Resources Bulletin, No. 3.