R ESEARCH ARTICLEdoi: 10.2306/scienceasia1513-1874.2009.35.268

ScienceAsia 35 (2009): 268275

Areal rainfall estimation using spatial interpolationtechniquesWisuwat Taesombat, Nutchanart Sriwongsitanon

Department of Water Resources Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900,Thailand

Corresponding author, e-mail: fengnns@ku.ac.thReceived 13 Jun 2008Accepted 1 Sep 2009

ABSTRACT: Accuracy in runoff and flood estimation is important for mitigating water related problems. The accuracydepends on the methods used for areal rainfall approximation. The thin plate spline (TPS) technique was introduced in thisstudy for daily areal rainfall approximation in the Upper Ping river basin and was compared with the areal rainfall estimatedfrom two conventional techniques, the isohyetal and Thiessen polygon techniques. Two data sets of maximum rainfallregistered in August 2001 and September 2003 at 68 non-automatic rainfall stations located in the basin and nearby areaswere used in the analysis. The TPS technique was carried out in conjunction with two separate sources of digital elevationmodel (DEM), namely, GLOBE-DEM and SRTM-DEM, which were downloaded from the NOAA and NASA websites andhave horizontal resolutions of 1 km and 90 m, respectively. The TPS technique proved to provide more accurate results ofrainfall estimation than the other two techniques. The coarser DEM resolution (GLOBE-DEM) performed marginally betterin rainfall estimation than the finer DEM resolution (SRTM-DEM).

KEYWORDS: ANUSPLIN software, digital elevation model, Upper Ping river basin

INTRODUCTION

Rainfall plays an important role in the hydrologiccycle which controls our water supplies and waterdisasters. Knowing the nature and characteristics ofrainfall, we can conceptualize and predict its effectsin runoff, infiltration, evapotranspiration, and wateryield1. Many rainfall-runoff models have been de-veloped over the last few decades to estimate runoffcharacteristics, mainly using rainfall data as well asother catchment area and meteorological parameters.Acquiring more accurate rainfall data is thereforecrucial to improve the hydrograph prediction results.Since rainfall is never evenly distributed over thearea of study due to the topographic variability ofthe catchment areas, it is preferable to have as manyrainfall stations as possible to estimate the areal rain-falls which represents the actual rainfalls over thebasin. Unfortunately, it is not possible to installrainfall stations in as many locations as were hopeddue to limiting factors such as budget constraints,inaccessibility of certain areas, or lack of availablestaff.

Several areal rainfall estimation techniques arecurrently used for averaging rainfall depths collectedat ground stations. The isohyetal and Thiessen poly-gon techniques are conventional techniques that are

usually applied to estimate the areal rainfall over theentire basin2. However, the fundamental principlesof applying these techniques may produce inaccu-rate results because of the effects of topographicalvariation and the limited number of available rainfallstations. Alternative techniques are therefore neededto improve the accuracy of areal rainfall estimation.Two of the most well-known alternative techniquesthat have been generally applied are the geostatisticsand the thin plate splines (TPS) techniques. Geo-statistics, which is based on the theory of regionalizedvariables, has been accepted because it is able toassess spatial correlation among neighbouring obser-vations to predict attribute values at unsampled loca-tions3. Several authors including Tabios and Salas4,and Phillips et al5 concluded that the geostatisticalprediction technique (kriging) provides better esti-mates of rainfall than conventional techniques such asthe Thiessen polygon and inverse distance weighting(IDW) techniques. However, Dirks et al6 found thatthe kriging method does not significantly improvepredictions compared to the simpler techniques suchas IDW in the area with high-resolution networks(e.g., 13 raingauges over a 35 km2 area).

The TPS technique, which was introduced byHutchinson7, 8, can also be used to interpolate spa-tial rainfalls more accurately than the conventional

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ScienceAsia 35 (2009) 269

techniques, especially for mountainous areas. Thistechnique can generate meteorological surfaces usinga trivariate function of latitude, longitude, and ele-vation of meteorological stations together with theterrain elevation. It was proved to be a robust tech-nique for dealing with noisy multivariate data andwas applied in many countries such as Australia9, 10,Canada11, and Thailand12. Price11 revealed that theTPS technique produced better results for elevation-dependent spatial interpolation of monthly climaticdata from sparse weather station networks than didthe statistical method termed gradient plus inverse-distance-squared. Ekasingh12 applied four spatial in-terpolation techniques comprising (Thiessen polygon,IDW, kriging, and TPS) to monthly meteorologicaldata of 305 daily rainfall stations, 73 air temperaturestations, and 12 sunlight radiation stations in ChiangMai and Pitsanulok Provinces. The results showedthat the TPS technique gave the lowest RMSE valuesfor climate spatial interpolation. Boer et al13 appliedfour forms of kriging and three forms of TPS to predictmonthly maximum temperature and monthly meanprecipitation in Jalisco State of Mexico. The trivariateregression-kriging and trivariate TPS showed the bestperformance. The authors also pointed that TPS issimpler than kriging, which can be very significantfrom a practical point of view.

In this study, we applied three different techniques(TPS, isohyetal and Thiessen polygon) for interpolat-ing the areal rainfall over the study site (the UpperPing river basin, Northern Thailand).

BASIN OVERVIEW

The Upper Ping river basin covers an area of approx-imately 25 370 km2 in the provinces of Chiang Maiand Lamphun, Northern Thailand. The BhumibolDam is the downstream end of the Upper Ping riverbasin and separates the Ping river basin into the upperand lower parts14. The Upper Ping river basin canbe separated into 14 sub-basins (Fig. 1). The UpperPing river basin is mostly covered by forest and steepmountains, which form a line from the northern to thesouthern parts of the basin. The weather is monsoontype, with a rainy season from May to October andsupplementary rains from occasional westward stormdepressions originating in the Pacific. Mean tempera-tures for a 30 year period, recorded at the Chiang Maimeteorological station, varied from 14 C in Januaryto 36 C in April.

Fig. 1 Upper Ping river basin map showing the location ofrain gauges.

DATA COLLECTION

Rainfall dataDaily rainfall data were collected from 81 rainfallstations located within and around the Upper Pingriver basin between 1988 and 2006. The consistencyof the rainfall data was investigated using the doublemass curve technique. Rainfall data at 68 rainfallstations were shown to be reliable and were thereforeused for further analysis. To be able to distinguishthe effectiveness of each technique for areal rainfallinterpolation, large amounts of rainfall give betterresults than small amounts7, 8.

Two periods of rainfall registered in August 2001and September 2003, which had average rainfalldepths over the data network of around 252.11 and220.96 mm, respectively, were then chosen for furtheranalysis. The number of rainfall stations locatedwithin the 15 sub-basin areas of the Upper Ping riverbasin and nearby area is shown in Table 1. The aver-age rainfall registered in August 2001 and September2003 over each sub-basin is also presented.

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Table 1 Number of rainfall stations (N ) in each sub-catchment area in the Upper Ping river basin and theiraverage rainfall in August 2001 and September 2003.

Sub-catchment Area N Average rainfall (mm)(km2) Aug 2001 Sep 2003

Ping Section 1 1972 2 309.55 291.85Mae Ngat 1282 3 223.97 237.70Mae Taeng 1956 4 293.38 257.20Ping Section 2 1723 10 291.46 291.74Mae Rim 566 2 228.70 186.15Mae Kuang 2680 7 349.10 194.44Mae Khan 1732 4 310.35 271.50Mae Li 2080 3 222.43 186.10Mae Klang 616 2 176.15 200.10Ping Section 3 3180 3 176.80 151.05Upper Mae Chaem 1965 1 435.40 273.70Lower Mae Chaem 1930 3 248.93 197.70Mae Hat 521 1 192.90 156.50Mae Tun 3167 2 129.50 191.65Nearby Area - 21 193.07 226.99Total Area 25 370 68 252.11 220.96

Digital elevation modelTwo sources of digital elevation model (DEM) datacovering an area of 53 100 km2 in the Upper Ping riverbasin and some parts of Myanmar between longitude97.8 to 99.6 and latitude 16.9 to 19.85 were down-loaded from NOAA-GLOBE15 and NASA-SRTM16.The DEM data provided by these two organiza-tions have horizontal resolutions of around 1 kmand 90 m, respectively. Hastings and Dunbar15 andGorokhovich and Voustianiouk17 applied the DEMdata from NOAA-GLOBE and NASA-SRTM, respec-tively, and they concluded that the vertical accuracyprovided by these two data sources are around 20 and16 m, respectively, which are not much different. Byusing these two sources of DEM data in the analysis,we can investigate whether the horizontal resolutionof DEM data would have any impact on the accuracyof areal rainfall interpolation.

RAINFALL INTERPOLATION TECHNIQUESThin plate spline techniqueThe TPS technique is a general technique for smooth-ing a continuous surface by minimizing the curvatureof the surface23. In this study, the TPS technique wasapplied to interpolate daily rainfall data over the studyarea. To equilibrate the variance of the noise acrossthe rainfall data network and to reduce the skew in theraw data, the square root transformation was applied

to the observed rainfall values using24

r(1/2)i = f(xi, yi, hi) + i i = 1, 2, . . .n, (1)

where f is a smooth function of the longitude (xi),latitude (yi), and elevation (hi), ri is the rainfallrecorded at the location i, n is the number of lo-cations, and i are random error terms (assumed tobe normally distributed with zero mean and variance2) associated with rainfall data measurement and themodel deficiency. The unit of the observed rainfall ismm and varies according to the longitude and latitudecoordinates (in degrees), whereas the unit of elevationis km. As a result, the elevation scale is around 100times larger than horizontal coordinates9.

The general thin-plate smoothing spline estimateof the function g is obtained by minimizing

1n

ni=1

[r(1/2)i f(xi, yi, hi)

]2+ Jm(f)

over a class of suitably smooth functions25. Thefirst term is the average squared Euclidean distancebetween the observed data and fitted values, and theJm(f) term is the mth order roughness penalty con-sisting of the integral of squared mth spatial deriva-tives of f . In this study we use m = 2 and J2(f)equals

f2xx+f2yy+f

2hh+2f

2xh+2f

2xy+2f

2yh dxdy dh.

The smoothing parameter determines a balancebetween the fidelity to the data and the degree ofsmoothness of the fitted spline function f . Thisparameter is usually determined by minimizing thegeneralized cross validation (GCV). The GCV is anestimate of predictive error of the spline surface. It iscalculated by removing each data point and summingthe square of the difference of each point from asurface fitted by all other data points26.

Thiessen polygon techniqueThe Thiessen polygon technique was introduced toestimate equivalent uniform depth27. This techniqueassumes that an average value over the same area ofa Thiessen polygon is taken to be equivalent to thepoint value located at the centroid of this polygon. Ahypothetical basin with three rainfall stations is shownin Fig. 2 For this basin, encompassing n Thiessenpolygons, the areal rainfall over the basin (PT) iscomputed from

PT =ni=1

TiPi,

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ScienceAsia 35 (2009) 271

where Pi is the observed rainfall at the centroid of theith polygon, and the weighting factor Ti is given by

Ti =AiAT

,

where AT is the total area of the basin, and Ai isthe area defined by the intersection of the Thiessenpolygon and the basin boundary.

The Thiessen polygon technique is suitable forapplication over relatively flat and expansive areas.However, this technique assumes that precipitationvaries linearly between stations and is therefore un-suitable for use in mountainous regions which have aneffect on the precipitation amount29.

Isohyetal techniqueAn isohyetal map shows lines of equal precipitation.A sample of isohyetal lines is shown in Fig. 2.The fitted isohyets were generated using the bivariateTPS technique by considering only two independentvariables namely the longitude (xi) and latitude (yi)coordinates. Using this technique, (1) is replaced by

r(1/2)i = f(xi, yi) + i i = 1, 2, . . ., n,

The second order derivative for the smoothing param-eter and minimization of the GCV are also applied forinterpolating the isohyetal lines.

METHODDEM generationTo assist with comparisons, the DEM resolutionswere transformed into 100 m using a nearest neigh-bour method in the ARCVIEW GIS software (version

222

223

224

225

226

227

228

229

230

231

232

233

234

Fig 2. Hypothetical basin with three point rainfall stations and associated Thiessen 235

Polygons and Isohyetal defined28 236

237

i

n

i

iT PTP = =1

(4) 238

AA

TT

i

i=

(5) 239

where Pi is the observed rainfall at the centroid of the polygon (i); Ti is a weighting 240

factor for a particular rainfall station; n is the number of Thiessen Polygons in the 241

basin; AT is the total area of the basin; and Ai is the area defined by the intersection of 242

the Thiessen Polygon and the basin boundary. 243

The Thiessen Polygon technique is suitable for application over relatively flat and 244

expansive areas. However, this technique assumes that precipitation varies linearly 245

between stations and is therefore unsuitable for use in mountainous regions which 246

have an effect on the precipitation amount29. 247

Isohyetal technique 248 The isohyetal map shows lines of equal precipitation drawn the same way as a 249

topographic contour map is drawn. A sample of isohyetal lines is shown in Figure 2. 250

The fitted isohyets were generated using bivariate TPS technique by considering only 251

two independent variables namely the longitude ( ix ) and latitude ( iy ) coordinates. 252

Using this technique, the equation (1) will be 253

niyxfr iiii ,..,2,1),()2/1(

=+= (6) 254

where all variables are the same as explained in the equation (1). The second order 255

derivative for the smoothing parameter and minimization of the GCV are also applied 256

Pi

Ai

Basin Boundary

Isohyetal lines

Thiessen Polygons

AT

Ai+1

Ai+2

Pi+1

Pi+2

Fig. 2 Hypothetical basin with three point rainfall stationsand associated Thiessen polygons and Isohyetal defined 28.

3.2)19. Ground elevation of those 68 selected rainfallstations can be later defined using these generatedDEM data. The generated DEM data, rainfall loca-tions, and their ground elevations were later used asthe input data for ANUSPLIN 18.

Investigation of topographical effect on rainfalldepthsRainfall depths generally vary with space and time andtend to increase with increasing elevations because ofthe orographic effect of mountainous terrain, whichcauses the air to be lifted vertically, and the conden-sation occurs due to adiabatic cooling3, 20. Hevesiet al21, 22 revealed that there is a significant correlationof around 0.75 between average annual precipitationand their elevation recorded at 62 rainfall stations inNevada and southeastern California. To investigatewhether this occurred here, the average annual rainfallof each rainfall station between 1988 and 2006 wereplotted against its elevation in the Upper Ping riverbasin. A linkage between the two parameters wouldmean that it is therefore possible to increase theaccuracy of areal rainfall interpolation by applyinga topographic parameter (ground elevation of rainfallstation) as proposed in this study.

Areal rainfall estimationIn this study, the interpolation methods describedabove were carried out by applying ANUSPLIN, de-veloped by Hutchinson23, to generate a surface of in-terpolated daily rainfalls in conjunction with observedelevations in the Upper Ping river basin. Input dataconsisted of the generated DEM data covering theUpper Ping river basin, daily rainfall at 68 stations aswell as their observed locations and elevations. Theoutputs from ANUSPLIN were areal rainfall surfaceswhich correspond to point rainfalls and DEM data. Asummary of the statistical indicators can be printed toshow the accuracy of point rainfall estimation usingthe cross-validation technique. The output of arealrainfall surfaces in the text file can be later imported togenerate a grid format in the GIS environment. Thissoftware was also used to generate the isohyetal map.

Evaluation of the accuracy of spatial interpolationtechniquesThe cross-validation technique was achieved by re-moving data from one observation point at a time (j),taken from all of the available observation points inthe data set and then estimating the value of the re-moved observation point data using the data from theremaining (n 1) observation points. This technique

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272 ScienceAsia 35 (2009)

is used to evaluate how well the neighbouring stationsestimate the missing value30.

The accuracy of spatial interpolation techniqueswas evaluated by using the following three statisticalindicators. The mean error (ME) is given by

ME =1n

ni=1

(Roi Rei), (2)

where n is the number of rain events, Roi is theobserved rainfall depth at a time (i), and Rei is theestimated rainfall depth at a time (i). A positive MEshows that the estimated rainfall is generally underes-timated, while a negative sign shows it is generallyoverestimated. The mean absolute error (MAE) isgiven by

MAE =1n

ni=1

|Roi Rei|.

The root mean square error (RMSE) is given by

RMSE =

1n

ni=1

[Roi Rei]2.

The MAE and RMSE are used as indicators of themagnitude of extreme errors. Lower MAE and RMSEvalues indicate greater central tendencies and gener-ally smaller extreme errors.

RESULTS AND DISCUSSIONDEM GenerationThe elevations generated using the SRTM-DEM andGLOBE-DEM covering the selected area are between26 to 2520 m, and 33 to 2487 m above mean sea level,respectively. The elevation of each rainfall station canbe specified from these two generated maps. Fig. 3shows a scatter plot of the elevations of each rainfallstation derived from SRTM-DEM and GLOBE-DEM.The accumulated different value of ground elevationsgenerated from SRTM-DEM and GLOBE-DEM at thesame rainfall stations presented by the mean errors(ME) is shown to be approximately 0.58 m. Thisdifferent value is not so great when compared to theresolution differences of these two data sources thatare quite large (90 m for SRTM-DEM and 1 km forGLOBE-DEM). It can be concluded that two differenthorizontal resolutions of DEM data used in this studydid not have much impact on the vertical accuracy.

Relationship between rainfall depths and observedlocationsThe relationships between the average annual rainfallof each rainfall station between 1988 and 2006 and

0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800 1000 1200 1400 1600

68 Rainfall stations' ground elevation derived from SRTM-DEM (m MSL)

68

Rain

fall

sta

tio

ns

' g

rou

nd

ele

va

tio

n d

eri

ve

d f

rom

GL

OB

E-D

EM

(m

MS

L)

Fig. 3 Ground elevations of each rainfall station derivedfrom SRTM-DEM and GLOBE-DEM.

Y = 0.6419X + 823.44

R2= 0.6918

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400

Ground Elevation of Rainfall Station (m MSL)

Avera

ge a

nn

ual ra

infa

ll d

uri

ng

1988

-2006 (

mm

)

Fig. 4 Relationship between the average annual rainfall ofeach rainfall station and its elevation in the Upper Ping riverbasin.

its elevation are plotted as shown in Fig. 4. The figureshows that the average annual rainfalls tend to increasewith increasing observed elevations with a coefficientof determination of 0.7. It can be seen that rainfallstations located in the Upper Ping river basin andnearby area, show the same tendency between rainfalldepths and their station locations.

Areal rainfall estimations using three spatialinterpolation techniquesDaily areal rainfall depth estimates in the Upper Pingriver basin that occurred in August 2001 and Septem-ber 2003 were created and shown as histograms inFig. 5 and Fig. 6, respectively. In addition, maps ofmaximum areal rainfalls that occurred on 11 August2001 and 13 September 2003 were generated usingthree different techniques and are illustrated in Fig. 7and Fig. 8, respectively.

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ScienceAsia 35 (2009) 273

Table 2 Differences of areal rainfall depths (in mm) using various techniques for rainfall events in 2001 and 2003.TPS-SRTM TPS-GLOBE Isohyetal Thiessen polygon

2001 2003 2001 2003 2001 2003 2001 2003

TPS-SRTM - - 0.01 0.23 1.01 0.82 1.38 1.01TPS-GLOBE 0.01 0.23 - - 1.02 0.58 1.39 0.78Isohyetal 1.01 0.82 1.02 0.58 - - 0.37 0.19Thiessen polygon 1.38 1.01 1.39 0.78 0.37 0.19 - -

TPS-SRTM = TPS technique with SRTM-DEM; TPS-GLOBE = TPS technique with GLOBE-DEM

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Are

al

rain

fall

am

ou

nt

in t

he

Up

pe

r P

ing

riv

er

ba

sin

(m

m)

TPS-SRTM

TPS-GLOBE

ISOHYET

THIESSEN POLYGON

Fig. 5 Histograms of daily areal rainfall depths in August2001.

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Are

al

rain

fall

am

ou

nt

in t

he

Up

pe

r P

ing

riv

er

ba

sin

(m

m)

TPS-SRTM

TPS-GLOBE

ISOHYET

THIESSEN POLYGON

Fig. 6 Histograms of daily areal rainfall depths in Septem-ber 2003.

The differences of areal rainfall depths generatedby three different techniques for rainfall events inAugust 2001 and September 2003 are presented in Ta-ble 2. The rainfall depths calculated by the techniquespresented in the first row were used as Roi in (2),whereas the techniques presented in the first columnwere used as Rei. Areal rainfall depths calculatedby the TPS-SRTM and TPS-GLOBE are close withmean errors of around 0.01 and 0.23 mm, respec-tively (Table 2). Areal rainfall depths calculated by

Fig. 7 Maps of areal rainfall depths in the Upper Pingriver basin on 11 August 2001 generated by (a) TPS-SRTM(b) TPS-GLOBE (c) Isohyetal technique (d) Thiessen poly-gon.

Fig. 8 Maps of areal rainfall depths in the Upper Ping riverbasin on 13 September 2003 generated by (a) TPS-SRTM(b) TPS-GLOBE (c) Isohyetal technique (d) Thiessen poly-gon.

the conventional techniques (Isohyetal and Thiessenpolygon) are also close to each other with mean errorsof 0.37 and 0.19 mm, respectively. However,rainfall depths produced by TPS and conventionaltechniques are much more different.

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274 ScienceAsia 35 (2009)

Table 3 Values of the statistical indicators for three spatialinterpolation techniques.

Indicator TPS-SRTM TPS-GLOBE Iso Th poly

ME (mm) 0.53 0.50 0.94 1.98MAE (mm) 3.94 3.81 5.16 15.61RMSE (mm) 8.50 8.42 9.70 28.15 0.59 0.61 0.48 0.37r 0.70 0.71 0.56 0.06

Evaluation of the accuracy of spatial interpolationtechniquesDaily rainfall data at each station was removed at eachtime and the remaining data were used to estimatethe missing one by applying three spatial interpolationtechniques. Table 3 shows that the TPS techniqueproduced smaller values of ME, MAE, and RMSEthan the isohyetal and Thiessen polygon techniques.The TPS-GLOBE produced an insignificant improve-ment in daily rainfall estimation compared to the TPS-SRTM. The TPS and isohyetal techniques providedan underestimate of areal rainfall depths (positiveME) whereas the Thiessen polygon technique overes-timated areal rainfall depths.

The correlation between point rainfall estimationusing three different techniques and the observeddata were tested by fitting lines between estimatedand observed rainfalls. The slope () of the linearregression line and its correlation coefficient (r) ofeach technique are given in Table 3. The TPS-GLOBEand TPS-SRTM give values of closer to 1 thanthe other techniques. The values of r from the TPStechniques are also higher. The results show thatthe TPS technique is better for rainfall estimationbetter than the isohyetal technique and much betterthan the Thiessen polygon technique. The coarserDEM resolution (GLOBE-DEM) performed slightlybetter than the finer DEM resolution (SRTM-DEM).Although the difference was not significant in ourcase, this result is consistent with that from the studiesof Hutchinson7, 8, who found that the 10 km DEMresolution gave the least values of RMSE in rainfallestimation among the range of DEM resolutions be-tween 2.5 and 20 km. Moreover, Sharples et al24 alsofound that the optimum scale of the resolution of DEMdata is around 510 km among the range between250 m and 90 km.

Acknowledgements: This work was partially supportedby the thesis and dissertation support fund from the Grad-uate School, Kasetsart University. We are also gratefulto the Royal Irrigation Department, Department of Water

Resources, and the Thai Meteorology Department for pro-viding the data and information used in this study.

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