research article how well do gridded datasets of observed

Research ArticleHow Well Do Gridded Datasets of Observed Daily PrecipitationCompare over Australia

Steefan Contractor Lisa V Alexander Markus G Donat and Nicholas Herold

Climate Change Research Centre and ARC Centre of Excellence for Climate System Science UNSW AustraliaLevel 4 Mathews Building Sydney NSW 2052 Australia

Correspondence should be addressed to Steefan Contractor scontractorunsweduau

Received 31 May 2015 Revised 10 August 2015 Accepted 11 August 2015

Academic Editor Charles Jones

Copyright copy 2015 Steefan Contractor et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Daily gridded precipitation data are needed for investigating spatiotemporal variability of precipitation including extremeshowever uncertainties related to daily precipitation products are large Here we compare a range of precipitation grids for AustraliaThese datasets include products derived solely from in situ observations (interpolated datasets) and two products that combineboth remote sensed data and in situ observations We find that all precipitation grids have similar climatologies for annualaggregated precipitation totals and annualmaximumprecipitationThe temporal correlations of daily precipitation values are higherbetween the interpolated datasets but the correlations between the most widely used interpolated product (AWAP) and the tworemotely sensed products (TRMM and GPCP) are still reasonable Our results however point to distinct structural uncertaintiesbetween those datasets gridding in situ observations and those datasets deriving precipitation estimates primarily from satellitemeasurements All datasets analysed agree well for low to moderate daily precipitation amounts up to about 20mm but diverge atupper quantiles indicating that substantial uncertainty exists in gridded precipitation extremes over Australia

1 Introduction

Rainfall is vital to maintaining our water resources andsustaining life on our planet Surprisingly however manyexisting rainfall products exhibit differences that are oftenlarger than can be explained by observational or method-ological uncertainties [1 2] In addition many productsperform poorly at capturing daily rainfall variations andparticularly rainfall extremes [3ndash5] This has made it difficultto provide the essential underpinning that is required formodel evaluation or detection and attribution studies forexample

Point-based precipitation measurements are often grid-ded to create high-resolution daily regional datasets thatare crucial for climate monitoring at national scales andfor model evaluation There are now a plethora of differentgridded products developed with different resolutions andconstruction methods for many regions of the world forexample E-OBS for Europe [6] APHRODITE for Asia [7]AWAP for Australia [8] and CLARIS for South America[9] Users of datasets however are not always aware of their

inherent uncertainties and often they might not be fit forthe purpose for which they are being used [2 10 11] Forinstance uncertainties arise around the representativenessof the gridded values produced [12] the sensitivity of thechosen interpolation technique to changing network density[5] andor the ability of the gridded product to representprecipitation extremes [4] For example Hofstra et al [5]used the European E-OBS high-resolution gridded dataset toillustrate the effect of station network density on daily precipi-tation estimates noting problems especially when examiningextreme rainfall characteristics In addition Dunn et al[13] investigated structural andmethodological uncertaintieswhen creating global grids of climate extremes and found thatvariations in station network and the interpolation methodused account for the largest uncertainties A particularchallenge when calculating grids of daily precipitation is thehigh spatial variability of precipitation fields In particular onshorter time scales precipitation fields are spatially discon-tinuous although they are more continuous on longer timescales [14]

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2015 Article ID 325718 15 pageshttpdxdoiorg1011552015325718

2 Advances in Meteorology

In addition to daily gauge-based rainfall products thereare also many remotely sensed or merged products whichare often also used for monitoring and evaluation (egCMORPH [15] PERSIANN [16] and TRMM [17]) Manyof these products however have been shown to exhibitsubstantial differences in their representation of rainfall andespecially rainfall extremes [3 18] Given the considerableuse of these products within themeteorological hydrologicaland climate communities it would seem prudent to betterquantify some of these uncertainties and provide guidelinesfor users on the potential use and misuse of these datasetsparticularly in relation to long-term assessment

Using Australia as a case study the purpose of thispaper is to highlight some of the structural uncertainty thatis inherent in daily precipitation products through use ofcommon interpolation schemes and also to assess how thiscompares with existing gridded in situ-based datasets andsatellite-derived products which are often used in hydrome-teorological applications In addition we showhow structuraluncertainty manifests between gauge-based and satellite-based products and provide an assessment of how griddedproducts perform at capturing local precipitation extremes

2 Materials and Methods

21 Data We use several different gridded datasets in orderto represent daily precipitation estimates for Australia fromin situ satellite-based andmerged products Datasets chosenwere the in situ-based Australian Water Availability Project(AWAP) and the merged in situ and satellite-based datasetsfrom the Tropical Rainfall Measuring Mission (TRMM) andthe Global Precipitation Climatology Project One-DegreeDaily (GPCP 1DD) product AWAP [8 19] is a dataset createdby the Australian Bureau of Meteorology by gridding dailygauge data on a 5 km times 5 km grid using the Barnes succes-sive correction method (httpwwwbomgovauclimate)TRMM 3B42 Daily V7 [17 20] is a 025∘times 025∘ resolutiondataset spanning 50∘Nndash50∘S that combines precipitationestimates from multiple satellite sources to create a dailyprecipitation estimate in the period from 1998 to presentThis estimate is rescaled with respect tomonthly gauge-basedprecipitation totals where possible for improved accuracyFinally GPCP 1DD version 12 [21 22] combines remotesensed data withmonthly gauge data to createmonthly globalprecipitation estimates with a 25∘ times 25∘ resolution Thisdataset is then combined with high spatial and temporalresolution infrared data from various satellites to create aglobal daily precipitation estimate at a 1∘times1∘ resolution for theperiod from 1996 to present The data from all three datasetswere regridded to a common 05∘ times 05∘ grid over Australiausing a first-order area-conservative remapping technique[23] Subsequently throughout the paper the datasets willbe referred to as AWAP TRMM and GPCP with TRMMand GPCP being collectively referred to as ldquomergedrdquo datasetssince they combine remotely sensed and in situ-based data Itshould be noted that TRMM and GPCP use monthly gaugeanalysis so the intensity and occurrence of daily rainfallare determined by remote sensing As a result TRMM andGPCP are likely to be reasonably independent of AWAP We

compare the different datasets for the 16-year period 1998ndash2013 as this period is common to all datasets (eg TRMMwas only available from 1998)

In addition to the above we calculate six daily pre-cipitation grids using different interpolation schemes andbased on point-based observational data derived from theGlobalHistorical ClimatologyNetworkDaily (GHCN-Daily)archive [24 25] a database of daily weather and climaticinformation from land-based stations across the globe Wedo this to try to understand how uncertainty might manifestthrough the use of common interpolation techniques andunderstand how this uncertainty differs in comparison tothe merged products In addition to these six interpolateddatasets we also calculate a dataset Grid [Station] Average(GA) which is simply an unweighted average of all stationsinside a grid cell without interpolationThis dataset providesa reference for comparison to all of the nine other datasets

Across Australia GHCN-Daily currently contains dailyprecipitation values for 8361 stations (Figure 1) over theperiod of 1998 to 2013 of which only a subset of stations(4500 to 6500 depending on the day) were used for griddingeach day This is because the number of operational andreporting stations varies over the period of 1998 to 2013(data downloaded in January 2015) GHCN-Daily data forAustralia were interpolated on a regular 05∘times 05∘ gridcovering Australia A comparison of GHCN-Daily stationswith the stations used by the merged datasets TRMM andGPCP showed that on average there were approximately1000 additional GHCN-Daily stations available with themost prominent differences around the north and northwestcoastlines (not shown)

Note that although all datasets represent cumulative dailyprecipitation over a 24 h window the start and end timesof this window vary For example the time coverage ofobservations forAWAP starts at 0900 h local time inAustraliaon the day before the time stamp to 0900 h local time onthe day named For TRMM and GPCP on the other handthe time coverage starts at 2230 h GMT on the day before to2229 h GMT on the day of the time stamp This is equivalentto 0830 h Australian Eastern Standard Time (AEST) on theday of the time stamp to 0829 h AEST on the day after thetime stamp in Sydney NSWThis time difference varies fromsummer to winter due to daylight savings across Australiaand the use of varying time zones in the country These timedifferences were considered before calculating correlations byshifting the TRMMandGPCP data by a day tomatch as closeas possible the time intervals for comparison with the gauge-based grids

Also note that AWAP takes advantage of anomaly basedinterpolation rather than interpolating the raw gauge obser-vations directly Anomalies are calculated relative to dailyclimatologies This has the advantage of transforming thehighly varying observations into a set to which a smoothercurve can be fitted [26] Jones et al [26] also note that theclimatology provides more information than contained inindividual observations Furthermore they note that anoma-lies are weakly related to elevation making it more suitable tointerpolate station data using a two-dimensional analysis

Advances in Meteorology 3

minus10

minus20

minus30

minus40

Latit

ude (

∘)

120 130 140 150

Longitude (∘)

3 Perth

2 Alice Springs

4 Cairns

1 Sydney

5 Hobart

Figure 1 Map showing stations from the period of 1998 to 2013 inthe GHCN-Daily dataset A total of 8361 stations are shown herehowever on any given day between 1 Jan 1998 and 31 Dec 2013 thenumber of stations with usable precipitation observations varied inthe range of 4500 to 6500The red dots with labels from 1 to 5 denotethe locations of Sydney Alice Springs Perth Cairns and Hobartrespectively which are specifically referred to in Section 3 Refer tothe text for more details

Finally although our comparisons give an indication ofthe skill of various datasets in capturing daily extremeswe acknowledge that the merged datasets are developedwith the intention of preserving the mean behaviour ratherthan extremes For example GPCP 1DD preserves the totalmonthly precipitation derived from a combined satellite-gauge analysis [27] by multiplying a single conditional rainrate 119877

119888 by the 3-hourly fractional occurrence of rain in a day

derived from infrared radiometers on geosynchronous satel-lites Throughout this study we mention numerous reasonsfor the differing behaviour of precipitation estimates frommerged datasets all of which contribute to the uncertaintiesin the merged dataset extremes

22 Interpolation Methods TheGHCN-Daily data was inter-polated using six interpolation methods that were chosenbecause they are widely used in climate or environmentalmodelling and easily available with commonly used softwarepackages such as NCAR command language (NCL) RClimate Data Operators (CDO) and Python The imple-mentation of these methods often follows the default setupthat is common in many standard software packages Thisis done as people frequently use the default case Regardlessldquooptimumrdquo griding solutions often only considermean valuesrather than extremes Thus our attempt here is to includesome uncertainty in the results as might be present in anon-optimised implementation of a gridded product (suchas not taking account of distribution tails) The methods aredescribed as follows

221 Inverse Distance Weighting (IDW) This is a popularinterpolation method that has been used in many environ-mental applications (eg [28ndash32]) and it is applied as followslet119885(s

119894) be a set of 119899 observed values at locations s

119894Then the

predicted value 119885(s0) at a location s

0is given by

119885 (s0) =

sum119899

119894=0

120596119894119885 (s119894)

sum119899

119894=0

120596119894

(1)

where 120596119894is the weight given by 120596

119894= 1119889(s

0 s119894)119901 Here

119889(s0 s119894) represents the Euclidian distance between s

0and s119894

In general the distance in theweighting parameter is raised toa power 119901 where 0 le 119901 le 2 [28] In our study we use 119901 = 2This results in a higher weight for stations closer to the pointof interpolation than the ones further away thus accountingfor the localized nature of precipitation At any given pointof time the total number of 0mm gauge observations issignificantly higher than nonzero gauge observations Assuch using a weighted average of all stations would lower thepredicted values of the wet locations greatly and converselyincrease the estimate of precipitation in dry regions to anonzero value This was avoided by introducing a cut-offradius of 15 degrees latitude around the interpolated pointbeyond which the weights were set to zero This value waschosen as it is small enough to avoid stations from differentclimatic regions influencing grid values in regions of differentprecipitation climatology (eg tropics versus desert)

222 Cubic Spline (CS) The Akima spline interpolationmethod is implemented as per [33] The method is a bivari-ate generalisation of the cubic spline interpolation methoddescribed in [34] This is the most common cubic splinemethod implemented in R Cubic splines are very commoninmodelling climate variables [29 30 35] ldquothin plate splinesrdquoand ldquospline with tensionrdquo only differ from Akima splines bythe smoothing algorithm used (but exhibit similar proper-ties overall) and are commonly available in climate-specificpackages such as NCL and CDO The method is as followsThe 119909-119910 plane is triangulated based on the input data pointsand for each triangle a fifth degree polynomial in 119909 and 119910 isdetermined

119885 (119909 119910) =

5

sum

119894=0

5minus119894

sum

119895

119886119894119895119909119894

119910119895

(2)

The 21 coefficients 119886119894119895are obtained by deriving the function

values and first- and second-order derivatives at the verticesof the triangle This involves fitting a cubic polynomial tothe function values and deriving the partial derivatives ofthe function differentiated in the direction perpendicularto each side of the triangle [36] This method yields aresult with the accuracy of a cubic polynomial [33] UnlikeIDW and other weighted average methods cubic splineinterpolation is capable of extrapolating to values higherthan those observed and characteristically does so especiallyaround observations with steep gradients As a result itgenerates unreasonably high extrapolated values in someregions and negative precipitation in some other regionsThiswas mitigated by interpolating log(119885(s

119894) + 1) instead of119885(s

119894)


223 Triangulation with Linear Interpolation (TLI) Thismethod is analogous to cubic spline interpolation and evenuses the same function as CS above as described by [33]however instead of fitting cubic splines it performs linearinterpolation between the trianglersquos vertices This is an exactinterpolator and is capable of handling steep gradientsThe returned function however is not as smooth as CSinterpolation

224 Ordinary Kriging (OK) Ordinary kriging and thefollowing twomethods are weighted averagemethods similarto IDW that is the predicted values are defined as aweighted average of observed values Ordinary kriging andother variants of kriging (universal kriging [6 37] cokriging[37] indicator kriging [6] simple kriging [37] etc) are allstochastic methods that is they incorporate the concept ofrandomness in the spatial processes [28] Ordinary kriging iscommonly available in high level GIS software packages [28]and Stahl et al [31] and Jarvis and Stuart [35] among othershave used it to grid daily air temperature The weights forkriging depend on the spatial correlation between the datawhich is estimated by a theoretical semivariogram (a functionwhich indicates the degree of spatial dependence) Thetheoretical semivariogram is obtained by fitting a nonlinearfunction (model) to the experimental semivariogram Thisexperimental semivariogram relates the average variance inobservations to distances between the points of interest andsurrounding gauges and is defined by

120574 (119889) =

1

2 |119873 (119889)|

sum

119873(119889)

(119885 (s119894) minus 119885 (s

119895))

2

(3)

Here119873(119889) is the set of all distances 119889(s119894 s119895) is the Euclidean

distance between s119894and s

119895 and 119885(s

119894) and 119885(s

119895) are the

observed values In this study we have fitted the semi-variogram to a spherical model The characteristic trait ofa spherical model is that beyond a decorrelation lengthscale the variance remains unchanged This is suitable forprecipitation systems which are often highly localised

225 Natural Neighbour Interpolation (NNI) This is anotherweighted average interpolation method (eg [6 38]) wherethe weights are calculated as follows Let 119875(s

119894) be a polygon

around the gauge location s119894such that any locations inside

119875(s119894) are closer to s

119894than any other gauge locations Such

polygons are known as Thiessen polygons Let 119875(s119894) be a

set of such polygons for the gauge locations s119894 and let

119876(s119895) be another set of Thiessen polygons for the set s

119895 =

s119894 cup s0 where s

0is the location where interpolation needs to

be performed Then the set of weights 120596119894 are defined by the

ratio

120596119894=

Area (119875 (s119894) cap 119876 (s

0))

Area (119876 (s0))

(4)

226 Barnes Objective Analysis (BOA) BOA is anotherpopular weighted average method (eg [8 39 40]) where theweights 120596

119894 are calculated using

120596119894= 119890minus(119889(s0 s119894)119896)2

(5)

where 119889(s0 s119894) is the Euclidean distance between the point

of interpolation s0and the gauge locations s

119894 and 119896 is the

length scale parameter that governs the rate of fall-off of theweights Subsequently two more ldquopassesrdquo were performedusing the slightly modified formula for predicted values andsuccessively smaller values of 119896

1198851015840

(s0) =119885 (s0) +

sum119894

1205961015840

119894

(119885 (s119894) minus119885 (s119894))

sum119894

1205961015840

119894

(6)

where 119885(s0) is the predicted value after the previous pass We

chose a three-pass scheme as it has been shown to producea more accurate analysis compared to a two-pass analysiswhile a four-pass scheme shows only marginal improvement[41] For each subsequent pass 119896 is reduced by a factor of120574 = 03 The permissible values for 120574 according to Barnes[42] are between 02 and 04 while Koch et al [39] definethese in the range of 02 and 1 A smaller 120574 produces a moredetailed analysis however the level of detail is limited byvarious factors such as density of observations errors in dataand the presence of subgrid scale atmospheric processes [39]Our 120574 is in agreementwithWeymouth et al [41] who also griddaily precipitation for Australia using BOA Based on Kochrsquosanalysis and setting 120574 to 03 the original value for the lengthscale 119896 can be derived from

119896 = radic35139 (

2Δ119899

120587

) (7)

where Δ119899 is the average separation between stations Assum-ing a regular grid this separation can be calculated by Δ119899 =radic(total areanumber of stations) which results in a value of119896 approximately equal to 50 km We have chosen howevera more generous value (as in [41]) of 1∘ latitude accountingfor the irregularity of the station network especially thelarge data-sparse regions in the centre of Australia Anotherpractical reason for choosing a larger 119896 is that it avoidsexcessively large regions with missing values in the centre ofAustralia As per our settings these missing value regions arecomparable in size and shape to AWAP (see Figures 2 3 and5)

The purpose of this study is not to find the best methodof interpolation for gridding daily in situ precipitation obser-vations or even to optimise the methods described here tofind the most accurate or consistent daily gridded datasetThis is primarily due to the fact that the ldquotruerdquo values of area-averaged daily precipitation are unknown across space sincewe do not have observations at all locationsWe simply aim toquantify the envelope of uncertainty resulting from commonchoices made in interpolation techniques using methodsthat are readily available in common software packages Wenote that there are indications for which methods can befurther pursued and optimised as well as indications forwhich methods can be ruled out

The next section delineates the results from comparingall of the ten daily precipitation datasets for AustraliaWhere correlations are shown they were calculated using theSpearman rank correlation function to account for the non-Gaussian nature of daily precipitation


AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 800 1600 2400 3200 4000

Figure 2 Maps of total annual precipitation at each grid point of Australia averaged over the period from 1998 to 2013 using three existinggridded datasets (AWAP TRMM and GPCP) and seven other gridded datasets calculated for the purposes of this study based on dailyprecipitation data from the GHCN-Daily dataset Refer to the text for more details Units mm


AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250

Figure 3Maps of annual maximum daily precipitation at each grid point of Australia averaged over the period from 1998 to 2013 using threeexisting gridded datasets (AWAP TRMM and GPCP) and seven other gridded datasets calculated for the purposes of this study using dailyprecipitation data from the GHCN-Daily dataset Refer to the text for more details Units mm


AWAP versus TRMM

Mean correlation = 058

10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)

Figure 4 Maps of correlations of daily precipitation over the period of 1998 to 2013 at each grid point in Australia Correlations betweenAWAP and TRMM are shown in (a) AWAP and GPCP in (b) and TRMM and GPCP in (c)

3 Results

Figure 2 shows maps of average annual precipitation totalover the period from 1998 to 2013 for the ten datasetscompared in this study Broadly the spatial patterns ofprecipitation from each product agree reasonably well andappear ldquorealisticrdquo That is high annual rainfall is observedprimarily in the tropical north and Tasmania with reasonablyhigh amounts on the coastlines especially the east coast Alldatasets show that precipitation is concentrated in the northeast south-east and a small region around Perth in south-western Australia The datasets also well represent Australiarsquosarid and semiarid regions in central and western parts of thecontinent

There are however some noteworthy differences Dueto the lower density of stations AWAP masks out theprecipitation estimates in some parts of western AustraliaDue to its cut-off radius IDW produces regions of missingvalues similar toAWAP andBOAwhereas the other griddingmethods return values in the data-sparse regions Withoutinterpolation however spatial coverage would be substan-tially reduced as can be seen from the GA maps in Figures2 and 3 The merged products also provide data everywherePrecipitation estimates from CS are unreasonably high in thedata-sparse parts of central western Australia since this is

the arid region of Australia Ordinary kriging also returnednegative daily precipitation estimates in 24 of cases ofwhich less than half a percent were under minus1mm Thenegative values greater than minus1mm have been set to 0mmthroughout this study while the remaining negative valueshave been masked out The negative precipitation valuesoccurred in all regions and no particular areas were affectedmore severely than the others These negative values are anoutcome of the negativeweights in kriging Kriging allows theweights to be negative since the only condition on the weightsof kriging is unbiasedness that is the weights must add up to1 Methods to deal with negative weights exist [43] and havebeen used in other studies [31]

The annual maximum daily precipitation for all datasetsaveraged over the period of 1998 to 2013 is shown inFigure 3 All datasets follow a similar spatial structure tothe average precipitation shown in Figure 2 that is wetterannual maxima in the north and the east coast graduallydecreasing towards the south The lowest annual maximumprecipitation is observed in the regions around the GreatAustralian Bight in South Australia and parts of westernAustralia and in all but the CS datasetThis region representsthe ldquoextensive arid corerdquo of the country and furthermoremuch of South East Australia experienced an extended dry


IDW

AWAP


TRMM


GPCP


CS

Mean correlation = 058 Mean correlation = 037 Mean correlation = 030

TLI


OK


NN

I

00 02 04 06 08 10Mean correlation = 086



(a)Figure 5 Continued


AWAPBO

A


TRMM


GPCP


GA




(b)

Figure 5 Maps of correlations of daily precipitation time series from 1998 to 2013 at each grid location between the seven gridded datasetscreated for the purposes of this study and the established gridded datasets AWAP TRMM and GPCP The rows represent the seven newgridded datasets and the columns represent AWAP TRMM and GPCP respectively For example the map in the second row of the thirdcolumn depicts the correlations between CS andGPCP datasets A negative correlation (minus03) is seen only between CS andGPCP at a locationsouth of Sydney All mean correlations were calculated on an identical spatial domain except for those involving GA due to the presence ofadditional empty grid cells

spell from 1996 to 2009 [44] Note that although all but theCS datasets show similar spatial distributions of precipitationon a continental scale they vary in their patterns on regionalscales The varying distributions of the driest regions aroundthe Great Australian Bight are a good example of this Largerdifferences however can also be found most notably inthe CS and OK datasets in comparison with the remainingdatasets The maximum precipitation from the CS dataset is424mm at its maximum which is four times higher thanthe other datasets at the northern coastline of AustraliaThe highest annual maximum of GA at the same locationis 109mm Comparison of CS and OK with GA indicatesthat CS struggles in regions of low station density whereassurprisingly OK underperforms on the east coast where thestation density is high

In the regions around Sydney on the east coast andgoing slightly inland OKrsquos annual maximum rainfall is above500mmat a few selected points (9 in total) reaching 1240mmin one caseThese numbers are an order of magnitude higherthan the other datasets as seen in Figure 3 (the averagedannual maximum of GA is 132mm at the grid location whereOK records 1240mm) Furthermore the GPCP annual max-imum precipitation on the northern coastline of Australia islower than the other datasets This may be due to the fact

that the original GPCP 1DD dataset has a resolution of 1∘times1∘ which was regridded albeit conservatively on a 05∘ times 05∘grid Another reason for this could be thatHuffman et al 2001remove the highest 10 of conditional rain rates in order toremove outliers in the process probably also removing realprecipitation values [21]

To quantify the differences and agreement in temporalvariability of precipitation between various datasets weinvestigate local correlations between the different datasets(Figures 4 and 5) Figure 4 shows the correlation of the dailyprecipitation time series over the period of 1998 to 2013for each grid cell comparing AWAP TRMM and GPCPIn Figures 4 and 5 correlations are only performed at gridlocations where at least 90 of time series is commonbetween the two datasets This means that correlations arecalculated at each grid point on at least 5258 data valuesaccounting for daily values over the 16-year period Wenote that all three datasets are highly correlated althoughthe correlations between AWAP and TRMM and TRMMand GPCP are slightly higher than the correlations betweenAWAPandGPCP It comes as no surprise that the correlationsof the merged datasets with AWAP are lower in centralAustralia since the density of observations is lower in thisregion Lower correlations are also seen in the region around


Lake Eyre between all datasets including TRMM and GPCPLake Eyre is southeast of Alice Springs (see Figure 1) Asnoted earlier this region is one of the driest regions in thecountry Furthermore the correlation between the point-based AWAP and the merged datasets is higher in thenorth and gradually decreases moving south exhibiting asomewhat banded structure Remote sensed signals are oftenweaker at high latitudes related to attenuation issues dueto shallowness of the angle of measurement between thesatellite and the surface This could therefore account forthis banded correlation that we see between TRMM andGPCP Furthermore it is also well known that both TRMMand GPCP miss light rainfall events [45 46] Since northernAustralia receives higher rainfall than the South (Figures2 and 3) the uncertainty in GPCP and TRMMrsquos rainfallestimates may also increase towards the South

Figure 5 shows correlationmaps of the daily precipitationtime series over the period of 1998 to 2013 at each gridlocation between AWAP TRMM GPCP and the sevennew gridded datasets of GHCN-Daily data created for thepurpose of this study We immediately notice that the newgridded datasets show higher correlation with AWAP thanwith the two merged products TRMM and GPCPThe meancorrelations between the six new interpolated datasets andTRMM are in the range of 037 and 058 and the meancorrelations with GPCP are in the range of 030 and 051whereas the mean correlations between the interpolateddatasets and AWAP are in the range of 058 and 086 with 4of them above 080 (IDW TLI NNI and BOA) The meancorrelation between CS and GPCP is 030 and the meancorrelation between CS and TRMM is 037 Reminiscent ofthe correlations between AWAP and the merged datasetsthe correlations of the six new interpolated datasets withTRMM and GPCP also show a banded structure highercorrelations in the north and lower correlations in the southMoreover similar to AWAP the correlations with TRMMare also higher than those with GPCP Hence we concludethat all gridded datasets whether interpolated from in situdata or remote sensing based are broadly similar in termsof their temporal variability although the correlations alsopoint to structural uncertainties between the interpolatedfields on the one hand and the satellite-based datasets onthe other hand We note that the annual seasonal cycleof precipitation may contribute to the positive correlationhowever a separate investigation proved that this effect is notvery strong The mean correlations with the annual cyclesremoved (not shown) were notmore than 005 lower than themean correlations with the annual cycle More importantlywe believe we do not have a large enough sample size in thisstudy to calculate the annual cycle and anomalies properlyFinally we note that the correlations of GA are similarto those of the interpolated datasets Note however thatthe mean correlations of GA were calculated on a differentdomain compared to the other datasets due to the sparserspatial coverage

Despite the broad similarity in the general variations ofdaily precipitation we discovered that the extremes derivedfrom these can be quite different To demonstrate this thedaily precipitation quantiles of five stations (see Figure 1)

representing different climatic zones in Australia were com-pared to the quantiles of the corresponding grid box fromthe various gridded datasets (Figure 6) We see that thequantiles of all datasets up to 20mm are similar to the gaugeobservations as they lie on or near the 1-1 line shown inblack Subsequently quantiles related to higher precipitationamounts from all datasets increasingly diverge from eachother with the maximum variance observed in the highestquantiles for all five stations In the case of Cairns located intropical Northeast Australia (see Figure 1) where maximumprecipitation reaches 250mm all datasets with the exceptionof CS interpolation sit around 100mm This may be anoutcome of higher precipitation in Cairns and its immediatevicinity compared to the surrounding areas (both the annualaverage precipitation total and the maximum daily precipita-tion of the grid cell representing Cairns in Figures 2 and 3 arehigher than the surrounding grids) It must be noted that weare comparing a point to a grid so values lower than stationvalues in the gridded products are expected due to averagingdaily totals from several stations This varying interpretationbetween area and point value is commonly known as theproblem of change of support in statistics [47] Assuming agrid box value is representative of the (average) precipitationin the area of the grid box a reasonable expectation wouldbe that the gridded value would be close to the average ofthe different station values if stations were sufficiently denseand well-spaced Since stations however are often sparselyand irregularly distributed and precipitation fields are oftenspatially discontinuous the average of all stations may notrepresent the actual grid box average Since we cannot knowthe true average over a grid and hence its extreme values weaim instead to illustrate the envelope of uncertainty betweenthe gridded datasets pertaining to the extreme daily valuesFinally we see that TRMM overestimates the high rainfallpercentiles around Perth (see Figure 1) by a third relativeto AWAP however GPCP does not Based on Figure 3 wesee that both merged datasets overestimate the maximumannual precipitation compared to the interpolated datasetsin Southwest Australia In case of GPCP however thisinconsistency is not as spatially far reaching as Perth

As an additional quantification of performance we checkhow well the different gridded datasets preserve the areawithout rain on each day using the simple station average pergrid box (GA) as a reference Note that none of the griddingmethods have an explicit criterion to preserve this quantityWe test the percentage of days when the total number of drygrid cells (ie daily precipitation below 1mm) is conservedwithin 10 of the GA dataset (Table 1) This test was onlyperformed on the cells where GA had nonmissing valuesBOA and NNI preserve the total number of dry grid cellson more than 99 of days In contrast AWAP and GPCPpreserve the dry area on less than 45 percent of days

4 Discussion

Merged products portray a similar climatology for Australiacompared to the gridded datasets obtained by interpolatingstation data (Figures 2 and 3) however the correlationsbetween the gridded station-based datasets were lower with


Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200

AWAPGPCPTRMMInverse distance weightingCubic spline

Triangulation with linear interpolationOrdinary krigingNatural neighbor interpolationBarnes objective analysisGrid station average

Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000

Figure 6 Plots of quantiles of the in situ gauge observations at five different locations Sydney Alice Springs Perth Cairns and Hobartagainst the quantiles of all ten gridded datasets in this study including AWAP TRMM and GPCP and the seven new gridded datasets Thesymbols vary based on the type of dataset triangle for AWAP square for the merged datasets TRMM and GPCP circle for the interpolateddatasets and a diamond for the grid average The stations were chosen to represent the varying climatic regions across Australia For eachQQ pair119873 quantiles are plotted where119873 equals the number of nonmissing values in the dataset with the most missing values All numbershave units of mm


Table 1 Percentage of days when the total number of dry grid cells iswithin 10of that fromGAAmask corresponding to the nonemptycells of GA was applied before these calculations

Percentage of days when number ofdry grid cells is within 10 of GA

AWAP 4429TRMM 8746GPCP 4491IDW 5927CS 5665TLI 5857OK 7609NNI 9947BOA 9997

TRMM and GPCP than with the in situ-based AWAPThe obvious reason for this is the structural uncertaintyin the two different types of datasets one is created byinterpolation of point-based data while the other involvesderiving precipitation estimates from observables related toprecipitation instead of measuring daily cumulative rainfalldirectly For example both TRMM and GPCP miss manylight rain events whichmay account for the lower correlationsbetween AWAP and the merged datasets over the most aridregions of Australia [45 46] Infrared (IR) estimates can alsoexperience false positives from non-precipitating clouds andexperience the problem of attenuation of signals at higherlatitudes [21] Furthermore in order to remove unrealisticvalues (outliers) the top 10 of conditional rain rates fromthe IR estimates are removed in the production of GPCPAll of these issues with merged satellite-gauge datasets canresult in inconsistencies when comparing with gauge-baseddatasets on daily timescales We note that the authors ofthese datasets are aware of their lack of skill when comparedto gauge datasets on a daily scale [21 48] The intention ofreleasing the daily satellite-gauge analysis is to offer users theflexibility to compute temporal aggregates according to theirown requirements [21]

Structural differences between similar datasets such asbetween merged satellite-gauge products or interpolateddatasets may also exist For example as seen throughoutthis study regional differences are present between datasetscreated with different interpolation methods Furthermoresatellites make indirect measurements which are convertedinto precipitation estimates For example satellites mea-sure the brightness temperature of the microwave andinfrared signals and radar signals measure the amplitudeof the radio waves scattered off the clouds and rain dropsThese measurements are related to precipitation amount viacomplex relationships and the variation in the algorithmsused by TRMM and GPCP to estimate these relationshipsand combine them may also contribute to the differencebetween them For example the primary source for GPCPis infrared radiometers on geosynchronous satellites (geo-IR) [21] whereas TRMM uses microwave data from multiplelow earth orbit satellites and uses the geo-IR data to fill inthe gaps in coverage [17] Note however that both datasets

use identical methods to create amonthly combined satellite-gauge analysis [27] and use a similar algorithm to rescale thedaily estimates based on themonthly analysis [17]Microwaveradiometers also tend to be more accurate than IR data whenpredicting precipitation which may account for the slightlybetter correlations between AWAP and TRMM compared tocorrelations between AWAP and GPCP

Caution must also be exercised when comparing datasetswith different timings of observations especially on a dailyscale when differences in time zonesmay decrease the overlapbetween the respective datasets In this study shifting theTRMM and GPCP data a day backward relative to theinterpolated datasets resulted in (at best) a 235-hour overlapbetween the datasets over Sydney This overlap would reduceby 2 hours in Perth and change by an hour depending onthe use of daylight savings in the region Furthermore theinconsistencies in the grid locations and resolutions also bea source of difference This is seen in Figures 3 and 6 wherethe GPCP daily estimates regridded from 1∘ times 1∘ resolutionto 05∘times 05∘ are lower compared to the other datasets Allof these possible reasons for differences mentioned above actas caveats when performing comparisons between variousdatasets on a daily timescale

The comparison of the new interpolated datasets withestablished datasets provides an indication of the suitability(or lack thereof) of various schemes to interpolate dailyprecipitation Throughout this study CS interpolation hasconsistently returned overestimates of high precipitationquantiles in some regions and shown lower overall cor-relation with AWAP TRMM and GPCP This is becauseCS interpolation characteristically overestimates the interpo-lated values especially when interpolating noisy data withsteep gradients As such CS interpolation may be moresuitable to regularly spaced dense data with smooth changesbetween neighbouring observations and is often used forregridding fields from climate models [49] It is also knownthat temporal averagingminimises this small scale variabilityof daily precipitation while reducing the effect of randomobservational errors on the interpolation [26] As a resultspline interpolation with a smoothing algorithm such as thinplate splines (TPS) is popular for interpolating monthly data[26 30 35]

Ordinary kriging on the other hand assumes somepartially correlated structure over space which is useful forapplications in geology and mining [50] Mines are spatiallyslowly varying smaller in area compared to the Australiancontinent considered here and the density of observationswithin the decorrelation length scale is usually high On theother hand the characteristic length scales of precipitationsystems are much smaller than even in many cases the dis-tance between neighbouring gauge observations This strongspatial variability of precipitation complicates the process ofsemivariogram fitting making automatically fitted semivari-ograms (as in this study) less skilled It is possible howeverto conduct more complex semivariogram estimation such as3D semivariograms or anisotropic semivariograms [51 52]Multivariate krigingmethods which use external data such asradar data to calculate semivariograms can also be employedto improve the estimates [6 53] however Dirks et al [54]


discovered that for high density networks kriging does notimprove upon simpler methods such as IDW Furthermorekriging is not an exact interpolator which results in unrealis-tic maxima on the east coast in our study (Figure 3) Anotherdisadvantage of kriging is that it assumes (often falsely) thatthe interpolant is a random process that is stationary inspace This can sometimes be corrected by using differentsize and shapes of the search neighbourhood which in turncreates complications in stitching the analyses together so asto avoid discontinuities Finally kriging is a computationallytaxing scheme and took up to five times longer than theother methods in our case This may be an important factorto consider if the aim is to generate near real time analysisor incorporate much larger data networks There are manyvariants of kriging with each purpose designed to improvesome aspect of the analyses Our intention is to investigatethese methods further to understand how extremes can bepreserved in the interpolation process

The remaining methods (IDW TLI NNI and BOA)exhibited high skill in interpolating daily gauge data as theyall showed high correlations with AWAP and correlationssimilar to AWAP with the merged datasets All methods withthe exception of TLI are weighted average methods similarto AWAP which in part may explain the similar correla-tions however all methods including AWAP modelled theextremes disparately as seen in the Q-Q plots (Figure 6)adding to their uncertainty We note that the weighted aver-agemethods cannot shoot above the observations and neithercan TLI as it is an exact interpolator The advantages of thesemethods are that they are highly computationally efficientand handle irregular and noisy data well as highlighted bythis study

The interpolation for AWAP was done with Barnesobjective analysis as well [26]There are however differencesbetween the new BOA dataset and AWAP (Figure 5) Thismay partly be due to the difference in the parameters usedto determine the weights More importantly differencesalso arise due to the application of anomaly interpolationfor AWAP as mentioned in Section 21 The exact effectof using anomalies for gridding daily precipitation is stillunclear particularly with regard to extremes and shall beanother focus for further research Ultimately despite notinterpolating anomalies natural neighbour and linear andinverse distance weighting interpolation give near identicalresults to AWAP

5 Conclusions

We compare a range of gridded daily precipitation data forAustralia over the period of 1998 to 2013 Three existing dataproducts AWAP TRMM and GPCP which represent in situand merged in situremotely sensed products respectivelywere compared with six datasets that the authors calculatedusing in situ observations with six different interpolationtechniques For comparison we also added a grid thatsimply averages all station values within a grid box withoutinterpolation All datasets show similar spatial patterns ofprecipitation climatologies with the highest precipitationamounts occurring in the tropical north of Australia and

along the east coast and the lowest amounts in central westernparts of the continent

In terms of temporal variability there is generally goodagreement betweenmost of the different datasets interpolatedfrom station observations albeit there are regionally largerdifferences (lower correlations) for grids interpolated by ordi-nary kriging and cubic spline interpolation Correlations arelow between gridded observations and the merged productsbut the two merged datasets are positively correlated witheach other

The local distributions of precipitation are very similarbetween all datasets for low to moderate daily precipitationamounts of up to approximately 20mm Larger differencesin some locations of up to a factor of five are found forthe most extreme daily precipitation amounts This hasimplications for investigations of precipitation extremes interms of sensitivity of the results to the specific datasets used

There is no gridding method that consistently performsclosest to station observations but in particular cubic splineinterpolation shows a tendency to ldquoovershootrdquo in comparisonto station data and the other gridded products in particularin regions with steep spatial gradients of precipitation

Our results indicate that all datasets are able to simulatethe broad rainfall patterns across Australia It is clear thatthe merged products are as similar to each other as are thedatasets interpolated from in situ data but the two types ofdatasets (in situ-based and remotely sensed) are structurallydissimilar on daily timescales particularly outside of thetropics Our study shows that daily precipitation extremesare subject to large uncertainties across all gridded productsanalysed here irrespective of whether the datasets are derivedfrom in situ data or also contain remotely sensed dataOur recommendation to those investigating precipitationextremes is that a combination of different methods andproducts should be used in order to capture the level ofuncertainty that clearly exists at these higher quantiles Usinga single dataset would not faithfully capture this uncer-tainty creating false confidence in conclusions regarding theextreme end of the distribution

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study was supported by Australian Research Council(ARC) Grant CE110001028 and contributes to the WorldClimate Research Programme (WCRP) Grand Challenge onExtremes Markus Donat was also supported by ARC GrantDE150100456 Analysis was performed using Climate DataOperators software (httpscodezmawdeprojectscdo) R[55] and NCL [56]

References

[1] A Aghakouchak A Mehran H Norouzi and A BehrangildquoSystematic and random error components in satellite precip-itation data setsrdquo Geophysical Research Letters vol 39 no 9 pp3ndash6 2012


[2] H YinM G Donat L V Alexander and Y Sun ldquoMulti-datasetcomparison of gridded observed temperature and precipitationextremes over Chinardquo International Journal of Climatology vol35 no 10 pp 2809ndash2827 2015

[3] A Aghakouchak A Behrangi S Sorooshian K Hsu and EAmitai ldquoEvaluation of satellite-retrieved extreme precipitationrates across the central United Statesrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 2 Article ID D02115 2011

[4] A D King L V Alexander and M G Donat ldquoThe efficacy ofusing gridded data to examine extreme rainfall characteristicsa case study for Australiardquo International Journal of Climatologyvol 33 no 10 pp 2376ndash2387 2013

[5] N Hofstra M New and C McSweeney ldquoThe influence ofinterpolation and station network density on the distributionsand trends of climate variables in gridded daily datardquo ClimateDynamics vol 35 no 5 pp 841ndash858 2010

[6] N Hofstra M Haylock M New P Jones and C Frei ldquoCom-parison of six methods for the interpolation of daily Europeanclimate datardquo Journal of Geophysical Research vol 113 no 21Article ID D21110 2008

[7] A Yatagai K Kamiguchi O Arakawa A Hamada N Yasu-tomi and A Kitoh ldquoAphrodite constructing a long-term dailygridded precipitation dataset for Asia based on a dense networkof rain gaugesrdquo Bulletin of the American Meteorological Societyvol 93 no 9 pp 1401ndash1415 2012

[8] D A Jones W Wang and R Fawcett ldquoHigh-quality spatialclimate data-sets for Australiardquo Australian Meteorological andOceanographic Journal vol 58 no 4 pp 233ndash248 2009

[9] C G Menendez M De Castro A Sorensson and J-PBoulanger ldquoCLARIS project towards climate downscaling inSouth Americardquo Meteorologische Zeitschrift vol 19 no 4 pp357ndash362 2010

[10] E J Klok and A M G K Tank ldquoUpdated and extendedEuropean dataset of daily climate observationsrdquo InternationalJournal of Climatology vol 29 no 8 pp 1182ndash1191 2009

[11] B Mueller S I Seneviratne C Jimenez et al ldquoEvaluationof global observations-based evapotranspiration datasets andIPCC AR4 simulationsrdquo Geophysical Research Letters vol 38no 6 2011

[12] C-T Chen and T Knutson ldquoOn the verification and compari-son of extreme rainfall indices from climate modelsrdquo Journal ofClimate vol 21 no 7 pp 1605ndash1621 2008

[13] R J H Dunn M G Donat and L V Alexander ldquoInvestigatinguncertainties in global gridded datasets of climate extremesrdquoClimate of the Past vol 10 no 6 pp 2171ndash2199 2014

[14] M New M Todd M Hulme and P Jones ldquoPrecipitation mea-surements and trends in the twentieth centuryrdquo InternationalJournal of Climatology vol 21 no 15 pp 1899ndash1922 2001

[15] R J Joyce J E Janowiak P A Arkin and P Xie ldquoCMORPH amethod that produces global precipitation estimates from pas-sive microwave and infrared data at high spatial and temporalresolutionrdquo Journal of Hydrometeorology vol 5 no 3 pp 487ndash503 2004

[16] S Sorooshian K-L Hsu X Gao H V Gupta B Imamand D Braithwaite ldquoEvaluation of PERSIANN system satellite-based estimates of tropical rainfallrdquo Bulletin of the AmericanMeteorological Society vol 81 no 9 pp 2035ndash2046 2000

[17] G J Huffman R F Adler D T Bolvin et al ldquoTheTRMMMulti-satellite PrecipitationAnalysis (TMPA) quasi-globalmultiyearcombined-sensor precipitation estimates at fine scalesrdquo Journalof Hydrometeorology vol 8 no 1 pp 38ndash55 2007

[18] MB Sylla FGiorgi E Coppola andLMariotti ldquoUncertaintiesin daily rainfall over Africa assessment of gridded observationproducts and evaluation of a regional climate model simula-tionrdquo International Journal of Climatology vol 33 no 7 pp1805ndash1817 2013

[19] D A Jones W Wang and R Fawcett Australian WaterAvailability Project Daily 672 Gridded Rainfall 2014 httpwwwbomgovaujspawaprainindexjsp

[20] G J Huffman E F Stocker D T Bolvin E J Nelkin and R FAdler ldquoTRMM Version 7 3B42rdquo NASAGSFC Greenbelt MdUSA 2014 httpmiradorgsfcnasagovcgi-binmiradorpresentNavigationpltree=projectampdataset=TRMM 3B42 daily007ampproject=TRMMampdataGroup=Griddedampversion=007

[21] G J Huffman R F Adler M M Morrissey et al ldquoGlobalprecipitation at one-degree daily resolution from multisatelliteobservationsrdquo Journal of Hydrometeorology vol 2 no 1 pp 36ndash50 2001

[22] G J Huffman R F Adler M M Morrissey et al Global Pre-cipitation One-Degree Daily Data Set NASAGSFC GreenbeltMd USA 2014 ftpftpcgducareduarchivePRECIP

[23] P W Jones ldquoFirst- and second-order conservative remappingschemes for grids in spherical coordinatesrdquo Monthly WeatherReview vol 127 no 9 pp 2204ndash2210 1999

[24] M J Menne I Durre R S Vose B E Gleason and T GHouston ldquoAn overview of the global historical climatologynetwork-daily databaserdquo Journal of Atmospheric and OceanicTechnology vol 29 no 7 pp 897ndash910 2012

[25] M J Menne I Durre B Korzeniewski et al Global Histori-cal Climatology NetworkmdashDaily (GHCN-Daily) Version 320-upd-2015011506 NOAA National Climatic Data Center 2012ftpftpncdcnoaagovpubdataghcndaily

[26] D A Jones W Wang and R Fawcett ldquoClimate Data for theAustralian Water Availability Projectrdquo 2007

[27] G J Huffman R F Adler P Arkin et al ldquoThe global pre-cipitation climatology project (GPCP) combined precipitationdatasetrdquo Bulletin of the AmericanMeteorological Society vol 78no 1 pp 5ndash20 1997

[28] O Tveito ldquoSpatialisation of climatological and meteorologicalinformation with the support of GIS (Working Group 2)rdquo inThe Use of Geographic Information Systems in Climatology andMeteorology 2006

[29] D Kurtzman and R Kadmon ldquoMapping of temperature vari-ables in Israel a comparison of different interpolationmethodsrdquoClimate Research vol 13 no 1 pp 33ndash43 1999

[30] C Daly ldquoGuidelines for assessing the suitability of spatialclimate data setsrdquo International Journal of Climatology vol 26no 6 pp 707ndash721 2006

[31] K Stahl R D Moore J A Floyer M G Asplin and I GMcKendry ldquoComparison of approaches for spatial interpolationof daily air temperature in a large region with complex topogra-phy and highly variable station densityrdquo Agricultural and ForestMeteorology vol 139 no 3-4 pp 224ndash236 2006

[32] S S P Shen P Dzikowski G Li and D Griffith ldquoInterpolationof 1961ndash97 daily temperature and precipitation data onto albertapolygons of ecodistrict and soil landscapes of Canadardquo Journalof Applied Meteorology vol 40 no 12 pp 2162ndash2177 2001

[33] H Akima ldquoAlgorithm 761 scattered-data surface fitting thathas the accuracy of a cubic polynomialrdquo ACM Transactions onMathematical Software vol 22 no 3 pp 362ndash371 1996

[34] H Akima ldquoA new method of interpolation and smooth curvefitting based on local proceduresrdquo Journal of the ACM vol 17no 4 pp 589ndash602 1970


[35] C H Jarvis and N Stuart ldquoA comparison among strategies forinterpolating maximum and minimum daily air temperaturesPart II The interaction between number of guiding variablesand the type of interpolation methodrdquo Journal of AppliedMeteorology vol 40 no 6 pp 1075ndash1084 2001

[36] H Akima ldquoA method of bivariate interpolation and smoothsurface fitting for irregularly distributed data pointsrdquo ACMTransactions on Mathematical Software vol 4 no 2 pp 148ndash159 1978

[37] F J Moral ldquoComparison of different geostatistical approachesto map climate variables application to precipitationrdquo Interna-tional Journal of Climatology vol 30 no 4 pp 620ndash631 2010

[38] R Sibson ldquoA brief description of natural neighbour interpola-tionrdquo in Interpreting Multivariate Data vol 21 pp 21ndash36 1981

[39] S E Koch M Desjardins and P J Kocin ldquoAn interactiveBarnes objective map analysis scheme for use with satellite andconventional datardquo Journal of Climate amp Applied Meteorologyvol 22 no 9 pp 1487ndash1503 1983

[40] S K Sinha and S G Narkhedkar ldquoBarnes objective anal-ysis scheme of daily rainfall over Maharashtra (India) on amesoscale gridrdquo Atmosfera vol 19 no 2 pp 109ndash126 2006

[41] G Weymouth G A Mills D Jones E E Ebert and M JManton ldquoA continental-scale daily rainfall analysis systemrdquoTheAustralian Meteorological Magazine vol 48 pp 169ndash179 1999

[42] S L Barnes Mesoscale Objective Map Analysis Using WeightedTime-series Observations 1973

[43] C V Deutsch ldquoCorrecting for negative weights in ordinarykrigingrdquo Computers and Geosciences vol 22 no 7 pp 765ndash7731996

[44] P Holper ldquoClimate Change Science Information Paper Aus-tralian Rainfall Past Present and Futurerdquo 2011

[45] A Behrangi M Lebsock S Wong and B Lambrigtsen ldquoOnthe quantification of oceanic rainfall using spaceborne sensorsrdquoJournal of Geophysical Research Atmospheres vol 117 no 20Article ID D20105 2012

[46] A Behrangi G Stephens R F Adler G J Huffman BLambrigtsen and M Lebsock ldquoAn update on the oceanicprecipitation rate and its zonal distribution in light of advancedobservations from spacerdquo Journal of Climate vol 27 no 11 pp3957ndash3965 2014

[47] L Alexander and C Tebaldi ldquoClimate and weather extremesobservations modelling and projectionsrdquo in The Future ofthe Worldrsquos Climate pp 253ndash288 Elsevier Amsterdam TheNetherlands 2012

[48] G J Huffman A Pendergrass and National Center forAtmospheric Research Staff Eds TRMM Tropical RainfallMeasuring Mission The Climate Data Guide 2015 httpsclimatedataguideucareduclimate-datatrmm-tropical-rainfall-measuring-mission

[49] D W Pierce T P Barnett B D Santer and P J GlecklerldquoSelecting global climate models for regional climate changestudiesrdquo Proceedings of the National Academy of Sciences of theUnited States of America vol 106 no 21 pp 8441ndash8446 2009

[50] D Krige ldquoA statistical approach to some basic mine valuationproblems on the Witwatersrandrdquo Journal of the ChemicalMetallurgical and Mining Society of South Africa vol 52 no 6pp 119ndash139 1951

[51] Z Kebaili Bargaoui and A Chebbi ldquoComparison of two krig-ing interpolation methods applied to spatiotemporal rainfallrdquoJournal of Hydrology vol 365 no 1-2 pp 56ndash73 2009

[52] U Haberlandt ldquoGeostatistical interpolation of hourly precipita-tion from rain gauges and radar for a large-scale extreme rainfalleventrdquo Journal of Hydrology vol 332 no 1-2 pp 144ndash157 2007

[53] P Goovaerts ldquoGeostatistical approaches for incorporating ele-vation into the spatial interpolation of rainfallrdquo Journal ofHydrology vol 228 no 1-2 pp 113ndash129 2000

[54] K N Dirks J E Hay C D Stow and D Harris ldquoHigh-resolution studies of rainfall on Norfolk Island Part II interpo-lation of rainfall datardquo Journal of Hydrology vol 208 no 3-4pp 187ndash193 1998

[55] R D C Team R A Language and Environment for StatisticalComputing R Foundation for Statistical Computing ViennaAustria 2008

[56] Mini-Language Reference ldquoNCAR Command LanguagerdquoNational Center for Atmospheric Research 2013 httpwwwnclucareduDocumentManualsRef Manual

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


In addition to daily gauge-based rainfall products thereare also many remotely sensed or merged products whichare often also used for monitoring and evaluation (egCMORPH [15] PERSIANN [16] and TRMM [17]) Manyof these products however have been shown to exhibitsubstantial differences in their representation of rainfall andespecially rainfall extremes [3 18] Given the considerableuse of these products within themeteorological hydrologicaland climate communities it would seem prudent to betterquantify some of these uncertainties and provide guidelinesfor users on the potential use and misuse of these datasetsparticularly in relation to long-term assessment

Using Australia as a case study the purpose of thispaper is to highlight some of the structural uncertainty thatis inherent in daily precipitation products through use ofcommon interpolation schemes and also to assess how thiscompares with existing gridded in situ-based datasets andsatellite-derived products which are often used in hydrome-teorological applications In addition we showhow structuraluncertainty manifests between gauge-based and satellite-based products and provide an assessment of how griddedproducts perform at capturing local precipitation extremes

2 Materials and Methods

21 Data We use several different gridded datasets in orderto represent daily precipitation estimates for Australia fromin situ satellite-based andmerged products Datasets chosenwere the in situ-based Australian Water Availability Project(AWAP) and the merged in situ and satellite-based datasetsfrom the Tropical Rainfall Measuring Mission (TRMM) andthe Global Precipitation Climatology Project One-DegreeDaily (GPCP 1DD) product AWAP [8 19] is a dataset createdby the Australian Bureau of Meteorology by gridding dailygauge data on a 5 km times 5 km grid using the Barnes succes-sive correction method (httpwwwbomgovauclimate)TRMM 3B42 Daily V7 [17 20] is a 025∘times 025∘ resolutiondataset spanning 50∘Nndash50∘S that combines precipitationestimates from multiple satellite sources to create a dailyprecipitation estimate in the period from 1998 to presentThis estimate is rescaled with respect tomonthly gauge-basedprecipitation totals where possible for improved accuracyFinally GPCP 1DD version 12 [21 22] combines remotesensed data withmonthly gauge data to createmonthly globalprecipitation estimates with a 25∘ times 25∘ resolution Thisdataset is then combined with high spatial and temporalresolution infrared data from various satellites to create aglobal daily precipitation estimate at a 1∘times1∘ resolution for theperiod from 1996 to present The data from all three datasetswere regridded to a common 05∘ times 05∘ grid over Australiausing a first-order area-conservative remapping technique[23] Subsequently throughout the paper the datasets willbe referred to as AWAP TRMM and GPCP with TRMMand GPCP being collectively referred to as ldquomergedrdquo datasetssince they combine remotely sensed and in situ-based data Itshould be noted that TRMM and GPCP use monthly gaugeanalysis so the intensity and occurrence of daily rainfallare determined by remote sensing As a result TRMM andGPCP are likely to be reasonably independent of AWAP We

compare the different datasets for the 16-year period 1998ndash2013 as this period is common to all datasets (eg TRMMwas only available from 1998)

In addition to the above we calculate six daily pre-cipitation grids using different interpolation schemes andbased on point-based observational data derived from theGlobalHistorical ClimatologyNetworkDaily (GHCN-Daily)archive [24 25] a database of daily weather and climaticinformation from land-based stations across the globe Wedo this to try to understand how uncertainty might manifestthrough the use of common interpolation techniques andunderstand how this uncertainty differs in comparison tothe merged products In addition to these six interpolateddatasets we also calculate a dataset Grid [Station] Average(GA) which is simply an unweighted average of all stationsinside a grid cell without interpolationThis dataset providesa reference for comparison to all of the nine other datasets

Across Australia GHCN-Daily currently contains dailyprecipitation values for 8361 stations (Figure 1) over theperiod of 1998 to 2013 of which only a subset of stations(4500 to 6500 depending on the day) were used for griddingeach day This is because the number of operational andreporting stations varies over the period of 1998 to 2013(data downloaded in January 2015) GHCN-Daily data forAustralia were interpolated on a regular 05∘times 05∘ gridcovering Australia A comparison of GHCN-Daily stationswith the stations used by the merged datasets TRMM andGPCP showed that on average there were approximately1000 additional GHCN-Daily stations available with themost prominent differences around the north and northwestcoastlines (not shown)

Note that although all datasets represent cumulative dailyprecipitation over a 24 h window the start and end timesof this window vary For example the time coverage ofobservations forAWAP starts at 0900 h local time inAustraliaon the day before the time stamp to 0900 h local time onthe day named For TRMM and GPCP on the other handthe time coverage starts at 2230 h GMT on the day before to2229 h GMT on the day of the time stamp This is equivalentto 0830 h Australian Eastern Standard Time (AEST) on theday of the time stamp to 0829 h AEST on the day after thetime stamp in Sydney NSWThis time difference varies fromsummer to winter due to daylight savings across Australiaand the use of varying time zones in the country These timedifferences were considered before calculating correlations byshifting the TRMMandGPCP data by a day tomatch as closeas possible the time intervals for comparison with the gauge-based grids

Also note that AWAP takes advantage of anomaly basedinterpolation rather than interpolating the raw gauge obser-vations directly Anomalies are calculated relative to dailyclimatologies This has the advantage of transforming thehighly varying observations into a set to which a smoothercurve can be fitted [26] Jones et al [26] also note that theclimatology provides more information than contained inindividual observations Furthermore they note that anoma-lies are weakly related to elevation making it more suitable tointerpolate station data using a two-dimensional analysis


minus10

minus20

minus30

minus40

Latit

ude (

∘)

120 130 140 150

Longitude (∘)

3 Perth

2 Alice Springs

4 Cairns

1 Sydney

5 Hobart








119894Then the


0is given by

119885 (s0) =

sum119899

119894=0

120596119894119885 (s119894)

sum119899

119894=0

120596119894

(1)


119894= 1119889(s

0 s119894)119901 Here


0and s119894



119885 (119909 119910) =

5

sum

119894=0

5minus119894

sum

119895

119886119894119895119909119894

119910119895

(2)



119894) + 1) instead of119885(s

119894)




120574 (119889) =

1

2 |119873 (119889)|

sum

119873(119889)

(119885 (s119894) minus 119885 (s

119895))

2

(3)



119895 and 119885(s

119894) and 119885(s

119895) are the










119895 =




ratio

120596119894=

Area (119875 (s119894) cap 119876 (s

0))

Area (119876 (s0))

(4)



120596119894= 119890minus(119889(s0 s119894)119896)2

(5)



119894 and 119896 is the


1198851015840

(s0) =119885 (s0) +

sum119894

1205961015840

119894

(119885 (s119894) minus119885 (s119894))

sum119894

1205961015840

119894

(6)



119896 = radic35139 (

2Δ119899

120587

) (7)





AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 800 1600 2400 3200 4000



AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250



AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


minus10

minus20

minus30

minus40

Latit

ude (

∘)

120 130 140 150

Longitude (∘)

3 Perth

2 Alice Springs

4 Cairns

1 Sydney

5 Hobart








119894Then the


0is given by

119885 (s0) =

sum119899

119894=0

120596119894119885 (s119894)

sum119899

119894=0

120596119894

(1)


119894= 1119889(s

0 s119894)119901 Here


0and s119894



119885 (119909 119910) =

5

sum

119894=0

5minus119894

sum

119895

119886119894119895119909119894

119910119895

(2)



119894) + 1) instead of119885(s

119894)




120574 (119889) =

1

2 |119873 (119889)|

sum

119873(119889)

(119885 (s119894) minus 119885 (s

119895))

2

(3)



119895 and 119885(s

119894) and 119885(s

119895) are the










119895 =




ratio

120596119894=

Area (119875 (s119894) cap 119876 (s

0))

Area (119876 (s0))

(4)



120596119894= 119890minus(119889(s0 s119894)119896)2

(5)



119894 and 119896 is the


1198851015840

(s0) =119885 (s0) +

sum119894

1205961015840

119894

(119885 (s119894) minus119885 (s119894))

sum119894

1205961015840

119894

(6)



119896 = radic35139 (

2Δ119899

120587

) (7)





AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 800 1600 2400 3200 4000



AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250



AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




120574 (119889) =

1

2 |119873 (119889)|

sum

119873(119889)

(119885 (s119894) minus 119885 (s

119895))

2

(3)



119895 and 119885(s

119894) and 119885(s

119895) are the










119895 =




ratio

120596119894=

Area (119875 (s119894) cap 119876 (s

0))

Area (119876 (s0))

(4)



120596119894= 119890minus(119889(s0 s119894)119896)2

(5)



119894 and 119896 is the


1198851015840

(s0) =119885 (s0) +

sum119894

1205961015840

119894

(119885 (s119894) minus119885 (s119894))

sum119894

1205961015840

119894

(6)



119896 = radic35139 (

2Δ119899

120587

) (7)





AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 800 1600 2400 3200 4000



AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250



AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 800 1600 2400 3200 4000



AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250



AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


AWAP TRMM GPCP

IDW CS TLI

OK NNI BOA

GA

0 50 100 150 200 250



AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


AWAP versus TRMM


10

08

06

04

02

00

(a)

AWAP versus GPCP


10

08

06

04

02

00

(b)TRMM versus GPCP


10

08

06

04

02

00

(c)


3 Results






IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


IDW

AWAP


TRMM


GPCP


CS


TLI


OK


NN

I






AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


AWAPBO

A


TRMM


GPCP


GA




(b)












4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in







4 Discussion



Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Sydney200

150

100

50

0

200150100500

200

150

100

50

0

200150100500

Alice Springs

Hobart

120

100

80

60

40

20

0

120100806040200



Perth

120

100

80

60

40

20

0

120100806040200

Cairns500

400

300

200

100

0

5004003002001000
















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in















5 Conclusions









Acknowledgments


References




































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

research article how well do gridded datasets of observed

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