Assessment of Spatiotemporal Varying RelationshipsBetween Rainfall, Land Cover and Surface Water AreaUsing Geographically Weighted Regression

Stuart Brown & Vincent L. Versace & Laurie Laurenson &

Daniel Ierodiaconou & Jonathon Fawcett & Scott Salzman

Received: 27 December 2010 /Accepted: 28 July 2011 /Published online: 11 August 2011# Springer Science+Business Media B.V. 2011

Abstract Traditional regression techniques such as ordinaryleast squares (OLS) are often unable to accurately modelspatially varying data and may ignore or hide local variationsin model coefficients. A relatively new technique, geograph-ically weighted regression (GWR) has been shown to greatlyimprove model performance compared to OLS in terms ofhigher R2 and lower corrected Akaike information criterion(AICC). GWR models have the potential to improvereliabilities of the identified relationships by reducing spatialautocorrelations and by accounting for local variations andspatial non-stationarity between dependent and independentvariables. In this study, GWR was used to examine therelationship between land cover, rainfall and surface waterhabitat in 149 sub-catchments in a predominately agriculturalregion covering 2.6 million ha in southeast Australia. Theapplication of the GWR models revealed that the relation-ships between land cover, rainfall and surface water habitatdisplay significant spatial non-stationarity. GWR showedimprovements over analogous OLS models in terms ofhigher R2 and lower AICC. The increased explanatory powerof GWR was confirmed by the results of an approximatelikelihood ratio test, which showed statistically significantimprovements over analogous OLS models. The modelssuggest that the amount of surface water area in the landscape

is related to anthropogenic drainage practices enhancingrunoff to facilitate intensive agriculture and increased plantationforestry. However, with some key variables not present in ouranalysis, the strength of this relationship could not be qualified.GWR techniques have the potential to serve as a useful tool forenvironmental research and management across a broad rangeof scales for the investigation of spatially varying relationships.

Keywords Geographically weighted regression . Landuse . Climate change . Rainfall .Water resources

1 Introduction

Climate change is now widely accepted by the scientificcommunity and current research suggests that temperatureand rainfall patterns are likely to change dramatically overthe next 50 years [25]. Extended periods of drought andassociated reductions in precipitation, runoff and soilmoisture are forecasted. Hydrological models suggestgroundwater and stream flow will be under increasingstress [29]. With perennial surface water habitat beinglargely dependent on rainfall, an increased understanding ofthe effects of climate on aquatic habitat availability atregional scales is necessary for the development andimprovement of management plans designed to enhanceand conserve these habitats.

Global wetland extent is currently estimated at between 5.3and 12.8 million km2 with about half of the original extenthaving been lost [39, 57]. These extents, however, are notreliable as many countries lack comprehensive wetlandinventories [19]. Drainage of wetlands for agriculture isperceived to have caused the biggest loss of wetlands to date,with an estimated 26% of global wetland area being drainedfor intensive agriculture [57]. In Asia alone, annual decreases

S. Brown (*) : L. Laurenson :D. IerodiaconouSchool of Life and Environmental Sciences, Deakin University,PO Box 423, Warrnambool, VIC 3280, Australiae-mail: scbro@deakin.edu.au

J. FawcettSinclair-Knight-Mertz,Bendigo, VIC, Australia

V. L. Versace : S. SalzmanSchool of Information Systems, Deakin University,Warrnambool, VIC, Australia

Environ Model Assess (2012) 17:241–254DOI 10.1007/s10666-011-9289-8

of about 5,000 km2 are lost primarily to agriculture andthrough dam construction [57]. Although the availableinformation varies in resolution and spatial extent, theoverall trend indicates an indisputable reduction in surfacearea, condition and associated biodiversity of global wetlands[8, 57]. Perennial wetlands in particular are essential forecosystem function as biodiversity hotspots [13, 18, 54], inthe biogeochemical cycling of nutrients [7, 36], as droughtrefuges across a variety of spatial scales [3, 11, 28, 32, 33],as well as providing ecosystem services widely benefitinghuman populations. Unfortunately, freshwater ecosystemsare amongst the most threatened in the world [18, 37].Jensen [26] wrote that even though Australia is the driestinhabited continent, water is not valued enough to ensurewetlands, rivers, catchments and water supply resources areeffectively protected. Brinson and Malvarez [8] agreed andreported that due to the Australian climate, wetlands andanthropogenic activities are in direct competition for water andthat without reductions in human water usage there will be fewopportunities to improve the status of Australian wetlands overthe next few decades.

There have been numerous studies on the separated impactsof climate and land use changes on hydrology and waterquality [14, 49]. However, few studies examine the impacts ofclimate and land cover changes on the area of surface waterhabitats. There are several factors affecting surface hydrologyand surface water availability; rainfall variability [40], soiltype and infiltration capacity [44, 45], topography [15] andvegetation type [9, 31, 40, 41]. Vegetation has been shown toaffect surface hydrology, primarily by changing evapotrans-piration [31, 41], with temperate forested catchments display-ing statistically significant higher evapotranspiration thannon-forested catchments [41]. However, the effect of vegeta-tion impact on evapotranspiration has been shown to diminishas the area of a catchment increases [41].

Advances in data collection using a variety of spaced-based remote sensors have permitted the systematicacquisition of land cover data over large spatial andtemporal scales. The Landsat sensor is the longest runningof the land cover sensors and has been used extensively inthe production of land cover maps, in landscape ecologyresearch and in detecting land cover changes [55]. Thesensor provides cost-effective, high-resolution images(30 m in the visible bands) that are particularly useful forenvironmental monitoring due to the 16-day temporalresolution. These remotely sensed images coupled withstatistical modelling techniques have allowed scientists andnatural resource managers to begin to link pattern toprocess [22]. A common methodological framework toachieve this has been the use of regression techniques inconjunction with classified land use maps [51].

Traditionally, regression techniques have been limited tomethods such as ordinary least squares (OLS) regression

which is subject to some restrictive assumptions related tonormality and variance distributions [43]. These assump-tions include that residuals are not correlated (there is noauto-correlation) and that they are normally distributed witha mean of zero and display homogeneity of variance (i.e.homoscedasticity). According to Tu and Xia [46], studiesconcerned with the aquatic environment often violate theseassumptions resulting in additional problems such as spatialautocorrelation and spatial non-stationarity. Spatial autocorre-lation is a phenomenon where the values for a given variableat location x are related to the values for the same variable atlocations nearby. It is possible that different degrees of spatialautocorrelation can be present within the same dataset, andtherefore, global models to test for spatial autocorrelationwould fail to detect it [20]. Spatial non-stationarity occurswhen the relationships between the response and predictorvariables are not constant over space [20]. These issues ofspatial autocorrelation and non-stationarity can be a result ofmodel misspecification. For example, using OLS to identifypatterns that are known or thought to vary over space willlikely result in significant spatial autocorrelation betweenresiduals as the model will not be able to effectively explainlocal variations in the relationship.

Geographically weighted regression (GWR) has beendeveloped in an attempt to explore and explain spatiallyvarying relationships, by essentially allowing model param-eters to vary over space and thus attempt to overcome someof the restrictive assumptions of OLS regression [20].Fotheringham et al. [20] give a detailed explanation of thetheoretical background behind GWR and explain the appli-cability of the method to explore spatially varying relation-ships. The technique has broad applications across a numberof fields including health [38], forestry [30], aquatic science[46], social science [10], and economics [56]. GWR has alsobeen shown to provide better localised prediction results thanother techniques [59]. The strengths of GWRmake it an idealtechnique to explore the spatiotemporal varying relationshipbetween rainfall, land cover and area of surface water habitat.

The primary purpose of this paper is to evaluate thesuitability of two regression methods (GWR and OLS) toexplain spatially varying data in a predominately drylandcatchment in southwest Victoria, Australia. In addition tocomparing the two modelling approaches, the resultsgenerated will allow an assessment of the influence ofrainfall and land cover changes on surface water area at thesub-catchment and regional scale. Therefore, the secondarypurpose of the paper is to provide regional natural resourcemanagers with further information that will assist long-termstrategic catchment planning. A similar approach wasadopted by Tu and Xia [46] who used their paper not todetermine if any relationships existed between land use andwater quality but to examine if any interesting spatialvariations existed in the relationship between the variables.

242 S. Brown et al.

2 Study Site

The Glenelg Hopkins region lies southwest of the GreatDividing Range of eastern Australia and is located in the stateof Victoria (Fig. 1). It covers approximately 27,000 km2 andthe cities of Warrnambool, Ararat, Hamilton, Portland andthe western fringes of Ballarat are within its boundary. Theregion contains the Grampians Ranges in the north but isgenerally a low-lying series of catchments. The three majordrainage basins within the region are the Glenelg,Hopkins and Portland coast; drainage across the basinsis generally poor resulting in the formation of manylakes and wetlands [21]. The region experiences aMediterranean climate characterised by hot dry summersand cool, wet winters. Average annual rainfall ranges from500 mm/year around Lake Bolac to >900 mm/year in thefar south of the region and the upper reaches within theGrampians Ranges.

Agricultural land uses dominate the region, with dry landpasture and crops covering approximately 70% of the region.Pine (Pinus radiata) and Blue gum (Eucalyptus globulus)plantations are also a dominant feature of the landscapecovering about 2.8% and 4.9% of the region, respectively, in

2002 [24]. Remnant native vegetation covers approximately16% of the catchment and is largely accounted for by theGrampians National Park and the Lower Glenelg NationalPark. Figure 2 shows aggregated regional land cover in 2002based upon the classifications of Ierodiaconou et al. [24].

Since European settlement, land use in the region hasundergone dramatic changes [16, 24, 50]. Between 1980and 2002, 16% of the region underwent land covertransition [24]. The region contains approximately 44% ofVictoria’s wetlands, and it is thought that since Europeansettlement, over 75% of the regions wetlands have beenmodified by agricultural drainage [12].

Climate change scenarios forecast increasing stress onAustralia’s scarce freshwater resources [42, 52]. WithAustralia under conditions of major to severe drought50% of the time since records began [34], future climatescenarios indicate a continuing trend of rainfall deficiency.Although the entire study region experiences low inter-annual rainfall variability [6, 17], reductions in rainfall areexpected for the region with a decrease of −4% by 2030and −10% by 2070. Evaporation is expected to increase by2% by 2030 and by 6% by 2070 [17]. Reductions in runofffor this region are expected to be between −35% and −40%

Fig. 1 Location of the study site

Assessment of Spatiotemporal Varying Relationships 243

during the summer months for 2030, with decreases greaterthan −50% by 2070 [27].

The region has been identified as a potential ‘foodbowl’, and in the face of climate change, an intensificationof agricultural pursuits in the region can be expected. Witha strategically changing land cover and serious reductionsin runoff predicted as a result of climate change, water andland managers in this region need a greater understandingof where surface water habitats are likely to be affected byfuture climate and land cover changes.

3 Data Collection and Methods

3.1 Sampling Sites and Land Cover Data

Polygons for the sampling sites were obtained from the GlenelgHopkins Catchment Management Authority and representsalinity management units used within the region and are basedon existing sub-catchments within the region [1]. Polygons thatwere smaller than 2.5 km2 were removed from the dataset asthey were determined to be artefacts of the digitisation processand were not included in the analyses. Removal of thesefragments resulted in 149 sub-catchments being used in thestudy. Sub-catchment size ranged from 2.5 to 716 km2.

Land cover data for the region were obtained fromIerodiaconou et al. [24]. The data were classified fromLandsat TM and Landsat ETM+ sensors and have a spatialresolution of 30 m. The accuracy of the 2002 dataset is 91%(KHAT=0.895) and was obtained using a supervisedclassification method employing the enhanced maximumlikelihood classifier. Unsupervised classification methodswere employed for the 1980 and 1995 datasets as noground truth data were available, and hence, accuracyassessment for these datasets was limited. Comparisonswith Australian Bureau of Statistics data indicated resultingland cover data were of a similar order of magnitude [24].Land cover data were aggregated from 11 level 1 classes for1980 and 1995 and 12 level 1 classes for 2002 to fourclasses for the analyses. For the analyses in this paper, theland cover data were aggregated to minimise issues ofcolinearity between land uses. The four classes were perennialwater, plantation forestry (pine+blue gum), agriculture (dry-land cropping, dryland pasture, irrigated agriculture, irrigatedpasture) and remnant native vegetation. Other classes thatwere excluded from the study included area subject toinundation (for issues of auto-correlation with area ofperennial water) and sand and urban areas (due to being avery small component of the catchment). The area of each ofthe land classes was calculated using the Tabulate Area tool

Fig. 2 Aggregated regional land cover in 2002 (Ierodiaconou et al. [24])

244 S. Brown et al.

from the Spatial Analyst extension for ArcGIS 9.3.1. Figure 3displays regional land cover within the salinity catchments ateach observation (1980, 1995 and 2002).

3.2 Climate Data

Monthly rainfall data with a 5-km resolution was obtainedfor Australia between 1979 and 2002 from the Bureau ofMeteorology (www.bom.gov.au). Long-term average annualrainfall data between 1961 and 1990 were also obtained.Temperature data were not used as temperatures across theregion display very little variation both temporally andspatially. All rainfall data were clipped to a minimum areabounding rectangle of the Glenelg Hopkins region, reprojectedto GDA Zone 54 and re-sampled to 30-m resolution using thenearest neighbour method to conserve pixel values. Therainfall data were re-sampled as some of the smaller fringingsub-catchments are less than 5 km2 and there were issues withthe calculation of average pixel values.

Total rainfall for the 12 months prior to each observationwas calculated by summing the monthly rainfall rasters forthe region. Average total annual rainfall for each polygonwas then calculated using the isectpolyrst command in theGeospatial Modelling Environment add-on for ArcGIS [5].The long-term average (1961–1990) annual rainfall for eachpolygon was calculated using the same command.

To identify patterns of spatial variation in precipitation, arainfall residual was calculated. This was done by subtractingthe average total annual rainfall from the long-term averageannual rainfall for each polygon. The rainfall residual for eachpolygon was then used in the analyses as the climatic variable.

3.3 Modelling Methods

The dependent variable (area of perennial water) wasassessed for normality using histograms and calculatingskewness and kurtosis coefficients. The raw data for allyears displayed a distinct positive skew and was log(x+1)transformed before the analyses. The independent variables

were not transformed. The GWR analyses were performedusing GWR 3.0 software with outputs then imported toArcGIS for further analyses. OLS analyses were performedwithin ArcGIS 9.3 using the ordinary least squares tool. Sixdifferent models were run for each observation (i.e. 1980,1995 and 2002), using both OLS and GWR for a total of 36models. Log(x+1) area of perennial water was used in allmodels as the dependent variable. The models used wererainfall, where rainfall residual was used as the independentvariable; mixed land cover, where areas of the threedifferent aggregated land covers were used as the indepen-dent variables; TotalAg, RemnVeg and plantation, where thearea of each respective land cover class was used as theindependent variable; the three land cover classes were runseparately in order to avoid issues of multicollinearityamong land cover variables. This is a similar approach tothat presented by Tu and Xia [46]. Finally, an all-variablesmodel was also run, which was a combination of therainfall and mixed land cover models.

3.3.1 Modelling Background

Traditional regression modelling techniques such as OLSassume that patterns in the data are spatially constant, andtherefore, parameter estimates are the same for the entire studyarea. The parameter estimates of an OLS model can thereforebe considered global statistics and can hide importantvariations in the spatial distribution and relationship betweenthe independent and dependent variables. OLS is thereforeconsidered a ‘global’modelling approach. An OLSmodel canbe expressed as:

y ¼ b0 þXpi¼1

biþ #iþ ( j

where y is the dependent variable, β0 is the intercept, βi is theglobal parameter estimate (coefficient) for the independentvariable xi, p is the number of independent variables and ε isthe error term.

Fig. 3 Regional land use at each observation (Ierodiaconou et al. [24]). From left to right, 1980, 1995, 2002

Assessment of Spatiotemporal Varying Relationships 245

GWR is an extension to traditional OLS regressiontechniques that allows local rather than global statistics tobe estimated and explored. By calculating local statistics,spatial relationships between the variables in the model canbe easily examined and patterns identified [20]. As GWRestimates local statistics, it is considered to be a ‘local’model and is more appropriate to use when relationships arethought to or are known to vary spatially.

GWR is an improvement on OLS modelling and isexpressed as:

yj ¼ b0ðuj; vjÞ þXpi¼1

biðuj; vjÞxij þ ( j

where y is the dependent variable uj and vj are thecoordinates for the observation j, β0(uj, vj) is the interceptfor location j, βi(uj, vj) is the local parameter estimate forthe independent variable xi at location j and ε is the errorterm [46].

GWR employs a weighted distance decay function formodel calibration. This assumes that observations closertogether will have more impact on each other than onobservations further apart. The weighting function forincluding related samples can be calculated using theexponential distance decay function:

wij ¼ exp�d2ijb2

!

where wij is the weight of observation j for observation i, dijis the distance between observation i and j and b is thekernel bandwidth. When the distance between observationsis greater than the kernel bandwidth, the weight rapidlyapproaches zero [20]. With the GWR software, both fixedand adaptive bandwidths can be chosen. Fixed bandwidthkernel calculates a bandwidth that is held constant overspace, whereas the adaptive bandwidth kernel can adaptbandwidth distance in relation to variable density; band-widths are smaller where data are dense and larger whendata are sparse [20, 46].

In this study, all GWR models used the adaptive kernelbandwidth as sample densities varied spatially. The optimalbandwidth distance was determined automatically in GWR3.0 using the corrected Akaike information criterion (AICC).

3.3.2 Model Comparisons

A number of tests were conducted to compare the perfor-mance of GWR and OLS models. The comparison wasperformed by comparing R2 and AICC values betweenmodels. In addition to using AICC to calculate an optimalbandwidth distance, the GWR 3.0 software calculatesanother AICC value which is used for comparisons between

different models. Higher R2 values indicate the model’sability to explain more variance in the dependent variable asa function of the independent variables. The AICC was usedin this instance as a test between models, with smaller valuesindicating better, more parsimonious results. The AICC is anindicator of model accuracy and complexity where decreasesin the AICC value indicate a closer approximation of themodel to reality [43, 46]. Statistically significant modelimprovements between GWR and OLS models wereidentified using an approximate likelihood ratio (ALR) testwhich is based on the F test (see [20], p. 94). If the results ofthe ALR test are significant, then the GWR model isconsidered a statistically significant improvement over theOLS model.

3.3.3 Residual Analysis and Tests for SpatialAutocorrelation and Variance

The standardised residuals of the GWR and OLS modelswere checked for normality through visual histograminterpretation. Standardised residuals of the OLS andGWR models were also analysed for spatial autocorrelationusing global Moran’s I and local indicators of spatialassociation (LISA) analysis. Global Moran’s I values canrange from −1 to 1. A value of 1 indicates perfect spatialautocorrelation where high values, or low values, clustertogether. A value of −1 indicates perfect negative spatialautocorrelation with values representing a checkerboard[46]. A value of 0 indicates perfect random spatialvariability. LISA measures the degree of local spatialautocorrelation at each sampling point by using a localisedMoran’s I. Global Moran’s I and LISA were calculatedusing GeoDa 0.9.5-i (Beta) analysis software [2].

Results of the Monte Carlo significance test wereincluded in the GWR output to identify statisticallysignificant spatial variation in the model variables. Thiswas used in conjunction with the results of the ALR test asan indicator of the applicability of GWR to improveparameter estimates over OLS. As one of the assumptionsof OLS is that parameters are constant over space, adeviation from this condition would suggest that OLS willnot be a good predictor under these circumstances.

4 Results

4.1 Comparisons Between OLS and GWR ModellingApproaches

Improvements in both R2 and AICC were observed forGWR models over OLS counterparts for all models used inthe study (Table 1). All OLS models displayed non-normalresiduals, while six of 18 GWRmodels displayed non-normal

246 S. Brown et al.

residuals. All GWR models displayed higher R2 values thanthe analogous OLS models. Additionally, all GWR models,with the exception of the 1980 rainfall model, had smallerAICC values by at least 3. All of the OLS models displayedsignificant (p≤0.05) global spatial autocorrelation, whileonly five of 18 GWR models displayed significant globalspatial autocorrelation (Table 1). Coefficients betweenmodels and model types displayed substantial variation(Table 2). In some cases, an order of magnitude differencewas found between the OLS model coefficients and themedian GWR coefficients for the same model. This was alsoobserved for model R2 values (Table 2). Mixes of negativeand positive coefficients were also seen across models, modeltypes and years. The results of the Monte Carlo significancetest showed that for the 1980 models, all independentvariables with the exception of area of plantation in the

plantation, mixed and all-variables models displayed non-significant spatial variability. The results for the 1995 modelsshowed that all variables in the mixed and all-variablesmodels, area of plantation in the plantation model and rainfallresidual in the rainfall model all displayed significant (p≤0.05)spatial variation. The results of the 2002 models showed thatarea of remnant native vegetation in the RemnVeg, mixed andall-variables models, area of plantation in the plantation,mixed and all-variables models and the area of agriculture inthe all-variables model all displayed significant (p≤0.05)spatial variation. Statistically significant improvements ofparameter estimates by GWR modelling were supported bythe results of the ALR test which demonstrated that all GWRmodels, with the exception of the 1980 rainfall model, werestatistically significant (p≤0.05) improvements over compar-ative OLS models (Table 1).

Model Year Type AICC Adj R2a Moran’s I ALR test

Total agriculture 1980 OLS 621.43 0.15 0.23 3.82GWR 599.37 0.43 −0.01

1995 OLS 638.83 0.13 0.24 3.85GWR 616.21 0.41 −0.01

2002 OLS 566.55 0.27 0.15 3.34GWR 552.06 0.49 −0.06

Remnant native vegetation 1980 OLS 636.27 0.05 0.24 6.04GWR 615.30 0.22 0.09

1995 OLS 650.74 0.05 0.24 7.38GWR 523.75 0.25 0.05

2002 OLS 610.63 0.02 0.24 4.89GWR 588.24 0.22 0.08

Plantation 1980 OLS 646.58 −0.01 0.20 6.57GWR 628.53 0.14 0.11

1995 OLS 661.07 −0.01 0.19 5.91GWR 640.77 0.15 0.04

2002 OLS 614.80 0.00 0.19 4.16GWR 591.26 0.30 −0.03

Mixed land cover 1980 OLS 614.64 0.20 0.21 5.72GWR 594.37 0.34 0.11

1995 OLS 631.47 0.18 0.23 3.46GWR 618.18 0.56 −0.04

2002 OLS 561.25 0.31 0.16 3.43GWR 546.06 0.54 0.00

Rainfall 1980 OLS 638.92 0.04 0.13 2.43*GWR 637.83 0.26 0.03

1995 OLS 660.96 −0.01 0.19 3.21GWR 649.77 0.40 −0.08

2002 OLS 615.62 −0.01 0.17 4.77GWR 599.09 0.15 0.02

All variables 1980 OLS 607.90 0.24 0.15 3.47GWR 600.37 0.31 0.12

1995 OLS 633.59 0.18 0.23 3.41GWR 621.39 0.55 −0.01

2002 OLS 562.37 0.31 0.17 3.45GWR 555.86 0.65 −0.02

Table 1 Results of OLS andGWR analysis

Italics indicates statisticallysignificant (p≤0.05) residualglobal spatial autocorrelation

*p>0.05 (non-significant modelimprovement over OLS)a Adjusted R2 values for GWRmodels are mean values

Assessment of Spatiotemporal Varying Relationships 247

4.2 Results of GWR Modelling

The single land cover models (TotalAg, RemnVeg andplantation) all appear to effectively explain spatial differencesin the relationships between the dependent and independentvariables with higher R2 values observed where eachindependent land use dominates the landscape (Fig. 4). Theability of the respective land cover models to explain therelationship drops off in areas dominated by other land uses(Fig. 4). Rainfall residual was not as effective at explainingthe spatial variation in surface water area, with relativelypoor R2 values when compared to the other models (Table 1;Fig. 4). The results of the mixed and all-variables models are

very similar in regards to the strength of the relationship andthe spatial distribution of the R2 values (Table 1; Fig. 4).

Area of total agriculture displayed a mix of both negativeand positive parameter coefficients with negative coefficientsbeing observed in five of the nine models in which it was avariable. Remnant native vegetation displayed positivecoefficients for all 3 years of the RemnVeg model butdisplayed negative coefficients in the 1995 and 2002 mixedland cover and all-variables models. Area of plantation wasshown to exhibit negative coefficients across all years of allmodels, with the single exception of the 2002 plantationmodel, while rainfall residual displayed negative coefficientsacross all models and all years (Table 2).

Table 2 Three number parameter summaries for the independent variables in each of the models

Model Year Variable OLS Min Med Max

Total agriculture 1980 AreaTotAg 0.000076 −0.000019 0.000072 0.000192

1995 AreaTotAg 0.000074 −0.000044 0.000063 0.000191

2002 AreaTotAg 0.000094 0.000017 0.000095 0.000225

Remnant native vegetation 1980 AreaRemnVeg 0.000094 0.000049 0.000116 0.000206

1995 AreaRemnVeg 0.000103 0.000055 0.000133 0.000218

2002 AreaRemnVeg 0.000065 0.000037 0.000109 0.001327

Plantation 1980 AreaPlantation 0.000088 −0.004437 0.000571 0.014575

1995 AreaPlantation 0.000068 −0.003393 0.000396 0.047937

2002 AreaPlantation 0.000076 0.000109 0.000362 0.005562

Mixed land cover 1980 AreaTotAg 0.000073 0.000040 0.000127 0.000189

AreaRemnVeg 0.000095 0.000020 0.000057 0.000102

AreaPlantation −0.000227 −0.003216 −0.000097 0.005110

1995 AreaTotAg 0.000071 −0.000052 0.000069 0.000213

AreaRemnVeg 0.000109 −0.008884 0.000058 0.000844

AreaPlantation −0.000206 −2.425454 −0.000919 0.171425

2002 AreaTotAg 0.000097 0.000018 0.000091 0.000172

AreaRemnVeg 0.000082 −0.002094 0.000035 0.000207

AreaPlantation −0.000084 −0.000608 0.000140 0.002078

Rainfall 1980 RainfallResidual −0.011264 −0.043310 0.003815 0.032137

1995 RainfallResidual −0.001741 −0.233331 0.004776 0.142154

2002 RainfallResidual 0.002483 −0.008178 0.008076 0.019550

All variables 1980 AreaTotAg 0.000065 0.000038 0.000059 0.000098

AreaRemnVeg 0.000108 0.000031 0.000128 0.000181

AreaPlantation −0.000052 −0.002663 −0.000067 0.005309

RainfallResidual −0.011385 −0.011895 −0.006856 0.003595

1995 AreaTotAg 0.000070 −0.000058 0.000069 0.000199

AreaRemnVeg 0.000113 −0.003077 0.000083 0.000453

AreaPlantation −0.000225 −1.683904 −0.001422 0.068710

RainfallResidual 0.000864 −0.077771 0.007208 0.035508

2002 AreaTotAg 0.000096 −0.000012 0.000086 0.000197

AreaRemnVeg 0.000091 −0.003060 0.000057 0.000578

AreaPlantation −0.000099 −0.001428 0.000187 0.003697

RainfallResidual 0.003306 −0.027894 0.007957 0.043652

The min, median and max coefficients are for the GWR models

248 S. Brown et al.

Results of LISA analysis of the residuals for the GWRmodels demonstrate very little local spatial autocorrelation(Fig. 5). Temporally and spatially, the results for all modelsshow that GWR is much better at accounting for spatial non-stationarity of variables than OLS. This is displayed throughvery minimal statistically significant clustering (i.e. residualsare not clustered with other comparative residuals).

5 Discussion

5.1 Model Performance and Interpretation

The higher R2 and lower AICC values associated with theGWR models support previous research suggesting thatGWR is better at explaining spatially varying relationships

than OLS [20, 46, 59]. The distribution of the R2 values(Fig. 4) confirms our assertion that there is a spatially varyingrelationship between land cover and the area of surface waterwithin the region. The increased explanatory power of GWRwas confirmed by the results of the ALR test, which showedstatistically significant improvements over analogous OLSmodels. Interpretation of residual histograms also supportedthe ability of GWR to better model spatially varying datawith six of 18 models displaying non-normal residualscompared to all OLSmodels displaying non-normal residuals.Global and local residual analysis also confirmed that GWR isa better predictor of spatially varying relationships with five of18 GWR models displaying significant global spatial auto-correlation compared to 17 of the 18 OLS models (Table 1).The results of the LISA analysis demonstrate the ability ofGWR to better model spatially varying data with very

Fig. 4 Results of the GWR models showing local R2 values for each of the models. Top to bottom, 1980, 1995, 2002. Left to right, area ofagriculture, area of remnant native vegetation, area of plantation, mixed land cover, rainfall residual, all variables

Fig. 5 Results of the LISA analysis showing localised spatial autocorrelation of GWR model residuals. Top to bottom, 1980, 1995, 2002. Left toright, area of agriculture, area of remnant native vegetation, area of plantation, mixed land cover, rainfall residual, all variables

Assessment of Spatiotemporal Varying Relationships 249

minimal clustering of residuals (Fig. 5) indicating that theGWR models are not over or underestimating the magnitudeof the dependent variable in a spatially correlated fashion [59].Furthermore, the assumptions of OLS regression have notbeen met, and therefore, the validity of the models isquestionable. When OLS assumptions are violated, regressionefficiency is reduced and model results can be misinterpreted[43]. In particular, the spatial autocorrelation issues of theOLS analyses (Table 1) severely limit the inferences that canbe drawn from the analyses. As OLS has assumed therelationship to be stationary but has presented spatiallycorrelated residuals, the relationship is therefore not stationary.In contrast, the application of GWR reduced global spatialautocorrelation of residuals and displayed minimal localspatial autocorrelation and therefore presents a statisticallymore reliable model. The comparatively poor performance ofthe OLS models (non-normal residuals, relatively low R2,spatial autocorrelation of residuals) compared to the GWRresults further reinforce the utilisation of new regressiontechniques such as GWR when investigating relationships thatare believed or known to vary spatially.

The processes affecting the distribution of surface waterwithin a landscape are a combination of soil/water interactions[45], vegetation [9, 31, 41] and topography [15]. Within ourstudy area, we found that there is a spatially and temporallyvarying relationship between land cover and the distributionof surface water within the region. The performance of themixed land cover model and the all-variables model werevery similar in terms of the spatial and temporal distributionof R2 values (Fig. 4). This suggests that in this instance landcover is capable of explaining the relationship between areaof surface water and land cover type, independent of rainfall.While this seems counterintuitive as rainfall is the primarydriver of the hydrological cycle, the history of agriculturaldevelopment in the study area can offer an explanation of thisresult. Specifically, the results of the mixed land cover modelssuggest that the surface area of water in the landscape islikely related to anthropogenic drainage practices whichenhance runoff to facilitate intensive agriculture and thedecreased runoff associated with increased plantation forestry[9, 41, 47, 48]. These factors (land cover changes andassociated changes in drainage and run off) have possiblycontributed to the available rainfall being less likely to be ableto maintain existing surface water habitat. Furthermore, themodel also suggests that rainfall variability has therefore hadless influence in the reduction of the area surface water withinthe region than anthropogenic drainage has impacted theseareas. However, as rainfall is an essential part of thehydrological cycle, the results of the all-variables modelshould not be ignored. The coefficients for the 2002 all-variables model are presented below (Fig. 6). The all-variables model coefficients display similar distributions tothe individual land cover (TotalAl, RemnVeg and plantation)

models R2 with higher coefficients observed where aparticular land use dominates (Fig. 6).

Agricultural land uses dominate throughout the Hopkinsbasin, and therefore, the highest coefficients are observedthroughout that basin for area of total agriculture. Similarly, asremnant native vegetation dominates the Grampians NationalPark in the north-central area of the region, the highestcoefficients are seen in this area for area of remnant vegetation.It is noteworthy that high coefficients are generated in theHopkins basin for area of plantation. This is interestingbecause, while blue gum forestry expansion was a region wideland use change [24], the ability of area of plantation toexplain surface water conditions is greatest in the Hopkinsbasin where the introduction of blue gum plantations was at asmaller scale than that observed in the other regional basins[24] and particularly interesting as the area of pine plantationswithin the area of the high coefficients is limited. However,the size of the coefficients output by the analyses (Table 2;Fig. 6) suggests that there are other factors controlling thedistribution and area of surface water within the region. Theseare likely soil type/infiltration capacity and topographicalvariables such as slope.

The presence of negative coefficients within the all-variables model for both area of remnant native vegetationand area of plantation is expected as previous research hasshown that both of these land cover types reduce runoffcompared to agricultural land [9, 41, 48, 58] and hencenegatively affect surface water accumulation. What was notexpected, however, was the presence of negative coefficientsfor rainfall. Rainfall was shown to have a number of negativecoefficients across models, years and model types (Table 2;Fig. 6). This is counterintuitive as it suggests that in areaswhere there is less rainfall, there will be more surface waterarea. We suspect that this may be a result of using eitherrainfall residual as the rainfall variable or timing of theLandsat image capture. The use of total annual rainfall, asopposed to rainfall residual, will need to be investigated infuture research. The timing of the Landsat image capturecould have also affected model results with the use of arainfall residual. If there had been a year of below averageannual rainfall but the months leading up to the imagecapture were relatively wet, there would be a lot of surfacewater across the catchment. Instances like this would limitthe ability of a rainfall residual to accurately explain surfacewater differences between catchments.

5.2 Changes in Land Cover and Drainage

Since European settlement, large-scale changes in the land-scape have occurred within the region [24] and it is estimatedthat 75% of the region’s wetlands have been severelymodified by agricultural drainage [12]. Contemporary changes(1995–2002) in land cover have largely been associated with

250 S. Brown et al.

the widespread adoption of dryland cropping (∼6.5%increase) and the development of blue gum plantation forestry(E. globulus) (∼5% increase) [24]. Detailed transition analysisby Versace et al. [50] reported that expansions in cropping andforestry land uses did not affect the distribution or percentagecover of remnant native vegetation within the region and thatsystematic gains in dryland cropping and blue gum forestryoccurred at the expense of dryland pasture.

A partial explanation of the expansion of dryland crops inthe region was the decline in profitability of traditionaldryland pastures and sheep grazing and the development ofraised-bed cropping technologies which allowed land ownersto crop in previously waterlogged soils [50]. Consequently,the expansion of dryland cropping within the region mayhave contributed to altering the hydrological dynamics of theregion by affecting runoff and decreasing the amount ofwaterlogged soils. The pastures that dryland cropping hasreplaced were largely poorly drained and during times ofhigh rainfall existed on waterlogged soils. As a result, therewas likely more surface water habitat, albeit ephemeral,

found before the widespread introduction of raised-bedcrops. The introduction of blue gum plantation forestry inthe region between 1995 and 2002, at the expense of drylandpasture, was a response to economic and environmentalconditions by both farmers and timber companies [24, 50].Runoff across the region has decreased and may be partiallyattributed to increased water consumption by deep-rootedwoody vegetation as a result of greater rain interception anddeeper root systems than perennial pastures and non-irrigatedagricultural crops [4, 53]. Turner et al. [47] compared meanannual runoff between grassland and native Eucalyptusforests from two rainfall zones of 800 and 1,200 mm. Thecomparisons showed that grassland had a mean annualrunoff of 210 and 493 mm, while the Eucalyptus forests hadmean annual runoff of 45 and 228 mm from the respectiverainfall zones. As much of the study region has annualrainfall below 800 mm, it is not inconceivable that theexpansion of blue gum forestry within the region hasaffected runoff. Afforestation has also been shown to exhibitsometimes severe impacts on water resources [48, 58]. Van

Fig. 6 Spatial distribution ofvariable coefficients for the2002 all-variables mode.Clockwise from top left, areaof agriculture, area of remnantvegetation, rainfall residual,area of plantation

Assessment of Spatiotemporal Varying Relationships 251

Dijk et al. [48] reported that for an 800-mm rainfall zone, landcover transition from perennial pastures to forestry (eitherplantation or revegetation) resulted in an average water yieldreduction of about 1.5 ML for each hectare planted. Manylong-term land use management decisions can be verysensitive to changes in physical climate conditions, and thereis an awareness that many decisions already occurring need totake long-term climate change into account [23]. From anintegrated water resources management perspective, those incharge of maintaining resources need to take into account theeffects of land cover changes that can drastically altercatchment hydrology and prepare for consequences thatmay not be observed for some time. However, the influenceof rainfall and temperature variability should be assessedindependently when quantifying the hydrological effect ofland cover changes [31]. Meinke and Stone [35] propose thatchanges in agricultural industries (whether crops or pastures)occur on inter-decadal scales (10–20 years) with broaderland use changes (e.g. agricultural or natural systems)occurring on multi-decadal scales (>20 years). Thesedecisions, particularly those related to water infrastructureand land use planning, have consequences over 50–200 years[23]. Whilst blue gum forestry is not likely to expand in thefuture due to prevailing economic factors, quantifying theirexpansion from their 2002 extent could provide furtherevidence of increased plantation forestry severely impactingregional hydrological dynamics and further limiting theability of rainfall to maintain the ever decreasing surfacewater habitat within the region. There is anecdotal evidencethat land cover changes in the region post 2002 have seen thefurther southward expansion of dryland cropping as a resultof observed and expected rainfall changes within the region,coupled with economic drivers beyond the region. Withwetland systems continuing to recede and with smallchanges in climate expected within the region [17], empiricalevidence gained from this study suggests that the decliningstate of regional wetlands is linked to the dynamic nature ofregional land cover and the associated hydrological changes.

6 Conclusions

Over the next 50 years, the climate of the world is expected tochange quite drastically as a whole. In some regions, however,climate changes are not expected to be as severe, and otherfactors may pose a more immediate, but arguably manageable,threat to aquatic ecosystems. This study has demonstrated thesuperior ability of GWR to model spatially varying relation-ships over OLS regression. Studies concerned with any formof spatial analyses need to take the limitations of OLS andother, similar linear regression methods into consideration andinvestigate newer, more suitable methods when attempting toexplain spatial relationships. It also demonstrated through the

application of GWR to historical land cover and rainfall datathat land use change can influence surface water area within acatchment; however, the effects of land cover changes couldnot be quantified as some key variables on soil type/infiltrationcapacity and topographical variables such as slope were absentfrom our analyses. Future work will include these variables asthey becomemore readily available and accurate.Managementagencies have a responsibility to ensure that they are aware ofthe impacts of these changes on the resources they areresponsible for and methods like those presented here maydo a great deal in increasing that understanding. Whileplanning for the future should no doubt include the possibilitiesof a changing climate seriously affecting water resources,changes in land cover cannot be underestimated in their abilityto alter topography, runoff and drainage at catchment scales.

Acknowledgements The authors wish to express thanks to the GlenelgHopkins CMA for providing funding in support of this project.

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