The impact of interpolated daily temperature data on landscape-wide predictions of invertebrate pest phenology

Agriculture, Ecosystems and Environment 94 (2003) 169–181

The impact of interpolated daily temperature data onlandscape-wide predictions of invertebrate pest phenology

Claire H. Jarvisa,∗, Richard H.A. Bakerb, Derek Morganba Department of Geography, University of Edinburgh, Drummond Street, Edinburgh EH8 9XP, UK

b Central Science Laboratory, Sand Hutton, York Y041 1LZ, UK

Received 10 September 2001; received in revised form 18 February 2002; accepted 4 March 2002

Abstract

Insect phenology depends upon temperature, and data from scattered synoptic weather stations are the principle inputs forphenology models used in decision support systems. The paper assesses the spatial dynamics of the penalty, as measuredthrough errors in the timing of predicted insect development stages, that results when entomologists use daily maximum andminimum temperature data from the nearest station to a location, in comparison with an interpolated temperature equivalent,to drive their models. Jack-knife cross-validated estimates of temperature were propagated through an example phenologymodel, in this case for codling moth (Cydia pomonella). The intention was to contrast the effect of two interpolation methodson phenological results through time at different geographical locations.

Use of weather data from the nearest UK meteorological data station (174 points) for phenological modellingdoubledthe error in predicted development dates for first generation development when compared with the use of landscape-wideinterpolated daily temperature data. The results are based on a partial thin plate spline interpolation methodology: the figuresare spatial and temporal averages for mainland England and Wales. Overall, spline interpolations provide phenology resultsthat either exceed or are as good as nearest neighbour techniques for 75% of locations over England and Wales, taking firstand second generation developmental stages into account. In a minority (21%) of cases nearest neighbour strategies (Voronoimethods) performed better, with an average 18-day improvement in the predictions of development date over the spline methodon those occasions. Where splines performed best, their performance exceeded that of the Voronoi method by an averageof 25 days. Nearest neighbour techniques did not necessarily perform well in lowland areas, indicating findings of potentialsignificance to those considering input data requirements when modelling insect ecology.© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Insect pest; Phenology; Interpolation; GIS

1. Introduction

A number of climate-dependent agricultural pestphenology and population models are being developedto improve the targeting of control measures for insect

∗ Corresponding author.Tel.: +44-131-650-2662; fax:+44-131-650-2524.E-mail address: [email protected] (C.H. Jarvis).

pests, a trend which is likely to continue (Way and VanEmden, 2000). Most commonly these models are usedin conjunction with synoptic meteorological data or aweather generator from the nearest recording station(e.g.Finch et al., 1996; Morgan, 2000; Shirley et al.,1999). Only rarely are geographically distributeddaily temperature data used to drive models in insectecology with the aim of providing more locally rel-evant information (e.g.Russo et al., 1993). Although

0167-8809/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0167-8809(02)00030-0

170 C.H. Jarvis et al. / Agriculture, Ecosystems and Environment 94 (2003) 169–181

‘solutions to pest problems must be location, cropand pest specific’ (Strand, 2000), the exploitation ofgeographical information science (GIS) methods haslargely been limited to the display of risk computedby entomological process models at discrete locationswhere meteorological readings have been made (e.g.Parker and Turner, 1996).

Initial investigations highlighted the potential ben-efits of linking spatially referenced temperature datawith applied pest phenology models in order toimprove the timing of control actions at locationswhere temperature records are unavailable (Jarviset al., 1999). These results were, however, aggregatedsummaries for England and Wales. Key questionsremaining when considering the value of the data foragricultural purposes relate to the spatial and tempo-ral variation in performance of the interpolated data,assessed in phenological terms, in comparison withnearest neighbour approaches.

Focusing particularly on location, this paper ex-plores the potential of integrating continuous spatiallyreferenced daily maximum and minimum temperaturesurfaces (Jarvis and Stuart, 2001a,b) with a phenologymodel for an insect to improve the local relevancyof pest predictions. Drawing upon cross-validationmethods commonly used in the ecological and sta-tistical literature (e.g.Cressie, 1991; Vanclay andSkovsgaard, 1997), a number of error metrics weredeveloped that, in contrast to other recently reportedwork (e.g.Crosetto et al., 2000), allowed the explo-ration of the variation in phenological error at differ-ent locations across the landscape. Also explored arethe correctness and reliability of the simulated resultsfrom a theoretical perspective, in the manner of aquality assessment (e.g.Scholten and Udink ten Cate,1999), for later field validation. Issues relating to theprovision of input data are important since the choiceof appropriate meteorological input data is one of theconsiderable interests for developers of agriculturaldecision support systems.

2. Methodology

2.1. Modelling framework

Codling moth (Cydia pomonella, Lepidoptera: Tor-tricidae) is a major pest of apple and pear production

world wide, and the accurate timing of biological orchemical controls at the susceptible larval stage is crit-ical to successful management. A computer model forcodling moth development has been developed whichpredicts the emergence of each life-stage of the pest(Morgan, 1992), and has been validated for the UK(Morgan and Solomon, 1993). The model requiresdaily maximum and minimum temperature inputs topredict the timing of pest activity, expressed as thedates on which critical phases of the life-cycle (stageand per cent emergence) occur. This provides an indi-cation of the windows in which effective managementcampaigns are feasible. Temperature-based non-linearlogistic functions are used to estimate individual de-velopmental rates for each stage of development. Inorder to incorporate the photoperiod, day length iscomputed on the basis of latitude. The model assumesthat a nominal number of pests overwinter as pupae,and that diapause is broken as a result of increasingday length and temperatures.

Surfaces of daily maximum and minimum tem-peratures over England and Wales were producedusing two different interpolation approaches, andthe resultant predictions were compared. The useof temperature data from ‘nearest neighbour’ me-teorological stations is currently implicit within thepractical application of insect phenology models.This practice is known as the Voronoi method, whichattributes the value at any point across the landscapeto be that of the nearest data point, creating a tes-sellated output surface (Fig. 1a). Firstly therefore,landscape-wide phenologies were computed using

Fig. 1. (a) Voronoi polygon and (b) continuous grid interpolation.

C.H. Jarvis et al. / Agriculture, Ecosystems and Environment 94 (2003) 169–181 171

this simple technique. Secondly, the partial thin platespline method of interpolation (Hutchinson, 1991)was used as a more sophisticated means to computegridded daily maximum and minimum temperatures(Fig. 1b). The spline software uses automatic gener-alised cross-validation to optimise a smoothing func-tion, with the aim of minimising significant departuresbetween predicted and actual values of temperatureat the data points. In this case, the partial spline isestimated fromn temperature valueszi measured attwo- or three-dimensional position coordinatesxi andp covariate valuesψij at each data point. The partialspline is then determined by the (suitably smooth)function f and thep coefficientsβj that minimise

n∑j=1

[zj − f (xi)−

p∑k=1

βjkψjk

]2

+ λIm(f ) (1)

whereλ is the smoothing parameter,Im(f) the ‘smooth-ness seminorm’ defined in terms ofmth order partial

Fig. 2. Location of meteorological stations in relation to the terrain of England and Wales.

derivatives of the functionf, ψ the Euclidean distancescaling function with coefficientsβ, andp the numberof partial linear covariates.

This process was guided by environmental covari-ates such as the elevation, height above the localvalley floor, distance from the sea and degree of ur-banisation (Jarvis and Stuart, 2001a). The selection ofthe partial thin plate spline method followed an earliercomparison between interpolators (Jarvis and Stuart,2001b), which achieved average root mean square(r.m.s.) errors of 0.8 and 1.14◦C for daily maximumand minimum temperatures, respectively. Data from174 meteorological sites were used to determine thesurfaces (Fig. 2).

The interpolated temperature surfaces and thebiological model were integrated using GIS prin-ciples by custom-built FORTRAN code, looselycoupled with a proprietary GIS (Jarvis, 2001). Theresulting system, named ‘GEOBUG’ (Fig. 3), pro-duced temporally and spatially explicit predictions of


Fig. 3. GEOBUG, an interpolation engine to link point temperature data with temperature dependent biological models.

pest events throughout England and Wales, termedlandscape-wide phenologies, distinct from those com-puted solely at the location of meteorological stations.A time-series of interpolated temperature data wasconstructed for each 1 km grid square over Englandand Wales and predictions of the phenology of spe-cific events in the pest life-cycle were made at eachgrid location. The benefits of using these surfaces asinput to the model at each grid square rather thaninterpolating the model results (e.g.Régnière, 1996;Schaub et al., 1995; Tiilikkala and Ojanen, 1999) havebeen shown earlier (Jarvis et al., 1999). These includehigher modelling accuracies and a guaranteed logicalprogression between pest development stages overtime.

Errors attributed to the geographical modellingwere measured using jack-knife cross-validation(Efron and Gong, 1983). For each initial pointsource of temperatures in turn, the data for that lo-cation were omitted from analysis for a completemulti-temporal run of interpolations to produce an in-dependent estimate of phenology for that site. Theseestimates were subsequently collated to produce anapproximation of the ‘actual’ error distribution. Inthis manner input temperature data were subjectedto geographical uncertainties, but the phenologymodel used was regarded for the purpose of this ex-ercise as without error: variations reported in this

paper should be attributed to input data methodologyalone.

2.2. Investigations using GEO BUG

GEO BUG was used to estimate the dates at whichkey life-stage events of the pest were likely to occurin 1 km grid cells across England and Wales. Tem-perature data recorded in 1976 were used as this wasa particularly warm year and favourable to outbreaksof codling moth populations. Results were computedusing both partial thin plate spline and Voronoi inter-polation techniques, and comparisons between meth-ods were made for each stage in the development ofthe codling moth. These were imported into a propri-etary GIS for visualisation and analyses in order toinvestigate three questions:

• Are interpolated temperature inputs an improve-ment over ‘nearest neighbour’ temperatures?

• If so, is the improvement consistent between stagesof development and regions?

• How do the two methods of interpolation compareat similar locations?

Jack-knifed residual errors in predicted dates for50% emergence of each major stage of developmentof the codling moth (adult, egg, larva, pupa) were cal-culated. These error results were summarised using


Fig. 4. Emergence dates for ‘fully spatial’ codling moth phenologies computed using temperatures constructed using partial thin platesplines (left) and Voronoi polygons (right) for (a, b) initial emergent adults, (c, d) first generation eggs and (e, f) first generation larvae(50% development), 1976.


Fig. 5. Emergence dates for ‘fully spatial’ codling moth phenologies computed using temperatures constructed using partial thin platesplines (left) and Voronoi polygons (right) for (a, b) first generation pupae, (c, d) first generation adults and (e, f) second generation larvae(50% development), 1976.


Fig. 6. Cross-validation error (days) in date at which 50% emergence is reached in England and Wales for major developmental stages.

the r.m.s. statistics to provide an aggregated indicationof interpolator performance over the country. The sizeof absolute residual error (measured in days) achievedat the same point locations over England and Walesusing Voronoi and spline techniques was compared.Differences in errors when using the two interpolationmethods were computed at individual point locations,averaged and mapped.

Fig. 7. Proportion of cases where errors using Voronoi polygons (v) are of greater magnitude than those computed using partial thin platesplines (s).

3. Results

Gridded results of the dates at which 50% emer-gence is expected for the initial emergent adults, firstgeneration eggs and larvae, and first generation pu-pae, adults and second generation larvae were plottedin Figs. 4 and 5, respectively. The results indicatethat the completion of a single generation within a


calendar year is unlikely in upland areas (Fig. 5a),and that a second generation of larvae would be con-fined within the southeast (Fig. 5e). Differences inthe date at which the earliest and latest emergenceof first generation pupae might be expected over thecountry reached up to 174 days, while a span of130 days across the landscape occurred among firstgeneration adults. This contrasts with a range of ap-proximately 50 days in the emergence dates for theinitial emergent adults and first generation eggs.

Although there was similarity between the spatialdistribution of predicted results produced using bothtechniques, differences in computed pest emergencedates occurred within upland areas containing littlemeteorological data, such as the Lake District andPennines, where the Voronoi estimates tended to over-estimate emergence dates relative to the spline-basedresults (Figs. 4 and 5). When synoptic meteorolog-ical stations were located in upland areas however,the reverse was observed. For Kent, a large regionindicates the unlikely scenario of zero developmentwhen using Voronoi, while for Gloucestershire thereverse situation was indicated when using nearestneighbour approaches. Additionally, emergence datesfor second generation larvae were on average 11 daysearlier than those computed by spline techniques. Thisgeneral tendency for Voronoi to suggest earlier emer-gence dates was illustrated over all developmentalstages.

Fig. 6 provides a comparison of the accuracy ofpartial thin plate spline interpolation compared tothe Voronoi polygon method. For both the initialadults and all stages of first generation codling moth,r.m.s. errors in estimated dates of emergence for1976 computed using nearest neighbour techniquesoutperformed the partial thin plate splines. On av-erage for the first generation, the errors computed

�

Fig. 8. Degree to which estimates of (a) initial adults and (b)first generation larvae computed using partial thin plate splinetemperature data outperformed those produced using Voronoi, forindividual station locations across England and Wales (Julian datedifference in residuals). Negative values are those where the accu-racy of spline results exceeds those of the Voronoi method. Positivevalues indicate where Voronoi perform better than splines. Sta-tions showing extreme differences in residual results are labelledindividually.


using Voronoi polygons were more than twice thoseof the interpolated method. While the overall pro-portion of occasions where spline errors are belowthose of Voronoi at any one site falls as the model runprogresses, even for second generation larvae the fullinterpolation approach is beneficial (Fig. 6).

While spatially averaged r.m.s. figures provide anoverall measure of the relative efficiency of each

Fig. 9. Locations where predicted pest emergence dates computed using Voronoi polygons outperformed estimates computed using partialthin plate splines for (a) initial adult, (b) first generation egg, (c) larval and (d) pupal 50% emergence (days difference).

method, investigating their underlying variability isalso important since errors may vary considerablyacross different components of the landscape. The pro-portion of locations in the landscape at which errorswere reduced through the use of the partial thin platespline method exceeded 65% for the first generation,and overall the splines conferred no disadvantage overVoronoi in over 75% of the cases (Fig. 7). Results


Fig. 10. Difference in average absolute error between Voronoi and partial thin plate spline results across 174 original data points overEngland and Wales.

relating to individual sites are shown for initial adultsand first generation larvae inFig. 8where the absolutevalue of the spline r.m.s. error minus the correspond-ing value computed using Voronoi polygons is plotted.Extremes follow a mixture of highest cross-validationerrors resulting from Voronoi and spline methods.The highest values, located in upland moorland ar-eas in both cases (North Hessary Tor, WiddybankFell, seeFig. 2 for locations), occur because of ex-treme over-predictions in emergence date when usingVoronoi polygons to represent sites at high elevationsin areas of sparse data. Extreme Voronoi errors alsooccur at a number of coastal sites (e.g. Shoeburyness,Boscombe Down, seeFig. 2 for locations), where theweather stations are particularly unrepresentative oftemperature conditions. The locations of these relativeabsolute errors are plotted inFig. 9, which providesa spatially referenced view ofFig. 8 for the initialadults and first generation eggs, larvae and pupae.

For much of East Anglia and Lincolnshire (areasof intense arable and horticultural farming) splinesoutperform Voronoi (Fig. 9). Looking at commercialapple growing centres of Kent and Gloucestershire,splines perform well across all stages including thecrucial larval stage (Fig. 9c). Overall, there was nostatistically significant relationship between elevationand accuracy for the partial thin plate spline results.

The average magnitude between errors usingVoronoi interpolation and those using splines was cal-culated, andFig. 10 illustrates the average differencein absolute residual values categorised according tothe method that showed best results. The penalties ofchoosing partial thin plate spline interpolation overVoronoi at the minority of locations where they proveto be less accurate are considerably smaller (18 days,on average) in comparison to the reverse situation(25 days, on average). In keeping with the previousfigures, these margins were smaller for the secondgeneration. Overall, this suggests that there is little tobe lost and much to be gained by adopting the partialthin plate spline interpolation approach for provid-ing locally relevant temperature input data for thisphenological model.

4. Discussion

The decrease in errors of predictions of all firstgeneration developmental stages when using tem-perature data obtained from partial thin plate splineinterpolations, in comparison to nearest neighbourtechniques (Fig. 6), suggests that the method out-lined could be beneficial for other insect models. Thepoor performance of the Voronoi method across Kent


and the Vale of Evesham, areas where top fruit hasbeen traditionally grown in the UK, is likely to haveimplications for pest control aimed at the emerginglarvae. While the results for the second generation areless convincing, this arises in part as a result of themarginal probability of the second generation codlingmoth developing across England and Wales. Rootmean square errors are exacerbated by high residualsat sites where the possibility of development or viceversa is inaccurately predicted. Including this sec-ond generation to provide overall error statistics alsoreduces the proportion of occasions where splinesproduce higher accuracies than Voronoi, since beyondthe regions where second generation development ispotentially feasible both methods concur.

Partial thin plate splines were not universally op-timal, but the penalty for this choice over the otherwas slim relative to the use of nearest neighbour tech-niques. It is the case however that where interpolatedtemperature estimates were poorest, nearest neigh-bour techniques sometimes produced lower errors.The spatial distribution of errors for the predictionof codling moth life-cycle illustrated in this paperdiffered from that for accumulated temperature com-puted using identical input data (Jarvis, 1999), andthe distribution of errors for accumulated tempera-ture results varied from year to year. These findingssuggest that errors probably occur because of the in-teraction between the non-linearity of the structure ofthe model and the underlying temperature predictions.

The use of multiple error metrics to evaluate theresults, rather than a simple bounding aggregate errorfor each model input or output (e.g.Crosetto et al.,2000), implements the suggestion that analyses of er-ror using single metrics are incomplete (e.g.Azouzi,1999; Guisan and Zimmermann, 2000). However,both absolute and relative errors can be used tocontribute to the assessment of whether a model issufficiently accurate to satisfy its objectives: errorsin model results may not necessarily lead to errors indecision making. The number of days within whichan estimate must be bounded will vary accordingto the efficacy of the control method used and theprevailing weather conditions in particular. Increasedaccuracies in phenological information could be ex-pected to be most important for the biological controlagents because of their relatively shorter persistenceand higher product price. Whether the improvements

of 2–3 days in predicted emergence dates achieved inthe majority of areas and for all developmental stagesusing the partial thin plate spline method is of prac-tical significance will however only be known on apest-by-pest basis through extensive field validations.

Computerised decision making tools which incor-porate models of insect phenology are becoming morecommon (e.g. DESSAC (Brooks, 1998), MORPH(Walton, 1998)). The models driving such systemscontinue to grow in sophistication and predictiveability and are moving towards improved integrationbetween individual components of the system. Thetransfer of applied biological models from researchlaboratory to general use by the agricultural com-munity has met with mixed success. The reasons forthis slow uptake range forms the complexity of theunderlying biology which makes accurate modelsdifficult to achieve to issues relating to the usabilityof the software packages themselves. The focus insuch recent projects has therefore been largely on im-proving skills in interface design and communication.Investigating further the need for locally relevant me-teorological input data to such systems may also beworthy of attention: further work validating mappedpredictions against field data will be important.

Previously, uncertainties both within individualsub-components of the phenological modelling systemand within the biological models have been assessedtogether using trap catch data (Régnière et al., 1995;Schaub et al., 1995). Trap catches provide a practicaltest of the usability of the modelled landscape-widephenologies but do not allow a partitioning betweenerrors that arises as a result of using remote input dataversus errors within the underlying biological model.The value of the jack-knife cross-validation approachis that it provides a means of separating between them(Fig. 11). Examining the biological modelling errortogether with input error to identify their relative con-tribution to overall uncertainty will be an importantnext step in the research process, requiring stochas-tic rather than deterministic phenology models (e.g.Finch et al., 1996) and multiple realisations of equallyprobable input temperature surfaces within a moreintensive computing environment (e.g.Mineter et al.,2000).

More general benefits of the geographical mod-elling approach were also identified. Firstly, produc-ing maps as outputs allowed more detailed analyses of


Fig. 11. Sources of error in estimated landscape-wide phenologies.

the results in comparison with the point-based advicetraditionally provided (e.g.Finch et al., 1996; Parkerand Turner, 1996). In comparison with studies inEurope, the 1 km resolution for predicting the phenol-ogy of key life-cycle events was more accurate thanregions or crude grids (e.g.Jensen et al., 1997). Whilegeographical phenologies of indigenous insect pestshave been demonstrated in other countries (Régnière,1996; Schaub et al., 1995), national coverage at thisresolution has been rare. National coverage of inter-polated input data offers the potential for equitableaccess to quality data for running models. Addition-ally, interpolation approaches could be more widelyapplied to support combined agronomic models wheredecisions are likely to be location dependent.

5. Conclusions

Errors in the estimates from temperature-driveninsect phenology models relating solely to the remoteand scattered nature of meteorological stations havenot previously been assessed. Applications of GISwithin insect ecology are more commonly associ-ated with empirical relationships between biologicalsamples and landscape characteristics. Importantly,the r.m.s. errors in the date estimates across firstgeneration developmental stages of the codling mothwere found to halve using temperatures derived frompartial thin plate spline interpolations in comparisonto nearest neighbour techniques. Partial thin platesplines were as good as or better than Voronoi forestimating codling moth development at 75% of pointsample locations in England and Wales. Additionally,the occasional penalty for using splines is small incomparison to estimates computed using the nearestneighbour technique.

While effort and investment currently aims at im-proving entomological models, complementary workis also needed to improve the provision of input me-

teorological data. Even at the relatively crude 1 kmresolution used in this study, the use of interpolatedinput data rather than nearest neighbour informationallows the practical performance of well-establishedphenology models to be improved. The work is a stepin the direction towards more confident pest manage-ment advice, where individual control practices are‘increasingly used as a stiletto instead of a scythe’(Van Emden and Peakall, 1996) in both the spatialand temporal sense.

Acknowledgements

Claire Jarvis thanks central Science Laboratoryfor their sponsorship other Ph.D. studies at the de-partment of Geography, University of Edinburgh.Data were supplied by the UK Meteorological Officeand the Ordnance Survey. The ANUSPLIN softwarewas provided by Professor Michael Hutchinson ofAustralian National University.

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The impact of interpolated daily temperature data on landscape-wide predictions of invertebrate pest phenology