Benchmarking Knowledge-assisted Kriging for Automated Spatial Interpolation of Wind Measurements

Transcription

1 Benchmarkng Knowledge-asssted Krgng for Automated Spatal Interpolaton of Wnd Measurements Zlatko Zlatev, Stuart E. Mddleton, Galna Veres IT Innovaton Centre Unversty of Southampton Southampton, UK Abstract - We have benchmarked a novel knowledgeasssted krgng algorthm that allows regons of spatal coheson to be specfed and varograms calculated for each regon. The varogram calculaton tself s automated and spatal regons created va offlne automated segmentaton of ether expert-drawn Google Earth polygons or ASA alttude data. Our use-case s to create nterpolated wnd maps for nput nto a bathng water qualty model of mcrobal contamnaton. We benchmark our knowledge-asssted krgng algorthm aganst 7 other algorthms on UK met-offce wnd data (89 sensors). Our wnd estmaton results are comparable to standard ordnary krgng usng varograms created by an expert. When usng spatal segmentaton we fnd our krgng error maps reflect better the known spatal features of the nterpolated phenomenon. These results are very promsng for an automated approach allowng on-demand datasets selecton and real-tme nterpolaton of prevously unknown measurements. Automaton s mportant n progressng towards a pan-european nterpolaton servce capablty. Keywords: Data Fuson, Krgng, Spatal Interpolaton, Wnd Speed, Wnd Drecton, OGC, WPS Introducton In-stu meteorologcal sensor measurements are generally recorded by sensor hardware at pont locatons, requrng some form of spatal nterpolaton should estmates at other locatons be needed. Many spatal nterpolaton methods exst, both determnstc and geo-statstcal, wth accuraces dependent on the nature of the observed phenomena, spatal densty of sensors, temporal frequency of samplng and the consstency and accuracy of measurement. In the SAY project [6] we have developed an nterpolaton algorthm for handlng wnd measurements. Our use case s to generate spatal grds of estmated wnd measurements for contnual nput nto a bathng water qualty model [3] and subsequent lve predcton of mcrobal contamnaton levels of bathng water at beaches. Mcrobal contamnaton s mportant nformaton for coast guards when makng the decson as to f, and when, to close publc beaches. Our algorthms are phenomena ndependent, and n SAY we have also successfully appled them to ar polluton and ground dsplacement measurements. We present a knowledge-asssted krgng algorthm appled to hstorcal wnd measurements from the UK meteorologcal offce (UKMO) dataset archves [9]. We report cross-valdated results for wnd speed mean error (ME), root mean squared error (RMSE) and the range of estmated values. These results are compared drectly to results for seven alternatve nterpolaton methods reported n [7] on the same dataset. Our knowledge-asssted krgng algorthm takes as nput knowledge about known areas of spatal coheson, ether dentfed by an expert or heurstcally calculated from the CGIAR-CSI GeoPortal SRTM (90m resoluton) Dgtal Elevaton Dataset [8]; mult-regon ordnary krgng s then used to compute varograms for each regon. The computaton of the varograms s asssted by metadata representng wnd phenomenon characterstcs. Ths algorthm s hosted wthn an Open Geospatal Consortum (OGC) sensor servce framework [5], showng how sensor processng servces can be setup to 'plug and process' dfferent sensor measurement datasets on-demand. We outlne n secton 2 relevant related work, descrbe our algorthm n secton 3 and expermental results n secton 4. We dscuss and conclude n sectons 5 and 6. 2 Related work In addton to ordnary krgng [], whch s outlned n the next secton, there are a number of varants such as unversal krgng [3], where a trend n data s assumed, and co-krgng [], where covarates are provded n the same area as the prmary sampled measurement to assst n predcton. Our novel automated varogram selecton and mult-regon ordnary krgng approach s another krgng varant, makng use of expert knowledge about the phenomenon characterstcs and the spatal cohesveness n known regons to mprove predcton accuracy. Many general spatal nterpolaton technques [2] exst, wth most relevant ones ncludng trend surface analyss, nverse dstance weghtng, local polynomal nterpolaton and thn plate splne. Untl [7] few works had benchmarked these technques thoroughly for wnd

2 measurement nterpolaton, and our work bulds on these results for drect comparson. 3 Knowledge-asssted ordnary krgng Krgng [] s a statstcal technque for nterpolaton of random phenomenon that uses a lnear combnaton of measured values at observed spatal locatons to estmate the value at an unobserved locaton of nterest. In contrast to other nterpolaton technques, lke nverse dstance weghtng and thn plane splne, t uses a model of the phenomenon s spatal correlaton encoded as a corrrelogram or a sem-varogram. Krgng s an exact nterpolator, so t respects the observed values at the observed locatons, whch dfferentates t from nterpolaton technques lke local polynomal nterpolaton and trend surface analyss. For the purposes of our work we have used ordnary krgng wth a semvarogram correlaton model. When usng a semvarogram, the spatal correlaton of the phenomenon s quantfed by means of a sem-varance functon (), where (h) s the number of pars of observed locatons s a dstance h apart, and z(s ) s the observed value at s. ( h) 2 ˆ γ ( h) = [ ( ) ( )] ( ) z s + h z s () 2 h = The sem-varogram can be a functon of both dstance and drecton, so t can account for drecton-dependent varablty (ansotropc spatal pattern). For krgng, a smooth sem-varogram s requred and we use smooth parametrc functons as approxmate models of the semvarogram [2]. These smooth functons are ftted to the sem-varance functon, or to the expermental semvarogram obtaned by averagng the sem-varance functon over a set of dstance lags, and after a goodness of ft analyss the best fttng functon s selected [3] [4]. We refer to ths functon as a 'varogram model' and the expermental sem-varogram as an 'expermental varogram'. In our automated varogram model selecton we use eght dfferent famles of varogram models: sphercal, exponental, Gaussan, lnear, power, generalsed Bessel, sne hole-effect and cosne hole-effect. It s usual that a phenomenon expert wll select a partcular varogram model based on experence and ft the selected model to the avalable observatons. Human expert nterventon n the nterpolaton process s expensve and makes the nterpolaton process phenomena specfc. Our soluton, ordnary krgng wth automated varogram model selecton (AVMS), tackles ths problem by utlsng metadata representng hgh level phenomenon characterstcs and automatng the varogram model selecton. 3. Automated nterpolaton workflow The varous offlne and real-tme stages of our knowledge-asssted nterpolaton process s shown n Fgure. Fgure. Ordnary krgng wth automated varogram model selecton procedure. The frst stage s the data pre-processng stage, where data cleansng, normalsaton and all necessary data transformatons are performed. The pre-processng stage ncludes nput of knowledge-based descrptons for regons of spatal coheson and offlne preparaton usng segmentaton technques and heurstcs pror to run-tme. In the data post-processng stage, data de-normalsaton and reverse transformatons are performed. The core stages of ordnary krgng wth AVMS are the expermental varogram creaton, varogram model selecton, model optmsaton and ordnary krgng. A varogram s created for each regon of spatal coheson. Phenomenon metadata s setup va expert defned profle confguratons. 3.2 Offlne dentfcaton of knowledge about spatally coherent regons Regon calculaton s performed automatcally from ether expert drawn Google Earth spatal polygons (KML format) or from ASA alttude data (ASC format) from the CGIAR-CSI GeoPortal SRTM (90m resoluton) Dgtal Elevaton Dataset [8]. The polygons / alttude maps are rendered as greyscale mages and standard mage processng technques (colour reducton, bnary mask per colour, pxel blur, labellng and edge dentfcaton) used to segment maps nto unque regons sutable for nput nto the krgng process. Regon segmentaton s executed offlne, va an automated web servce, as part of the ntal confguraton stage pror to on-demand krgng.

3 We expect over mountanous ground the mean daly wnd speed wll have lower levels of spatal correlaton than flat land. The land/sea boundary wll also have an effect, especally snce our sensors are land-based. Fgure 2 shows the alttude segmentaton, whch we found to be somewhat over-segmented and too fne-graned for our wnd phenomena. Fgure 3 shows the regon segmentaton for the expert drawn polygons, whch produced the best results and are used n the experments later n ths paper. Fgure 2. Regon segmentaton based on CGIAR-CSI GeoPortal SRTM alttude data Fgure 3. Regon segmentaton based on polygons drawn by an expert for land/water and flat/hlly areas The output of the offlne regon segmentaton process are a set of comma separated varable (CSV) maps contanng regon labels for every nterpolaton pont, and nterregon neghbour lnkage whch s used later by the knowledge-asssted ordnary krgng algorthm. 3.3 Real-tme automated varogram model creaton The most crtcal part of the expermental varogram creaton stage s the selecton of lags. Lags need to be selected so they contan an optmal number of ponts, do not smooth out physcal phenomenon characterstcs and avod nose. Generally the ntal slope of the varogram carres the most nformaton, so our frst few lags contan a smaller number of ponts. If no hole-effect s expected lags subsequent to the ntal slope may contan a large number of ponts. If a hole-effect s expected these lags shall contan a lower number of ponts so the hole-effect s not smoothed out. The relatve number of ponts n a lag s specfed n the metadata suppled to the nterpolaton. In the next stage, the varogram model selecton, we ft our eght varogram models to the expermental varogram. The model shape s governed by a subset of the followng parameters: nugget, correlaton range, power, hole and sll. We use a weghted least squares fttng method to select a model that best fts the expermental varogram. We ntroduce expert knowledge about phenomenon by constranng the ftted model types and parameters values and thus obtan a varogram model reflectng the characterstcs of the phenomenon of nterest. For daly mean wnd speed we expect low levels of nose to be present n the observatons because of the averagng used to calculate the means (see secton 4.) and a low level of rapd phenomenon fluctuatons. In the phenomenon metadata we thus set the nugget to be constraned to maxmum of 20% of the sll. We expect the spatal correlaton of the daly mean wnd speed to decrease very slowly wth ncreasng the dstance. In the phenomenon metadata we thus set the lower and upper bounds of the correlaton range parameter to be relatvely hgh, respectvely 25% and 75% of the maxmum dstance n the expermental varogram. We don t expect a holeeffect so do not select models wth a hole-effect. After selectng the varogram model, parameter optmsaton s performed by mnmsng the mean error (ME, see equaton (2)) and the root mean square error (RMSE, see equaton (3)) calculated over 0-folds of cross-valdaton. We use smplex optmsaton wth a loss functon of sum of ME and RMSE. The phenomenon constrants are reflected n the loss functon by addng a hgh penalty value when the model parameters are outsde the ranges specfed n the phenomenon metadata. ext, ordnary krgng wth a movng neghbourhood s performed, usng the optmsed varogram model, and krgng mean and error computed. The krgng mean s the estmated value of the phenomenon at the locaton of nterest. The krgng error s a measure of how good the observatons locaton confguraton s for estmaton at the locaton of nterest. Ordnary krgng wth a movng neghbourhood s able to pck out varatons of the phenomenon mean along the nterpolated area. As the nterpolated area s relatvely

4 large n respect to the phenomenon scale we expect varatons n the mean. Thus, n the phenomenon metadata we have specfed a constraned movng neghbourhood consstng of the closest observatons to be used; the value of neghbours was chosen after expermentaton comparng results wth dfferent values. Ths choce can be automated by ncludng an addtonal parameter n the model optmsaton stage, whch we ntend to mplement n future versons. A pont map showng regon labels for the nterpolated area s suppled to our ordnary krgng procedure so we know whch regon each nterpolated pont belongs to. The observatons belongng to a partcular regon are used for workng out the varogram of that regon. If there are not enough observatons avalable for a gven regon, observatons from the neghbourng regons are used n order to buld the raw varogram. The mnmum number observatons for the automated varogram estmaton s argmn(n*(n-)/2>3* lags ), where n s the number of observatons and lags s the number of lags n the varogram,.e. we have mnmum of 3 raw varogram ponts per lag. When computng estmates requrng observatons from a neghbourng regon we average the varograms of the home and the neghbourng regons. In the phenomenon metadata we have an nter-regon correlaton factor, r, rangng between 0 and, where 0 ndcates mnmal correlaton between the regons and ndcates hgh correlaton. We modulate averaged nterregon varograms by ncreasng the varogram values by a quantty equallng -r tmes the varogram sll, up to a value not larger than the sll. If the varogram doesn t have a sll, such as the power model, then varogram values are ncreased by a quantty equallng -r tmes the current varogram value. In ths way we ntroduce addtonal knowledge of factors nfluencng the phenomenon spatal correlaton. 4 Experments and results In the SAY project we have used our ordnary krgng wth AVMS for nterpolatng mcro-scale phenomena (e.g. ground dsplacement caused by underground tunnellng) and mn / meso-scale phenomena (e.g. wnd speed and drecton) yeldng meanngful results. In ths paper we drectly compare the performance of our algorthm aganst 7 well known algorthms and mplementatons on a benchmark data set. A defntve work n ths context s [7], where the performance of seven nterpolaton methods are compared on a dataset of daly mean wnd speeds obtaned from sensor data suppled by the UK meteorologcal offce (UKMO). Smlarly to [7] we have used leave-one-out cross valdaton and calculated the mean error (ME) and root mean square error (RMSE) as follows: RMSE = = ^ z ( s ) z( ) s where s the number of valdaton folds, z^(s ) s the estmated value and z(s ) s the observed value. 4. Data For our wnd speed experments we used the same dataset as [7] for 27 th of March 200, whch was orgnally obtaned from the UKMO. At ths date 89 sensors n England, Wales, South of Scotland and orthern Ireland reported at least 2 tmes, the readngs averaged to obtan daly mean wnd speeds. The daly mean wnd speeds vary from 2.2 to 3.6 m/s. Fgure 4 depcts the locatons and magntudes of the daly mean wnd speed observatons, where the sze of the dots s relatve to the magntude of the speed. 2 (3) Fgure 4. Locatons and relatve magntude of daly mean wnd speed observatons for 27 th of March 200. For our wnd drecton experments we used 27 th March 200 data from the UKMO dataset archve [9]. It contans 57 observatons wth daly mean wnd drectons. Fgure 5 depcts the locatons of the daly mean wnd drectons observatons, where the vectors show the drecton of the wnd. We apply our ordnary krgng wth AVMS to ths data and nterpolate on a grd wth a resoluton of 5km by 5km. For daly mean wnd speed we compare our results aganst the results publshed n [7]. In [7] no results are presented for daly mean wnd drectons (just wnd speed) so we just state our expermental results wthout comparson as a benchmark for other researchers. ME = = ^ z ( s ) z( ) s (2)

5 Fgure 5. Locatons of daly mean wnd drecton observatons for 27 th of March Daly mean wnd speed estmates benchmarkng In ths experment we compare our ordnary krgng wth AVMS algorthm aganst the 7 algorthms evaluated n [7]. We set our algorthm wth the followng parameters:. Expermental varogram lags percentles: 5, 0, 5, 20, 30, 40, 50, 60, 70, 80, 90, ugget boundares: 0 to 20% of the sll. 3. Correlaton range boundares: 25% to 75% of the maxmum varogram dstance. 4. Varogram models to use: sphercal, exponental, Gaussan, lnear, power or generalsed Bessel. Ordnary krgng - no regon knowledge used The frst experment s usng krgng wthout any knowledge of regons and nter-regon cohesveness. The daly mean wnd speed surface produced, shown n Fgure 6, s consstent wth the nput values over land, and s very smlar to the results found n [7]. Hgh wnd speeds are accurately estmated over the north, the north-east and north-west of England, and also over the Isle of Man. Low wnd speed are accurately estmated over the Mdlands, and the west and south-east of England. The krgng error, show n Fgure 7, s small where we have hgh concentraton of observatons and larger where there are smaller number of observatons. The RMSE, ME and the mn and max nterpolated values suggest that the performance of ordnary krgng wth AVMS s slghtly worse than the ordnary krgng n [7] and slghtly better than unversal krgng and local polynomal (see table ). It should be noted that our ordnary krgng wth AVMS needs only a mnmal nput and confguraton from users, unlke the classc manual approach used n [7]. Fgure 6. Daly mean wnd speed estmates [89 sensors, no regons, 5km x 5km grd resoluton, unt m/s] Fgure 7. Krgng error of wnd speed estmates [89 sensors, no regons, 5km x 5km grd resoluton]. otce how reported error s smoothed across coastlne and land. Ordnary krgng - coastlne regon knowledge provded Snce all sensors are land-based sea value estmates are n all probablty not very relable. Supplyng expert-drawn coastlne regon boundary knowledge can help n ths case. For our second experment we performed coastlne segmentaton on Google Earth drawn coastlne polygons and suppled the resultng regons to our ordnary krgng wth AVMS. For ths experment, the nter-regon correlaton factor r was set to 0. to ndcate that there are mnmal smlartes n the way sea and land measurements nfluence each other. The estmated mean wnd speed and the krgng error surfaces are shown n Fgure 8 and Fgure 9 respectvely. The n-land wnd speed estmates change only slghtly, wth the only notable dfferences n estmated land values over the Isle of Man. Comparng fgures 6 and 8 one can see that now there are more accurate hgh wnd speed values predcted as the manland observaton's nterference s dmnshed somewhat by the low nterregon correlaton factor. Ths result s also reflected n the algorthm's overall performance metrcs shown n table. The krgng error for the Isle of Man s very dfferent from the prevous krgng error wthout usng regon

6 knowledge; ths s clear comparng fgures 7 and 9. There s a clear jump n the krgng error on the land-sea borders ndcatng correctly that the wnd speed estmates over the sea areas are unrelable. regon. In contrast the spotty krgng error pattern n the northern regon, and n Wales and south-west of England, we nterpreted as needng much more dense observatons to acheve good estmates n these regons. Fgure 8. Daly mean wnd speed estmates [89 sensors, coastlne regons, 5km x 5km grd resoluton, unt m/s] Fgure 0. Daly mean wnd speed estmates [89 sensors, flat/hlly regons, 5km x 5km grd resoluton, unt m/s] Fgure 9. Krgng error of wnd speed estmates [89 sensors, coastlne regons, 5km x 5km grd resoluton]. otce the sharp error boundary at the coastlne. Ordnary krgng - flat/hlly regon knowledge provded For our last experment regardng wnd speed we provded doman knowledge about the dfferent terran topology (.e. flat land, hlly land, mountanous land), agan segmented nto regons. We used a hgher nter-regon correlaton factor of 0.9 snce these new regons are nland. Results wth these new regons are agan mproved and are comparable to ordnary krgng n [7] (see table ). The bas, ME, s decreased as s the RMSE and the mnmum and maxmum of the estmated values are also closer to those present n the raw data. The estmated wnd speed surface sown n Fgure 0 suggests that wth approprate regonalsaton the extremtes are more lkely to be dentfed but not smoothed out. The krgng error map, Fgure, now shows dstnct patterns n each of the dfferent regons. For example the krgng error over the Mdlands, South and South-East regon s very smooth, whch we nterpret as not needng very dense observatons to acheve good estmates n ths Fgure. Krgng error of wnd speed estmates [89 sensors, flat/hlly regons, 5km x 5km grd resoluton]. otce the sharp error boundares between spatal features and dfferent nter-regon error profles. 4.3 Daly mean wnd drecton estmaton Usng the same ordnary krgng wth AVMS setup as for the wnd speed experments we ran tests on the UKMO dataset for 27 th March 200 wth no regons defned. In our mplementaton of ordnary krgng we have a specal procedure [0] for handlng perodc values lke wnd drecton, whch ncludes vector rotaton and Cartesan transformaton and smulaton. Estmated wnd drecton vectors are vsualsed n Fgure 2. We use a 28km x 28km grd to make vsualsaton easer for arrow vectors. The ME and RMSE are gven n table 2. We fnd the ME, of degrees, and RMSE, of 3.66 degrees, n relatve terms very low consderng the worse case could be 80 degrees. The mean relatve absolute error (MRAE) s 6%. For our wnd speed experments MRAE vares from 22% to 23%.

7 For wnd speed we calculate MRAE as: MRAE = = ^ z ( s ) z( s ) / z( s ) and for wnd drecton we calculate MRAE as: MRAE ( perodc) = = ^ norm( z ( s ) z( s ) ) /80 where s the number of valdaton folds, z^(s ) s the estmated value, z(s ) s the observed value,. s the absolute value and norm() yelds a normalsed wnd drecton n the range of -80 to +80. The wnd drecton krgng error s shown n Fgure 3, wth normalsed values n the range of 0 to 360. Krgng error quantfes the observatons confguraton sutablty for estmatng at a partcular locaton and s not a measure of the estmaton error n tself. We are unaware of any other benchmark wnd drecton nterpolaton results so publsh here n the hope of provdng other researchers wth a benchmark result set. Method umber of Regons Inter-regon correlaton Exec-tme (mns) Krgng_ 0 n/a Krgng_2 4 coastlne 0. 8 Krgng_3 7 flat/hlly All methods use ordnary krgng wth AVMS Computer spec : 2 CPU's (2.4 GHz) wth 4 Gbyte RAM Method Mn estmate m/s Max estmate m/s RMS E m/s ME m/s Krgng_ Krgng_ Krgng_ Cokrgng [7] Ordnary krgng [7] Local polynomal [7] Unversal krgng [7] IDW [7] TPS [7] TSA [7] Table. Comparson of knowledge-asssted krgng to benchmark nterpolaton results reported n [7] Method ME RMSE degrees degrees Ordnary krgng wth AVMS Table 2. Wnd drecton estmate ME and RMSE [57 sensors, no regon, 28km x 28km grd resoluton] Fgure 2. Daly mean wnd drectons [57 sensors, no regon, 28km x 28km grd resoluton, unt degrees] Fgure 3. Krgng error for wnd drecton estmates [57 sensors, no regon, 28km x 28km grd resoluton] 5 Dscusson In our experments we have nvestgated methods to automatcally select varogram models and ways to ntroduce expert knowledge nto varogram calculaton process. Our results show the mpact usng dfferent levels of expert knowledge, about both the phenomenology and spatal areas of nterest, can have on estmaton error. Ths automated approach s n contrast to exstng methods [7] that rely on manual varogram tunng by experts. We thnk our approach offers a realstc route to provdng ondemand krgng servces that can nterpolate measurement datasets selected by users and that are unknown untl runtme. Ths level of automaton s becomng more mportant as we see European envronment agences sharng ncreasng amounts of sensor data under the ISPIRE drectve [5]. Such automaton, and a move away from manual tunng and confguraton, ncreases scalablty and could allow truly dynamc pan-european nterpolaton for wnd measurements and other phenomenology. The performance of our ordnary krgng wth AVMS algorthm s slghtly worse than that reported by ordnary

8 krgng n [7] wth expert tuned varogram. Partly ths s due to the expert's skll n manually tunng the varogram. However, our mplementaton s also only sotropc, whch accounts for some of the performance compared aganst the ansotropc ordnary krgng algorthm n [7]. We ntend to mplement ansotropc krgng n future releases. Where our knowledge-asssted approach offers the most mprovement, compared to basc ordnary krgng, s n the enhanced spatal defnton of the krgng error maps, and therefore mproved confdence n them. Ths s most clear n areas where no sensors are located (e.g. offshore n the sea). Ths result can be appled more wdely to other spatal features than hlls and coastlnes, at a varety of dfferent spatal scales, such as buldng footprnts and rver outlets. Though not the focus of our wnd nterpolaton paper, we have successfully nterpolated measured phenomenon ncludng ground dsplacement, water salnty and turbdty. 6 Concluson We have benchmarked a novel knowledge-asssted krgng algorthm that allows knowledge of regonal spatal coheson to be specfed and varograms calculated per regon. The varogram calculaton tself s automated and phenomenon specfc metadata allows us to confgure krgng for more than just wnd phenomenon. Spatal regons are created offlne automatcally by segmentaton of ether expert-drawn Google Earth polygons or ASA alttude data. Our use-case s to create wnd nterpolaton grds for nput nto a bathng water qualty model of mcrobal contamnaton, and subsequent decson support for beach attendants to make bathng rsk assessments. We benchmark our knowledge-asssted krgng algorthm aganst 7 other algorthms usng the same UK met-offce wnd measurement dataset reported n [7]. Wnd speed estmaton results are comparable, but not better than ordnary krgng, but the krgng error maps are much sharper and reflect the known spatal features better. We also provde results for wnd drecton nterpolaton. These results are very promsng consderng t s an automated approach allowng on-demand datasets to be selected and real-tme nterpolaton of measurements unknown a-pror. Automaton s mportant n moves towards a pan-european nterpolaton servce capablty makng use of European envronment agency data shared n complance wth the European ISPIRE drectve [5]. Ths work was funded by the European Commsson s IST Programme under contract FP6-IST SAY [6] References [] D.G. Krge, Two-dmensonal weghted average trend surfaces for ore-evaluaton, Journal of the South Afrcan Insttute of Mnng and Metallurgy 66: 3 38, 966 [2].A.C. Cresse, Fttng varogram models by weghted least squares, Journal of the Internatonal Assocaton for Mathematcal Geology 7: , 985 [3].A.C. Cresse, Statstcs for Spatal Data, John Wley and Sons: ew York, 993 [4] P.A. Burrough and R.A. McDonnell, Prncples of Geographcal Informaton Systems, Clarendon Press: Oxford, 998 [5] S.E. Mddleton (ed) et al, SAY Fuson and Modellng Archtecture, OGC Dscusson paper 0-00, 200 [6] SAY project, [7] W. Luo, M.C. Taylor and S.R. Parker, A comparson of spatal nterpolaton methods to estmate contnuous wnd speed surfaces usng rregularly dstrbuted data from England and Wales, Int. J. Clmatol, 28: , 2008 [8] CGIAR-CSI, GeoPortal SRTM (90m resoluton) Dgtal Elevaton Dataset, [9] UK Met Offce, MIDAS Land Surface Observaton Statons Data, [0] Z. Zlatev, S.E. Mddleton and G. Veres, Ordnary krgng for on-demand average wnd nterpolaton of nstu wnd sensor data, EWEC 2009, France, March 2009 [] A.G. Journel, C. Hujbregts, Mnng Geostatstcs, Academc Press: ew York, 978 [2].S. Lam, Spatal nterpolaton methods: a revew, The Amercan Cartographer 0: 29 35, 983 [3] Z.A. Sabeur (ed) et al, Development of envronmental nformaton tools for the predcton of water qualty rsks n bathng waters, Fnal Report to the Envronment Agency of England and Wales, Interreg ICREW project, Plot Acton 4: Forecastng bathng water qualty. Fnal Techncal Report/FIAL. 2st June 2006, pp28, 2006 [4] R.B. Stull, Meteorology for Scentsts and Engneers, 2nd Edton, Earth Scences seres, Cengage Learnng Publsher. ISB-3: , 999 [5] ISPIRE drectve, Drectve 2007/2/EC of the European Parlament, 4 March 2007