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Continuous Bayesian networks for probabilistic environmental risk mapping

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Abstract

Bayesian networks (BNs) are being increasingly applied to environmental research. Nonetheless, most of the literature related to environmental sciences use discrete or discretized data, which entails a loss of information. We propose a novel methodology based on continuous BNs to predict the probability that surface waters do not meet the standards, in relation to nitrate concentration, established by the European Water Framework Directive. In order to achieve our purpose, a Tree Augmented Naive Bayes (TAN), was developed and applied to estimate and map the risk of failing to meet the European standards established. The TAN models were tested by means of the k-fold cross validation method. The results revealed that the TAN model performed proper risk maps and suggested that poor water quality is highly probable in watersheds dominated by irrigated herbaceous crops. On the contrary, “good surface water status” is more likely to occur in areas where forest is notably present.

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Notes

  1. http://www.juntadeandalucia.es/ medioambiente/site/rediam.

  2. The DTM, with grid width 200 m, was provided by the Spanish National Geographic Institute (http://www.ign.es/ign/layoutIn/modeloDigitalTerreno.do).

  3. Risk level classes: very low=[0–0.1], low=(0.1–0.3], moderate=(0.3–0.5], high=(0.5–0.8] and very high=(0.8–1] (Dlamini 2011).

References

  • Aalders I, Hough RL, Towers W (2011) Risk of erosion in peat soils—an investigation using Bayesian belief networks. Soil Use Manag 27:538–549

    Article  Google Scholar 

  • Aguilera PA, Fernández A, Reche F, Rumí R (2010) Hybrid Bayesian network classifiers: application to species distribution models. Environ Model Softw 25(12):1630–1639

    Article  Google Scholar 

  • Aguilera PA, Fernández A, Fernández R, Rumí R, Salmerón A (2011) Bayesian networks in environmental modelling. Environ Model Softw 26:1376–1388

    Article  Google Scholar 

  • Aguilera PA, Fernández A, Ropero RF, Molina L (2013) Groundwater quality assessment using data clustering based on hybrid Bayesian networks. Stoch Environ Res Risk Assess 27(2):435–447

    Article  Google Scholar 

  • Ames DP, Neilson BT, Stevens DK, Lall U (2005) Using Bayesian networks to model watershed management decisions: an East Canyon Creek case study. J Hydroinformatics 7:267–282

    Google Scholar 

  • Barca E, Passarella G (2008) Spatial evaluation of the risk of groundwater quality degradation: a comparison between disjunctive kriging and geostatistical simulation. Environ Monit Assess 137:261–273

    Article  CAS  Google Scholar 

  • Borin M, Vianello M, Morari F, Zanin G (2005) Effectiveness of buffer strips in removing pollutants in runoff from a cultivated field in North-East Italy. Agric Ecosyst Environ 101:101–114

    Article  Google Scholar 

  • Borsuk ME, Stow CA, Reckhow KH (2004) A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis. Ecol Model 173:219–239

    Article  Google Scholar 

  • Bressan GM, Oliveira VA, Hruschka ER, Nicoletti MC (2009) Using Bayesian networks with rule extraction to infer risk of weed infestation in a corn-crop. Eng Appl Artif Intell 22:579–592

    Article  Google Scholar 

  • Causapé J, Quílquez D, Aragüés R (2006) Irrigation efficiency and quality of irrigation return flows in the Ebro river basin: an overview. Environ Monit Assess 117:451–461. doi:10.1007/s10661-006-0763-8

    Article  Google Scholar 

  • Chan T, Ross H, Hoverman S, Powell B (2010) Participatory development of a Bayesian network model for catchment-based water resource management. Water Resour Res. doi:10.1029/2009WR008,848

  • Diamantino C, Henriques MJ, Oliveira MM, Lobo-Ferreira JP (2005) Methodologies for pollution risk assessment of water resources systems. In: The fourth inter-celtil colloquium on hydrology and management of water resources

  • Dlamini WM (2011) Application of Bayesian networks for fire risk mapping using GIS and remote sensing data. GeoJurnal 76:283–296

    Article  Google Scholar 

  • Dyer F, ElSawah S, Croke B, Griffiths R, Harrison E, Lucena-Moya P, Jakeman A (2014) The effects of climate change on ecologically-relevant flow regime and water quality attributes. Stoch Environ Res Risk Assess 28:67–82

    Article  Google Scholar 

  • Eimers L, Weaver JC, Terziotti S, Midgette RW (2000) Methods of rating unsaturated zone and watershed characteristics of public water supplies in North Carolina. Technical report, U.S. Geological Survey. Water-Resources Investigations

  • Elvira-Consortium (2002) Elvira: An environment for probabilistic graphical models. In: Proceedings of the first European workshop on probabilistic graphical models (PGM’02), pp 222–230

  • Fernández A, Salmerón A (2008) Extension of Bayesian network classifiers to regression problems. In: Geffner H, Prada R, Alexandre IM, David N (eds) Advances in artificial intelligence—IBERAMIA 2008. Lecture Notes in Artificial Intelligence, , vol 5290. Springer, Lisbon, pp 83–92

  • Fernández A, Morales M, Salmerón A (2007) Tree augmented naïve Bayes for regression using mixtures of truncated exponentials: applications to higher education management. IDA’07. Lect Notes Comput Sci 4723:59–69

    Article  Google Scholar 

  • Fernández-Escobar R, Marin L, Sánchez-Zamora MA, García-Novelo JM, Molina-Soria C, Parra MA (2009) Long-term effects of N fertilization on cropping and growth of olive trees and on N accumulation in soil profile. Eur J Agron 31:223–232. doi:10.1016/j.eja.2009.08.001

    Article  Google Scholar 

  • Fienen MN, Masterson JP, Plant NG, Guitierrez BT, Thieler ER (2013) Bridging groundwater models and decision support with a Bayesian network. Water Resour Res 49:6459–6473

    Article  Google Scholar 

  • Foley JA, DeFries R, Asner GP, Barford C, Bonan G, Carpenter SR, Chapin FS, Coe MT, Daily GC, Gibbs HK, Helkowski JH, Holloway T, Howard EA, Kucharik CJ, Monfreda C, Patz JA, Prentice IC, Ramankutty N, Snyder PK (2005) Global consequences of land use. Science 309:570–574. doi:10.1126/science.1111772

    Article  CAS  Google Scholar 

  • Friedman N, Geiger D, Goldszmidt M (1997) Bayesian network classifiers. Mach Learn 29:131–163

    Article  Google Scholar 

  • Fytilis N, Rizzo DM (2013) Coupling self-organizing maps with a Naïve Bayesian classifier: stream classification studies using multiple assessment data. Water Resour Res 49:7747–7762

    Article  Google Scholar 

  • Gillentine J (2000) Source Water Assessment and Protection Program. Technical report, New Mexico Environmental Department. Drinking Water Bureau, Appendix E - WRASTIC Index: Watershed vulnerability estimation using WRASTIC

  • Giupponi C, Eiselt E, Ghetti P (1999) A multicriteria approach for mapping risks of agricultural pollution for water resources: the Venice Lagoon watershed case study. J Environ Manag 56:259–269

    Article  Google Scholar 

  • Grimm JW, Lynch J (2005) Improved daily precipitation nitrate and ammonium concentration models for the Chesapeake Bay Watershed. Environ Pollut 135:445–455

    Article  CAS  Google Scholar 

  • Huang C (2009) Integration degree of risk in terms of scene and application. Stoch Environ Res Risk Assess 23:473–484

    Article  Google Scholar 

  • Lahr J, Kooistra L (2010) Environmental risk mapping of pollutants: state of the art and communication aspects. J Total Environ 408:3899–3907

    Article  CAS  Google Scholar 

  • Langseth H, Nielsen TD, Rumí R, Salmerón A (2012) Mixtures of truncated basis functions. Int J Approx Reason 53(2):212–227

    Article  Google Scholar 

  • Langseth H, Nielsen T, Pérez-Bernabé I, Salmerón A (2014) Learning mixtures of truncated basis functions from data. Int J Approx Reason 55:940–956

    Article  Google Scholar 

  • Larrañaga P, Moral S (2011) Probabilistic graphical models in artificial intelligence. Appl Soft Comput 11:1511–1528. doi:10.1016/j.asoc.2008.01.003

  • Lauritzen SL (1992) Propagation of probabilities, means and variances in mixed graphical association models. J Am Stat Assoc 87:1098–1108

    Article  Google Scholar 

  • Lee SW, Hwang SJ, Lee SB, Hwang HS, Sung HC (2009) Landscape ecological approach to the relationships of land use patterns in watersheds to water quality characteristics. Landsc Urban Plann 92:80–89

    Article  Google Scholar 

  • Liang Wj, Zhuang Df, Jiang D, Pan Jj, Ren Hy (2012) Assessment of debris flow hazards using a Bayesian Network. Geomorphology 171–172:94–100

    Google Scholar 

  • Liao Y, Wang J, Guo Y, Zheng X (2010) Risk assessment of human neural tube defects using a Bayesian belief network. Stoch Environ Res Risk Assess 24:93–100

    Article  Google Scholar 

  • Markus M, Hejazi MI, Bajcsy P, Giustolisi O, Savic DA (2010) Prediction of weekly nitrate-N fluctuations in a small agricultural watershed in Illinois. J Hydroinformatics 12(3):251–261. doi:10.2166/hydro.2010.064

    Article  Google Scholar 

  • Moral S, Rumí R, Salmerón A (2001) Mixtures of truncated exponentials in hybrid bayesian networks. In: Benferhat S, Besnard P (eds) Symbolic and quantitative approaches to reasoning with uncertainty. Lecture notes in artificial intelligence, vol 2143. Springer, Lisbon, pp 156–167

  • Morales M, Rodríguez C, Salmerón A (2007) Selective naïve Bayes for regression using mixtures of truncated exponentials. Int J Uncertain Fuzz Knowl Based Syst 15:697–716

    Article  Google Scholar 

  • Moratalla A, Gómez-Alday JJ, Sanz D, Castano SC, de las Heras J (2011) Evaluation of a GIS-Based integrated vulnerability risk assessment for the Mancha Oriental System (SE Spain). Water Resour Manag 25:3677–3697

    Article  Google Scholar 

  • Moreno JL, Navarro C, de las Heras JD (2006) Abiotic ecotypes in south-central Spanish rivers: Reference conditions and pollution. Environ Pollut 143:388–396. doi:10.1016/j.envpol.2005.12.012

    Article  CAS  Google Scholar 

  • Palmsten ML, Holland KT, Plant NG (2013) Velocity estimation using a Bayesian network in a critical-habitat reach of the Kootenai River, Idaho. Water Resour Res 49:5865–5879

    Article  Google Scholar 

  • Passarella G, Vurro M, D’Agostino V, Giuliano G, Barcelona M (2002) A probabilistic methodology to assess the risk of groundwater quality degradation. Environ Monit Assess 79:57–74

    Article  CAS  Google Scholar 

  • Payraudeau S, van der Werf HM (2005) Environmental impact assessment for farming region: a review of methods. Agric Ecosyst Environ 107:1–19

    Article  Google Scholar 

  • Pérez-Miñana E, Krause PJ, Thornton J (2012) Bayesian Network fot the management of greenhouse gas emissions in the British agricultural sector. Environ Model Softw 35:132–148

    Article  Google Scholar 

  • Pollino CA, Woodberry O, Nicholson A, Korb K, Hart BT (2007) Parameterisation and evaluation of a Bayesian network for use in an ecological risk assessment. Environ Model Softw 22:1140–1152

    Article  Google Scholar 

  • Quinn JM, Monaghan RM, Bidwell VJ, Harris SR (2013) A Bayesian Belief Network approach to evaluating complex effects of irrigation-driven agricultural intensification scenarios on future aquatic environmental and economic values in a New Zealand catchment. Mar Freshw Res 64:460–474. doi:10.1071/MF12141

    Article  Google Scholar 

  • Rennie SE, Brandt A, Plant N (2007) A probabilistic expert system approach for sea mine burial prediction. IEEE J Ocean Eng 32:260–272

    Article  Google Scholar 

  • Ropero RF, Aguilera PA, Fernández A, Rumí R (2014) Regression using hybrid Bayesian networks: modelling landscape-socioeconomy relationships. Environ Model Softw 54:127–137

    Article  Google Scholar 

  • Ruiz R, Riquelme J, Aguilar-Ruiz JS (2006) Incremental wrapper-based gene selection from microarray data for cancer classification. Pattern Recognit 39:2383–2392

    Article  Google Scholar 

  • Scalon BR, Jolly I, Sophocleous M, Zhang L (2007) Global impacts of conversions from natural to agricultural ecosystems on water resources: quantity versus quality. Water Resour Res 43(W03):437

    Google Scholar 

  • Shenoy PP, West JC (2011) Inference in hybrid Bayesian networks using mixtures of polynomials. Int J Approx Reason 52(5):641–657

    Article  Google Scholar 

  • Shenton W, Hart BT, Chan TU (2014) A Bayesian network approach to support environmental flow restoration decisions in the Yarra River, Australia. Stoch Environ Res Risk Assess 28:57–65

    Article  Google Scholar 

  • Stone M (1974) Cross-validatory choice and assessment of statistical predictions. J R Stat Soc Ser B (Methodol) 36(2):111–147

    Google Scholar 

  • Sun R, Chen L, Chen W, Ji Y (2013) Effect of land use patterns on total nitrogen concentration in the upstream regions of the Haihe River Basin, China. Environ Manag 51:45–58

    Article  Google Scholar 

  • Tilman D, Fargione J, Wolf B, D’Antonio C, Dobson A, Howarth R, Schindler D, Schlesinger WH, Simberloff D, Swackhamer D (2001) Forecasting agriculturally driven global environmental change. Science 292:281–284. doi:10.1126/science.1057544

    Article  CAS  Google Scholar 

  • Troldborg M, Aalders I, Towers W, Hallett PD, McKenizie BM, Bengough AG, Lilly A, Ball BC, Hough RL (2013) Application of Bayesian Belief Networks to quantify and map areas at risk to soil threats: using soil compaction as an example. Soil Tillage Res 132:56–68

    Article  Google Scholar 

  • Uusitalo L (2007) Advantages and challenges of Bayesian networks in environmental modelling. Ecol Model 203:312–318

    Article  Google Scholar 

  • Verro R, Calliera M, Maffioli G, Auteri D, Sala S, Finizio A, Vighi M (2002) GIS-Based system for surface water risk assessment of agricultural chemicals. 1. Methodological approach. Environ Sci Technol 36:1532–1538

    Article  CAS  Google Scholar 

  • Verro R, Finizio A, Otto S, Vighi M (2009) Predicting pesticide environmental risk in intensive agricultural areas I: screeneing level risk assessment of individual chemicals in surface waters. Environ Sci Technol 43:522–529

    Article  CAS  Google Scholar 

  • Wang QJ, Robertson DE, Haines CL (2009) A Bayesian network approach to knowledge integration and representation of farm irrigation: 1. Model development. Water Resour Res. doi:10.1029/2006WR005,419

  • Wang Y, Witten IH (1997) Induction of model trees for predicting continuous cases. In: Proceedings of the poster papers of the European conference on machine learning, pp 128–137

  • Zhang NL, Poole D (1996) Exploiting causal independence in Bayesian network inference. J Artif Intell Res 5:301–328

    Google Scholar 

  • Zhang W, Li H, Sun D, Zhou L (2012) A statistical assessment of the impact of agricultural land use intensity on regional surface water quality at multiple scales. Environ Res Public Health 9:4170–4186. doi:10.3390/ijerph9114170

    Article  CAS  Google Scholar 

  • Zou Q, Zhou J, Zhou C, Song L, Guo J (2013) Comprehensive flood risk assessment based on set pair analysis-variable fuzzy sets model and fuzzy AHP. Stoch Environ Res Risk Assess 27:525–546

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Spanish Ministry of Economy and Competitiveness, through project TIN2013-46638-C3-1-P , by Junta de Andalucía through project P11-TIC-7821 and by ERDF-FEDER funds. A.D. Maldonado is being supported by the Spanish Ministry of Education, Culture and Sport through an FPU research grant, FPU2013/00547.

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Authors and Affiliations

  1. Department of Mathematics, University of Almería, Almería, Spain

    A. D. Maldonado & A. Salmerón

  2. Informatics and Environment Laboratory, Department of Biology and Geology, University of Almería, Almería, Spain

    P. A. Aguilera

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  1. A. D. Maldonado
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Correspondence to A. D. Maldonado.

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Appendix: Land uses

Appendix: Land uses

Land use variables incorporated into the data matrix. Percentage of occupation of each land use in the study area is shown in brackets.

1.

Urban (2.19 %) includes urban, industrial and commercial areas, landfills, mining deposits, communication infrastructure, parks, recreational and sport facilities and areas under construction

2.

Water (2.45 %) comprises surface waters in Andalusia, including rivers, artificial channels, lakes and reservoirs. For the study purposes, only waterbodies corresponding to rivers were taken into account

3.

Forest (47.52 %) includes forest, shrub and grassland cover

4.

Rainfed herbaceous crops (13.89 %) consist of non-irrigated herbaceous monocultures, with cereals (wheat, barley, oats) and leguminous crops (peas, chickpeas, beans) being the most copious crops

5.

Olive grove (21.08 %) is the main crop of inland Andalusia and consists of non-irrigated monocultures, excluding wild olive trees

6.

Vineyard1 a (0.28 %) consists of non-irrigated monocultures, devoted to grape production

7.

Rainfed woody crops a (0.67 %) comprise woody monocultures under rainfed conditions, such as almond, carob, fig, walnut or chestnut trees, excluding plots dedicated to logging activities

8.

Rainfed olive grove and vineyard crops a (0.03 %) are composed of mixtures of vine and olive trees under dry farming conditions

9.

Rainfed woody heterogeneous crops a (0.03 %) comprise vine and olive tree associations with other rainfed woody crops, where no dominance of any of the crops exists

10.

Abandoned olive grove a (0.19 %) comprises abandoned plots of woody crops, patently dominated by olive grove

11.

Abandoned woody crops a (0.03 %) include abandoned plots of undifferentiated woody crops

12.

Paddy fields b (0.07 %) consist of flooded parcels devoted

to rice cultivation

13.

Greenhouse crops b (0.10 %) consist of high yield crops under controlled conditions

14.

Irrigated herbaceous crops b (1.96 %) comprise permanently irrigated intensive herbaceous monocultures, including lettuce, asparagus, carrot, onion and garlic crops

15.

Partly irrigated herbaceous crops b (2.07 %) comprise both irrigated and non-irrigated (but liable to be irrigated) plots where herbaceous crops are grown

16.

Non-irrigated herbaceous crops b (0.49 %) consist of irrigated herbaceous crop areas that were not being watered at the moment of taking the image

17.

Partly irrigated woody crops c (0.14 %) are composed of both irrigated and non-irrigated (but liable to be irrigated) plots where woody crops are grown

18.

Citrus cropsc (0.64 %) include orange, lemon, mandarin and grapefruit trees, among other irrigated woody species

19.

Irrigated olive grove c (1.17 %) consists of irrigated olive tree monocultures

20

Tropical cropsc (0.00003 %) include avocado, cherimoya, mango and medlar trees, among other irrigated woody species

21.

Irrigated woody crops c (0.13 %) include other irrigated woody crops not aforementioned

22.

Irrigated woody heterogeneous crops c (0.1 %) consist of undifferentiated woody crop mixtures under irrigated conditions

23.

Rainfed herbaceous and woody crops d (0.63 %) consist of annual herbaceous crops associated with permanent woody crops under dry farming conditions

24.

Irrigated herbaceous and woody crops d (0.23 %) consist of annual herbaceous crops associated with permanent woody crops under irrigated conditions

25.

Partly irrigated herbaceous and woody crops d (0.02 %) comprise woody and herbaceous crop mixtures under either dry farming or irrigated conditions

26.

Non-irrigated herbaceous and woody crops d (0.01 %) are composed of woody and herbaceous crop mixtures which are situated on non-irrigated plots at the moment of taking the image

27.

Rainfed and irrigated herbaceous crops d (2.58 %) comprise undifferentiated herbaceous crop mixtures under either rainfed or irrigated conditions

28.

Rainfed and irrigated herbaceous and woody crops d (0.31 %) are composed of undifferentiated woody and herbaceous crop mixtures under either rainfed or irrigated conditions

29.

Rainfed and irrigated woody crops d (0.01 %) comprise undifferentiated woody crop mixtures under either rainfed or irrigated conditions

30.

Herbaceous crops and grasslands e (0.25 %) consists of land mainly occupied by undifferentiated herbaceous crops, with significant areas of grassland

31.

Herbaceous crops and woody natural vegetation e (0.19 %) is composed of land mainly covered by herbaceous crops, with a important portion occupied by woody natural vegetation

32.

Woody crops and grasslands e (0.02 %) consists of land mainly occupied by undifferentiated woody crops, with significant areas of grassland

33.

Woody crops and woody natural vegetation e (0.43 %) is composed of land mainly covered by woody crops, with a important portion occupied by woody natural vegetation

34.

Herbaceous and woody crops and natural vegetation e (0.19 %) includes other undifferentiated crop mixtures associated with natural vegetation, not aforementioned

  1. aLand uses included into the “General rainfed woody crop” category
  2. bLand uses included into the “General irrigated herbaceous crop” category
  3. cLand uses included into the “General irrigated woody crop” category
  4. dLand uses included into the “General miscellaneous crop” category
  5. eLand uses included into the “General agroforestry” category

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Maldonado, A.D., Aguilera, P.A. & Salmerón, A. Continuous Bayesian networks for probabilistic environmental risk mapping. Stoch Environ Res Risk Assess 30, 1441–1455 (2016). https://doi.org/10.1007/s00477-015-1133-2

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