Spatiotemporal Statistics: Analysis of Spatially and Temporally Correlated Throughfall Data: Exploring and Considering Dependency and Heterogeneity

  • Alexander TischerEmail author
  • Martin Zwanzig
  • Nico Frischbier
Part of the Ecological Studies book series (ECOLSTUD, volume 240)


It has long been recognized that single-trees, as major components of forest ecosystems, change the distribution of resources due to the abundance and the structure of their canopies. This includes both the vertical and horizontal dimensions of plant parts, such as the canopy, the stem, and the root system, as well as the changes in spatial properties during the vegetation period and tree life. Such properties relate for example, to canopy storage capacity with effects on water redistribution processes in forest ecosystems. Spatial and/or temporal variations in resource distribution affect patterns of plant communities, tree seedling establishment, and soil biogeochemical processes. Studies on ecosystem processes are therefore directly or indirectly related to the consideration of spatial and or temporal dependencies of observations. This chapter aims to show some approaches how heterogeneity of model residuals and correlations among observations can be assessed, described, and considered in empirical model building processes. Using an exemplary dataset on throughfall measurements, we demonstrate how linear and nonlinear mixed effects models can be applied and adapted to fulfill general model assumptions and to explore relationships of factors and variables. This chapter uses the same dataset as Chap.  7 and provides an electronic supplement including the sample dataset as well as fully documented computer code, which aims to serve as a guideline for conducting data analysis using the statistical software environment R.

Supplementary material

464883_1_En_8_MOESM1_ESM.r (46 kb)
groupedData_Test_v1 (R 46 kb)
464883_1_En_8_MOESM2_ESM.txt (1.1 mb)
throughfall_dataset_extended (TXT 1088 kb)


  1. Akaike H (1998) Information theory and an extension of the maximum likelihood principle. In: Akaike H, Parzen E, Tanabe K, Kitagawa G (eds) Selected papers of Hirotugu Akaike. Springer, New York, pp 199–213CrossRefGoogle Scholar
  2. Allen ST, Brooks JR, Keim RF, Bond BJ, McDonnell JJ (2014) The role of pre-event canopy storage in throughfall and stemflow by using isotopic tracers. Ecohydrology 7:858–868. CrossRefGoogle Scholar
  3. Allen ST, Keim RF, Barnard HR, McDonnell JJ, Brooks JR (2017) The role of stable isotopes in understanding rainfall interception processes: a review. WIREs Water 4:1–17. CrossRefGoogle Scholar
  4. Canham CD, Finzi AC, Pacala SW, Burbank DH (1994) Causes and consequences of resource heterogeneity in forests: interspecific variation in light transmission by canopy trees. Can J For Res 24:337–349. CrossRefGoogle Scholar
  5. Carl G, Kühn I (2007) Analyzing spatial autocorrelation in species distributions using Gaussian and logit models. Ecol Model 207:159–170. CrossRefGoogle Scholar
  6. Carlyle-Moses DE, Iida S, Germer S, Llorens P, Michalzik B, Nanko K et al (2018) Expressing stemflow commensurate with its ecohydrological importance. Adv Water Resour 121:472–479. CrossRefGoogle Scholar
  7. Carlyle-Moses DE, Laureano JSF, Price AG (2004) Throughfall and throughfall spatial variability in Madrean oak forest communities of northeastern Mexico. J Hydrol 297:124–135. CrossRefGoogle Scholar
  8. Chapin FS, Matson PA, Vitousek PM (2011) Principles of terrestrial ecosystem ecology, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  9. Crawley MJ (2013) The R book, 2nd edn. Wiley, ChichesterGoogle Scholar
  10. Dale MRT (2007) Spatial pattern analysis in plant ecology. Cambridge University Press, CambridgeGoogle Scholar
  11. Dale MRT, Fortin M-J (2015) Spatial analysis: a guide for ecologists, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  12. Engel M, Körner M, Berger U (2018) Plastic tree crowns contribute to small-scale heterogeneity in virgin beech forests—an individual-based modeling approach. Ecol Model 376:28–39. CrossRefGoogle Scholar
  13. Ford ED, Deans JD (1978) The effects of canopy structure on stemflow, throughfall and interception loss in a young Sitka spruce plantation. J Appl Ecol 15:905–917. CrossRefGoogle Scholar
  14. Frischbier N (2012) Study on the single-tree related small-scale variability and quantity-dependent dynamics of net forest precipitation using the example of two mixed beech-spruce stands. Dissertation. TUD Press, Dresden, GermanyGoogle Scholar
  15. Frischbier N, Wagner S (2015) Detection, quantification and modelling of small-scale lateral translocation of throughfall in tree crowns of European beech (Fagus sylvatica L.) and Norway spruce (Picea abies (L.) Karst.). J Hydrol 522:228–238. CrossRefGoogle Scholar
  16. Haining RP (2009) Spatial data analysis: theory and practice, 6th edn. Cambridge University Press, CambridgeGoogle Scholar
  17. Hefley TJ, Broms KM, Brost BM, Buderman FE, Kay SL, Scharf HR et al (2017) The basis function approach for modeling autocorrelation in ecological data. Ecology 98:632–646. CrossRefGoogle Scholar
  18. Hurlbert SH (1984) Pseudoreplication and the design of ecological field experiments. Ecol Monogr 54:187–211. CrossRefGoogle Scholar
  19. Keim RF, Link TE (2018) Linked spatial variability of throughfall amount and intensity during rainfall in a coniferous forest. Agric For Meteorol 248:15–21. CrossRefGoogle Scholar
  20. Keim RF, Skaugset AE, Weiler M (2005) Temporal persistence of spatial patterns in throughfall. J Hydrol 314:263–274. CrossRefGoogle Scholar
  21. Kellner KF, Swihart RK (2017) Simulation of oak early life history and interactions with disturbance via an individual-based model, SOEL. PLoS One 12:e0179643. CrossRefGoogle Scholar
  22. Kissling WD, Carl G (2008) Spatial autocorrelation and the selection of simultaneous autoregressive models. Glob Ecol Biogeogr 17:59–71. CrossRefGoogle Scholar
  23. Legendre P, Gauthier O (2014) Statistical methods for temporal and space-time analysis of community composition data. Proc R Soc B Biol Sci 281:20132728. CrossRefGoogle Scholar
  24. Marin CT, Bouten W, Sevink J (2000) Gross rainfall and its partitioning into throughfall, stemflow and evaporation of intercepted water in four forest ecosystems in western Amazonia. J Hydrol 237:40–57. CrossRefGoogle Scholar
  25. Metzger JC, Wutzler T, Dalla Valle N, Filipzik J, Grauer C, Lehmann R et al (2017) Vegetation impacts soil water content patterns by shaping canopy water fluxes and soil properties. Hydrol Process 31:3783–3795. CrossRefGoogle Scholar
  26. Mou P, Mitchell RJ, Jones RH (1993) Ecological field theory model: a mechanistic approach to simulate plant–plant interactions in southeastern forest ecosystems. Can J For Res 23:2180–2193. CrossRefGoogle Scholar
  27. Müller J (2009) Forestry and water budget of the lowlands in northeast Germany — consequences for the choice of tree species and for forest management. J Water Land Dev 13a:133–148. CrossRefGoogle Scholar
  28. Okland RH, Rydgren K, Okland T (1999) Single-tree influence on understorey vegetation in a Norwegian boreal spruce forest. Oikos 87:488–498. CrossRefGoogle Scholar
  29. Peters R, Lin Y, Berger U (2016) Machine learning meets individual-based modelling. Self-organising feature maps for the analysis of below-ground competition among plants. Ecol Model 326:142–151. CrossRefGoogle Scholar
  30. Pinheiro J, Bates D, DebRoy S, Sarkar D (2013) nlme: linear and nonlinear mixed effects models. R core teamGoogle Scholar
  31. Pinheiro JC, Bates DM (2000) Mixed-effects models in sand S-PLUS. Springer, New YorkCrossRefGoogle Scholar
  32. Popper KR (2002) Conjectures and refutations: the growth of scientific knowledge. Routledge, LondonGoogle Scholar
  33. Pukkala T, Kolström T (1992) A stochastic spatial regeneration model for Pinus sylvestris. Scand J For Res 7:377–385. CrossRefGoogle Scholar
  34. R core team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  35. Reifsnyder WE, Furnival GM, Horowitz JL (1971) Spatial and temporal distribution of solar radiation beneath forest canopies. Agric For Meteorol 9:21–37. CrossRefGoogle Scholar
  36. Roberts DR, Bahn V, Ciuti S, Boyce MS, Elith J, Guillera-Arroita G et al (2017) Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography 40:913–929. CrossRefGoogle Scholar
  37. Saetre P, Bååth E (2000) Spatial variation and patterns of soil microbial community structure in a mixed spruce-birch stand. Soil Biol Biochem 32:909–917. CrossRefGoogle Scholar
  38. Saetre P, Saetre LS, Brandtberg P-O, Lundkvist H, Bengtsson J (1997) Ground vegetation composition and heterogeneity in pure Norway spruce and mixed Norway spruce – birch stands. Can J For Res 27:2034–2042. CrossRefGoogle Scholar
  39. Schielzeth H, Nakagawa S (2013) Nested by design: model fitting and interpretation in a mixed model era. Methods Ecol Evol 4:14–24. CrossRefGoogle Scholar
  40. Schume H, Jost G, Katzensteiner K (2003) Spatio-temporal analysis of the soil water content in a mixed Norway spruce (Picea abies (L.) Karst.)–European beech (Fagus sylvatica L.) stand. Geoderma 112:273–287. CrossRefGoogle Scholar
  41. Wälder K, Frischbier N, Bredemeier M, Näther W, Wagner S (2008) Analysis of Of-layer humus mass variation in a mixed stand of European beech and Norway spruce: an application of structural equation modelling. Ecol Model 213:319–330. CrossRefGoogle Scholar
  42. Wälder K, Näther W, Wagner S (2009) Improving inverse model fitting in trees—anisotropy, multiplicative effects, and Bayes estimation. Ecol Model 220:1044–1053. CrossRefGoogle Scholar
  43. Weber P, Bardgett RD (2011) Influence of single trees on spatial and temporal patterns of belowground properties in native pine forest. Soil Biol Biochem 43:1372–1378. CrossRefGoogle Scholar
  44. Webster R (2001) Statistics to support soil research and their presentation. Eur J Soil Sci 52:331–340. CrossRefGoogle Scholar
  45. Wu H-I, Sharpe PJH, Walker J, Penridge LK (1985) Ecological field theory: a spatial analysis of resource interference among plants. Ecol Model 29:215–243. CrossRefGoogle Scholar
  46. Zimmermann A, Germer S, Neill C, Krusche AV, Elsenbeer H (2008) Spatio-temporal patterns of throughfall and solute deposition in an open tropical rain forest. J Hydrol 360:87–102. CrossRefGoogle Scholar
  47. Zimmermann B, Elsenbeer H (2008) Spatial and temporal variability of soil saturated hydraulic conductivity in gradients of disturbance. J Hydrol 361:78–95. CrossRefGoogle Scholar
  48. Zuur AF, Ieno EN, Saveliev AA (2017) Beginner’s guide to spatial, temporal, and spatial-temporal ecological data analysis with R-INLA, vol 7. Highland Statistics Ltd, NewburghGoogle Scholar
  49. Zuur AF, Ieno EN, Walker N, Saveliev AA, Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, New YorkCrossRefGoogle Scholar
  50. Zwanzig M, Schlicht R, Frischbier N, Berger U (2019) Primary steps in analyzing data: tasks and tools for a systematic data exploration. In: Levia DF, Carlyle-Moses DE, Iida S, Michalzik B, Nanko K and Tischer A (Eds.), Forest-Water Interactions. Ecological Studies Series, No. 240, Springer-Verlag, Heidelberg, Germany.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alexander Tischer
    • 1
    Email author
  • Martin Zwanzig
    • 2
  • Nico Frischbier
    • 3
  1. 1.Institute of GeographyFriedrich Schiller University JenaJenaGermany
  2. 2.Institute of Forest Growth and Forest Computer SciencesTechnische Universität DresdenTharandtGermany
  3. 3.Forestry Research and Competence CentreGothaGermany

Personalised recommendations