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Spatial and Temporal Variability of SPAS Attributes: Analysis of Spatial and Temporal Series

  • Klaus Reichardt
  • Luís Carlos Timm
Chapter

Abstract

Spatial and temporal variability of the soil-plant-atmosphere system is an important tool for the statistical analysis of several sets of data collected in the field. The techniques here seen allow the scientist to reveal characteristics of systems that cannot be analyzed by classical statistics methods. Various tools are presented, like the cross-correlogram, calculation of number of samples to be collected, spectral analysis, wavelets, and spectra. An introduction to multivariate analysis (wavelet analysis and multivariate empirical mode decomposition method) is given. A very extended analysis is made of the state-space methodology, introducing the matrix of coefficients and the matrix of observations. The Kalman Filter is also demonstrated in the context of the state-space analysis. Two approaches used in the state-space analysis are shown in detail with several practical examples: Shumway’s approach and West and Harrison’s approach.

References

  1. Addison PS (2017) The illustrated wavelet transform handbook: introduction, theory and applications in science, engineering, medicine and finance, 2nd edn. CRC Press, Boca Raton, FLGoogle Scholar
  2. Alemi MH, Shahriari MR, Nielsen DR (1988) Kriging and cokriging of soil water properties. Soil Technol 1:117–132CrossRefGoogle Scholar
  3. Ameen JRM, Harrison PJ (1984) Discount weighted estimation. J Forec 3:285–296CrossRefGoogle Scholar
  4. Aquino LS, Timm LC, Reichardt K, Barbosa EP, Parfitt JMB, Nebel ALC, Penning LH (2015) State-space approach to evaluate effects of land levelling on the spatial relationships of soil properties of a lowland area. Soil Tillage Res 145:135–147CrossRefGoogle Scholar
  5. Awe GO, Reichert JM, Timm LC, Wendroth O (2015) Temporal processes of soil water status in a sugarcane field under residue management. Plant and Soil 387:395–411CrossRefGoogle Scholar
  6. Bazza M, Shumway RH, Nielsen DR (1988) Two-dimensional spectral analyses of soil surface temperature. Hilgardia 56:1–28CrossRefGoogle Scholar
  7. Beskow S, Timm LC, Tavares VEQ, Caldeira TL, Aquino LS (2016) Potential of the LASH model for water resources management in data-scarce basins: a case study of the Fragata river basin, southern Brazil. Hydrol Sci J 61:2567–2578CrossRefGoogle Scholar
  8. Biswas A (2018) Scale–location specific soil spatial variability: a comparison of continuous wavelet transform and Hilbert–Huang transform. Catena 160:24–31CrossRefGoogle Scholar
  9. Biswas A, Si BC (2011) Application of continuous wavelet transform in examining soil spatial variation: a review. Math Geosci 43:379–396CrossRefGoogle Scholar
  10. Bremner JM (1960) Determination of nitrogen in soil by the Kjeldahl method. J Agric Sci 55:11–33CrossRefGoogle Scholar
  11. Brillinger DR (2001) Time series: data analysis and theory. Society for Industrial and Applied Mathematics, Philadelphia, PACrossRefGoogle Scholar
  12. Chatfield C (2004) The analysis of time series: an introduction, 6th edn. Chapman & Hall/CRC, Boca Raton, FLGoogle Scholar
  13. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Statist Soc Ser B 39:1–38Google Scholar
  14. Deutsch CV, Journel AG (1992) GSLIB. Geostatistical software library and user’s guide. Oxford University Press, New York, NYGoogle Scholar
  15. Dourado-Neto D, Timm LC, Oliveira JCM, Reichardt K, Bacchi OOS, Tominaga TT, Cassaro FAM (1999) State-space approach for the analysis of soil water content and temperature in a sugarcane crop. Sci Agric 56:1215–1221CrossRefGoogle Scholar
  16. Farge M (1992) Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 24:395–457CrossRefGoogle Scholar
  17. Flandrin P (2018) Explorations in time-frequency analysis. Cambridge University Press, Padstow CornwallCrossRefGoogle Scholar
  18. Gelb A (1974) Applied optimal estimation. Massachusetts Institute of Technology Press, Cambridge, MAGoogle Scholar
  19. Graps A (1995) An introduction to wavelets. IEEE Comp Sci Eng 2:50–61CrossRefGoogle Scholar
  20. Grinsted A, Moore JC, Jevrejeva S (2004) Application of cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes Geophys 11:561–566CrossRefGoogle Scholar
  21. Harrison PJ, Stevens CF (1976) Bayesian forecasting (with discussion). J R Statist Soc Ser B 38:205–267Google Scholar
  22. Hu W, Si BC (2013) Soil water prediction based on its scale-specific control using multivariate empirical mode decomposition. Geoderma 193-194:180–188CrossRefGoogle Scholar
  23. Hu W, Si BC (2016a) Multiple wavelet coherence for untangling scale-specific and localized multivariate relationships in geosciences. Hydrol Earth Syst Sci 20:3183–3191CrossRefGoogle Scholar
  24. Hu W, Si BC (2016b) Multiple wavelet coherence for untangling scale-specific and localized multivariate relationships in geosciences. Suppl Hydrol Earth Syst Sci 20:3183–3191CrossRefGoogle Scholar
  25. Huang NE, Shen Z, Long SR, Wu MLC, Shih HH, Zheng QN, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser AA 454:903–995CrossRefGoogle Scholar
  26. Hubbard BB (1998) The world according to wavelets: the story of a mathematical technique in the making, 2nd edn. A K Peters Ltd, Natick, MACrossRefGoogle Scholar
  27. Hui S, Wendroth O, Parlange MB, Nielsen DR (1998) Soil variability – infiltration relationships of agroecosystems. J Balkan Ecol 1:21–40Google Scholar
  28. James JF (2011) A student’s guide to Fourier transforms with applications in physics and engineering, 3rd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  29. Kalman RE (1960) A new approach to linear filtering and prediction theory. Trans ASME J Basic Eng 8:35–45CrossRefGoogle Scholar
  30. Katul GG, Wendroth O, Parlange MB, Puente CE, Folegatti MV, Nielsen DR (1993) Estimation of in situ hydraulic conductivity function from nonlinear filtering theory. Water Resour Res 29:1063–1070CrossRefGoogle Scholar
  31. Liu ZP, Shao MA, Wang YQ (2012) Estimating soil organic carbon across a large-scale region: a state-space modeling approach. Soil Sci 177:607–618CrossRefGoogle Scholar
  32. McGraw T (1994) Soil test level variability in Southern Minnesota. Better Crops Pot Phosp Inst 78:24–25Google Scholar
  33. Nielsen DR, Alemi MH (1989) Statistical opportunities for analyzing spatial and temporal heterogeneity of field soils. Plant and Soil 115:285–296CrossRefGoogle Scholar
  34. Nielsen DR, Wendroth O (2003) Spatial and temporal statistics – sampling field soils and their vegetation. Catena Verlag, Cremlingen-DesdedtGoogle Scholar
  35. Ogunwole JO, Timm LC, Ugwu-Obidike EO, Gabriels DM (2014a) State-space estimation of soil organic carbon stock. Int Agroph 28:185–194CrossRefGoogle Scholar
  36. Ogunwole JO, Obidike EO, Timm LC, Odunze AC, Gabriels DM (2014b) Assessment of spatial distribution of selected soil properties using geospatial statistical tools. Commun Soil Sci Plant Anal 45:2182–2200CrossRefGoogle Scholar
  37. Plackett RL (1950) Some theorems in least squares. Biometrika 37:149–157PubMedCrossRefGoogle Scholar
  38. Pole A, West M, Harrison J (1994) Applied Bayesian forecasting and time series analysis. Chapman & Hall, LondonCrossRefGoogle Scholar
  39. Rehman N, Mandic DP (2009) Empirical mode decomposition. Matlab code and data. http://www.commsp.ee.ic.ac.uk/~mandic/research/emd.htm.Google Scholar
  40. Rehman N, Mandic DP (2010) Multivariate empirical mode decomposition. Proc R Soc A 466:1291–1302CrossRefGoogle Scholar
  41. She DL, Liu DD, Peng SZ, Shao MA (2013) Multiscale influences of soil properties on soil water content distribution in a watershed on the Chinese Loess Plateau. Soil Sci 178:530–539CrossRefGoogle Scholar
  42. She DL, Tang SQ, Shao MA, Yu SE, Xia YQ (2014a) Characterizing scale specific depth persistence of soil water content along two landscape transects. J Hydrol 519:1149–1161CrossRefGoogle Scholar
  43. She DL, Xuemei G, Jingru S, Timm LC, Hu W (2014b) Soil organic carbon estimation with topographic properties in artificial grassland using a state-space modeling approach. Can J Soil Sci 94:503–514CrossRefGoogle Scholar
  44. She DL, Zheng JX, Shao MA, Timm LC, Xia YQ (2015) Multivariate empirical mode decomposition derived multi-scale spatial relationships between saturated hydraulic conductivity and basic soil properties. Clean Soil Air Water 43:910–918CrossRefGoogle Scholar
  45. She DL, Fei YH, Chen Q, Timm LC (2016) Spatial scaling of soil salinity indices along a temporal coastal reclamation area transect in China using wavelet analysis. Arch Agron Soil Sci 62:1625–1639CrossRefGoogle Scholar
  46. She DL, Qiana C, Timm LC, Beskow S, Hu W, Caldeira TL, Oliveira LM (2017) Multi-scale correlations between soil hydraulic properties and associated factors along a Brazilian watershed transect. Geoderma 286:15–24CrossRefGoogle Scholar
  47. Shumway RH (1988) Applied statistical time series analyses. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  48. Shumway RH, Stoffer DS (1982) An approach to time series smoothing and forecasting using the EM algorithm. J Time Ser Anal 3:253–264CrossRefGoogle Scholar
  49. Shumway RH, Stoffer DS (2000) Time series analysis and its applications. Springer, New York, NYCrossRefGoogle Scholar
  50. Shumway RH, Stoffer DS (2011) Time series analysis and its applications with R examples, 3rd edn. Springer, New York, NYCrossRefGoogle Scholar
  51. Shumway RH, Stoffer DS (2017) Time series analysis and its applications with R examples, 4th edn. Springer, New York, NYCrossRefGoogle Scholar
  52. Shumway RH, Biggar JW, Morkoc F, Bazza M, Nielsen DR (1989) Time-and frequency-domain analyses of field observations. Soil Sci 147:286–298CrossRefGoogle Scholar
  53. Si BC (2008) Spatial scaling analyses of soil physical properties: a review of spectral and wavelet methods. Vadose Zone J 7:547–562CrossRefGoogle Scholar
  54. Si BC, Zeleke TB (2005) Wavelet coherency analysis to relate saturated hydraulic properties to soil physical properties. Water Resour Res 41:W11424CrossRefGoogle Scholar
  55. Stevenson FC, Knight JD, Wendroth O, Van Kessel C, Nielsen DR (2001) A comparison of two methods to predict the landscape-scale variation of crop yield. Soil Tillage Res 58:163–181CrossRefGoogle Scholar
  56. Timm LC, Fante Júnior L, Barbosa EP, Reichardt K, Bacchi OOS (2000) Interação solo-planta avaliada por modelagem estatística de espaço de estados. Sci Agric 57:751–760CrossRefGoogle Scholar
  57. Timm LC, Reichardt K, Oliveira JCM, Cassaro FAM, Tominaga TT, Bacchi OOS, Dourado-Neto D, Nielsen DR (2001) State-space approach to evaluate the relation between soil physical and chemical properties. Czech Society of Soil Science and Soil Science Society of America, PragueGoogle Scholar
  58. Timm LC, Reichardt K, Oliveira JCM, Cassaro FAM, Tominaga TT, Bacchi OOS, Dourado-Neto D (2003a) Sugarcane production evaluated by the state–space approach. J Hydrol 272:226–237CrossRefGoogle Scholar
  59. Timm LC, Barbosa EP, Souza MD, Dynia JF, Reichardt K (2003b) State-space analysis of soil data: an approach based on space-varying regression models. Sci Agric 60:371–376CrossRefGoogle Scholar
  60. Timm LC, Reichardt K, Oliveira JCM, Cassaro FAM, Tominaga TT, Bacchi OOS, Dourado-Neto D (2003c) State-space approach for evaluating the soil–plant–atmosphere system. In: Achyuthan H (ed) Soil and soil physics in continental environment. Allied Publishers Private Limited, Chennai, pp 23–81Google Scholar
  61. Timm LC, Reichardt K, Oliveira JCM, Cassaro FAM, Tominaga TT, Bacchi OOS, Dourado-Neto D, Nielsen DR (2004) State-space approach to evaluate the relation between soil physical and chemical properties. Braz J Soil Sci 28:49–58Google Scholar
  62. Timm LC, Pires LF, Roveratti R, Arthur RCJ, Reichardt K, Oliveira JCM, Bacchi OOS (2006a) Field spatial and temporal patterns of soil water content and bulk density changes. Sci Agric 63:55–64CrossRefGoogle Scholar
  63. Timm LC, Gomes DT, Barbosa EP, Reichardt K, Souza MD, Dynia JF (2006b) Neural network and state-space models for studying relationships among soil properties. Sci Agric 63:386–395CrossRefGoogle Scholar
  64. Timm LC, Dourado-Neto D, Bacchi OOS, Hu W, Bortolotto RP, Silva AL, Bruno IP, Reichardt K (2011) Temporal variability of soil water storage evaluated for a coffee field. Aust J Soil Res 49:77–86CrossRefGoogle Scholar
  65. Timm LC, Reichardt K, Lima CLR, Aquino LA, Penning LH, Dourado-Neto D (2014) State-space approach to understand Soil-Plant-Atmosphere relationships. In: Teixeira WG, Ceddia MB, Ottoni MV, Donnagema GK (eds) Application of soil physics in environmental analysis: measuring, modelling and data integration. Springer, New York, NY, pp 91–129Google Scholar
  66. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78CrossRefGoogle Scholar
  67. Tukey JW (1980) Can we predict where ‘Time Series’ should go next? In: Brillinger DR, Tiao GC (eds) Directions in time series. Institute of Mathematical Statistics, Hayward, CA, pp 1–31Google Scholar
  68. Walkey A, Black IA (1934) An examination of the Degtjareff method for determining soil organic matter and a proposed modifications of the chromic acid titration method. Soil Sci 37:29–38CrossRefGoogle Scholar
  69. Warrick AW, Nielsen DR (1980) Spatial variability of soil physical properties in the field. In: Hillel D (ed) Applications of soil physics. Academic Press, New York, NY, pp 319–344CrossRefGoogle Scholar
  70. Wendroth O (2013) Soil variability. In: Lazarovitch N, Warrick AW (eds) Exercises in soil physics. Catena Verlag, Reiskirchen, pp 292–332Google Scholar
  71. Wendroth O, Al Omran AM, Kirda K, Reichardt K, Nielsen DR (1992) State-space approach to spatial variability of crop yield. Soil Sci Soc Am J 56:801–807CrossRefGoogle Scholar
  72. Wendroth O, Katul GG, Parlange MB, Puente CE, Nielsen DR (1993) A nonlinear filtering approach for determining hydraulic conductivity functions. Soil Sci 156:293–301CrossRefGoogle Scholar
  73. Wendroth O, Reynolds WD, Vieira SR, Reichardt K, Wirth S (1997) Statistical approaches to the analysis of soil quality data. In: Gregorich EG, Carter MR (eds) Soil quality for crop production and ecosystem health. Elsevier Science, Amsterdam, pp 247–276CrossRefGoogle Scholar
  74. Wendroth O, Jürschik P, Giebel A, Nielsen DR (1998) Spatial statistical analysis of on-site-crop yield and soil observations for site-specific management. In: International Conference on Precision Agriculture. American Society of Agronomy/Crop Science Society of America/Soil Science Society of America, Saint Paul, MN, pp 159–170Google Scholar
  75. Wendroth O, Jürschik P, Kersebaum KC, Reuter H, Van Kessel C, Nielsen DR (2001) Identifying, understanding, and describing spatial processes in agricultural landscapes – four case studies. Soil Tillage Res 58:113–127CrossRefGoogle Scholar
  76. Wendroth O, Koszinski S, Vasquez V (2011) Soil spatial variability. In: Huang PM, Li Y, Sumner ME (eds) Handbook of soil science, 2nd edn. CRC Press, Boca Raton, FL, pp 10.1–10.25Google Scholar
  77. Wendroth O, Yang Y, Timm LC (2014) State-space analysis in soil physics. In: Teixeira WG, Ceddia MB, Ottoni MV, Donnagema GK (eds) Application of soil physics in environmental analysis: measuring, modelling and data integration. Springer, New York, NY, pp 53–74Google Scholar
  78. West M, Harrison J (1989) Bayesian forecasting and dynamic models, 1st edn. Springer, LondonCrossRefGoogle Scholar
  79. West M, Harrison J (1997) Bayesian forecasting and dynamic models, 2nd edn. Springer, LondonGoogle Scholar
  80. Yang Y, Wendroth O (2014) State-space approach to field-scale bromide leaching. Geoderma 217-218:161–172CrossRefGoogle Scholar
  81. Yang Y, Wendroth O, Walton RJ (2013) Field-scale bromide leaching as affected by land use and rain characteristics. Soil Sci Soc Am J 77:1157–1167CrossRefGoogle Scholar
  82. Yang Y, Wendroth O, Walton RJ (2016) Temporal dynamics and stability of spatial soil matric potential in two land use systems. Vadose Zone J 15:1–15CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Klaus Reichardt
    • 1
  • Luís Carlos Timm
    • 2
  1. 1.Centro de Energia Nuclear na Agricultura and Escola Superior de Agricultura “Luiz de Queiróz”University of Sao PauloPiracicabaBrazil
  2. 2.Rural Engineering Department, Faculty of AgronomyFederal University of PelotasCapão do LeãoBrazil

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