Predicting magnesium concentration in needles of Silver fir and Norway spruce-a case study

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Monica Musio, a, , , Nicole Augustind, Hans-Peter Kahleb, Andreas Krallc, Edgar Kublinc, Rüdiger Unseldb and Klaus von Wilpertc

a Freiburg Centre for Data Analysis and Modelling, University of Freiburg, Eckerstr. 1, Freiburg D-79104, Germany

b Institute for Forest Growth, University of Freiburg, Tennenbacherstr. 4, Freiburg D-79085, Germany

c Forest Research Centre Baden-Württemberg, Wonnhaldestr. 4, D-79100, Freiburg/Br., Germany

d Department of Statistics, The University of Glasgow, 6128QQ, UK

Received 1 October 2002; Revised 13 January 2004; accepted 17 February 2004. Available online 31 July 2004.

Abstract
Different geostatistical methods are used to interpolate the spatial distribution of the foliar magnesium content of Silver fir and Norway spruce in the Black Forest. The data analysed are from a monitoring survey carried out in 1994 in the forest of Baden-Württemberg, a federal state in the south-west region of Germany. In this survey many potential explanatory variables are collected. The aim of this paper is to identify the best prediction method that can be useful in the future for cause-effect studies and environmental modelling. At the same time, causal relationships between the response variable and the predictors are investigated. Therefore, geostatistical methods with lowest prediction errors which simultaneously provide the highest explanation value had to be identified. The performance of different methods is measured using cross-validations techniques.

Author Keywords: Kriging; Geostatistics; Spatial prediction; Spatial statistics; Linear model; Foliar magnesium content; Black Forest; Norway spruce; Silver fir

Article Outline
1. Introduction
2. The data
3. Statistical methods
3.1. Model with independent errors
3.2. Geostatistical methods
3.3. Ordinary kriging and lognormal kriging
3.4. Universal kriging and kriging with external drift
3.5. Cokriging
3.6. Cross-validation
4. Data analysis and results for the magnesium in the needles
4.1. Exploratory analysis
4.2. Model with independent errors results
4.3. Cross-validations results
5. Discussion
Acknowledgements
References

Fig. 1. Scheme of the goals and abilities of the different methods used for evaluation.

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Fig. 2. Overview map. The area of the Black Forest grey shaded. The position of sampling points are marked with crosses and dots.

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Fig. 3. The empirical semi-variogram of log(Mg) with fitted semi-variogram models using maximum likelihood (ML) and the fit by eye.

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Fig. 4. Empirical and fitted semi-variogram of the residuals of model (10).

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Fig. 5. Cross-semivariogram models fitted for the cokriging.

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Table 1. Correlation between the response variable log(Mg) and possible explanatory variables containing tree specific characteristics calcium (Ca), manganese (Mn), potassium (K), phosphorus (P), nitrogen (N), age (BAlter) and tree type (BArt)

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Table 2. Correlation between the response variable log(Mg) and possible explanatory variables containing geographic and stand conditions, x-co-ordinate (Rechts), y-co-ordinate (Hoch), soil depth (Gruend) trophic class of the soil (Naehr), relief (GForm ), soil type (BTyp) and altitude (HoehenL)

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Table 3. Parameter estimates for the selected model with independent errors (drift parameters of KED)

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Table 4. Estimates of covariance parameters for OK, KED and UK

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Table 5. Mean squared prediction error for log(Mg) from the model with independent errors, ordinary kriging (OK), universal kriging (UK), kriging with external drift (KED) and cokriging (CK)