http://www.fao.org/globalsoilpartnership This presentation was made during Regional Conference on the Asian Soil Partnership that took place in Nanjing, China 08-11 Febraury 2012.The presentation was made by Dar-Yuan Lee, Kai , Kai-Wei Juang Juang, and Ten , Ten-Lin Liu Liu, and it presents Using Kriging Combined with Categorical Information of Soil Maps for Interpolating Soil Propertiesfor Properties. ©FAO: http://www.fao.org

1. UsingUsing KrigingKriging Combined withCombined with
Categorical Information of Soil MapsCategorical Information of Soil Maps
for Interpolating Soil Propertiesfor Interpolating Soil Properties
DarDar--Yuan Lee*Yuan Lee*11, Kai, Kai--WeiWei JuangJuang22, and Ten, and Ten--Lin LiuLin Liu33
1 Department of Agricultural Chemistry, National Taiwan University
2 Department of Agronomy, National Chiayi University
3 Tea Research and Extension Station, Taiwan

2. IntroductionIntroduction
Kriging interpolation is frequently used for
mapping soil properties in the analysis and
interpretation of spatial variation of soil.
Mapping quality could affect the performance of
site-specific management.
Soil map–delineation in existing soil maps
showing abrupt changes at the boundaries
between different soil types can provide
valuable categorical information for interpreting
variation in soil properties.

3. IntroductionIntroduction (continued)(continued)
In this study, map units were used to group sampled
observations, and the variation in soil properties was
separated into two parts: (i) between soil types (i.e., soil
type effect) and (ii) within each soil type (i.e., residual).
A kriging model combined with the information of soil
map–delineation, taking into account the variation
components of soil type effect and residual, was
proposed.
A comparison of performance of kriging combined with
soil map–delineation (KSMD) and ordinary kriging (OK)
was performed to assess the feasibility of KSMD for
improving the interpolation of soil properties.

4. MethodologyMethodology
The notation of (Aj) was used to quantify the information
of soil map–delineation as nominal data. The
observations are denoted with the same soil type (j).
Thus, each observation zj(xi) on one specific soil
property can be expressed as
where xij is the sampling location of z(xij), which is on the
polygon Aj. s(Aj) is the mean value of z(xij) over the
polygon Aj, and r(xij) is the residual.
z (xij) = s(Aj) + r(xij),

5. MethodologyMethodology (continued)(continued)
As s(Aj) and r(xij) are independent mutually and the
variation of r(xij) is assumed to be homogeneous over all
polygons. The variance σ2
z of z(xij) can be shown as:
rsz
222
σσσ +=
where the variance σ2
s indicates the spatial variation
between polygons. The variance σ2
r shows the overall
variation within polygons, which is defined homogeneously
as the intrinsic stationarity is assumed for kriging
estimation.

6. MethodologyMethodology (continued)(continued)
If the variance σ2
z of z(xij) is not as stationary as σ2
r
showing the variation of r(xij) within polygons, kriging
estimation will be more suitable on the variable
domain of r(xij) than that of z(xij).
A new approach, Kriging combined with soil map-
delineation (KSMD), for spatial interpolation of soil
properties was proposed.

7. sill
range
nugget
h
γ(h)
Semivariance: γ(h) = ½ Var[z(x+h) - z(x)]
=
−+=
N(h)
1i
ii
2^
)]z(xh)[z(x
2N(h)
1
(h)γ Σ
Commonly used interpolation: OrdinaryCommonly used interpolation: Ordinary krigingkriging

8. z(x1)
z(x2)
z(x3)
z(x4)
z(x5)
z(x6)
z(x7)z(x8)
z(xo) =?
z*(xo) = z(x1)λ1+z(x2)λ2+z(x3)λ3+z(x4)λ4
+ z(x5)λ5+z(x6)λ6+z(x7)λ7+z(x8)λ8
Commonly used interpolation: OrdinaryCommonly used interpolation: Ordinary krigingkriging
(continued)(continued)

9. KrigingKriging combined with soil mapcombined with soil map––delineationdelineation
(KSMD) vs. Ordinary(KSMD) vs. Ordinary krigingkriging (OK)(OK)
KSMD estimations
KSMD
The mean
value of each
soil type s(Aj)
The residual
r(xj)
Theoretical
assumption
Ok estimations
OK

10. The study site about 20 ha in
area, located at Changhua
county in mid-western
Taiwan
Case studyCase study
Changhua
TAIWAN

11. Chunliao (Cl, 0.77 ha)
Tingfanp (Ti, 3.86 ha)
Wanhoh (Wa, 7.15 ha)
Yuliao (Yl, 2.47 ha)
48 locations for sampling but not for validation
127 locations both for sampling and validation
Sampling locations: 175
N
Soil map classification and sampling configurationSoil map classification and sampling configuration

12. Statistics for soil textureStatistics for soil texture

13. Statistics for pH, M3Statistics for pH, M3--P, and M3P, and M3--CaCa

14. Analysis of variance (ANOVA) for soil type effectsAnalysis of variance (ANOVA) for soil type effects

15. The results of ANOVA showed that soil type effects were
significant on soil texture, pH, and M3-Ca, but not on M3-P.
Because soil texture, pH and soil calcium are dominated by
geological and pedological features, so the variation of their
observed data is significantly related to soil map-delineation.
In contrast, the soil P is usually influenced by historical practices
and fertilizer applications. Thus, the soil map-delineation is not
significant to the data of M3-P.
Soil type effect

16. h (meters) h (meters)
Original value: Z(x)
Residual: r(x)
VariogramsVariograms for soil texture, pH, M3for soil texture, pH, M3--P, and M3P, and M3--CaCa

17. Spatial structures of residuals vs. original values for
M3-P
The variograms of residuals r(xij) and original
values z(xij) for M3-P were much the same.
This indicated that soil types were not the main
sources of the spatial variation of M3-P.
This phenomenon was consistent with the
ANOVA testing and shows that the mean values
s(Aj) of M3-P between soil types were not
different significantly.

18. Spatial structures of residuals vs. original values for
soil texture, pH, and M3-Ca
For soil texture, pH, and M3-Ca, the variograms showed
that the spatial structures of the residuals r(xij) were
obviously different from those of the original values z(xij).
This indicates that the data of these soil properties were
not stationary over the whole site. The contribution of the
mean values s(Aj) of the soil types (called a local trend
effect) to the spatial variation of z(xij) was sufficiently
substantial to influence the kiging estimation.
It is necessary to come up with a derived method that
takes into account the local trend effect (i.e. soil type
effect) for spatial interpolation of these soil properties.

19. Subset: 30 locations
Random selection
Estimated values at 127
locations
OK and KSMD estimations
One iteration
1000 iterations
1000 mappings
respectively from OK and
KSMD estimations
Data set: 175 locations
Simulation procedure for OK and KSMD estimationsSimulation procedure for OK and KSMD estimations

20. OK mapping KSMD mapping
One realization for 30 sample values of M3One realization for 30 sample values of M3--CaCa
randomly drawn from the 175 observationsrandomly drawn from the 175 observations

21. Imprecision index:
)(xME)(xRMSE)(xIP o
2
o
2
o
2
−=
∑=
−=
1000
1i
ooio )]Z(x)(x*[Z
1000
1
)ME(xMean error:
Root mean squared error:
⎪⎩
⎪
⎨
⎧
⎭
⎬
⎫
−= ∑=
21/1000
1i
2
ooio )]Z(x)(x*[Z
1000
1
)RMSE(x
Xo is each of the 127 locations and i is denoted as the iteration number.
Comparison of OK and KSMD estimationsComparison of OK and KSMD estimations

22. Mean error of OK
MeanerrorofKSMD
Accuracies of OK and KSMD estimations forAccuracies of OK and KSMD estimations for
soil texture, pH, M3soil texture, pH, M3--P, and M3P, and M3--CaCa

23. In comparison of OK and KSMD estimations
for soil texture, pH, M3-P, and M3-Ca, mean
error values of KSMD are almost equal to
those of OK.
This indicates KSMD estimation is as
accurate as OK estimation.
Comparison of accuracies of OK and KSMDComparison of accuracies of OK and KSMD
estimationsestimations

24. Imprecision index of OK
ImprecisionindexofKSMD
Precisions of OK and KSMD estimations forPrecisions of OK and KSMD estimations for
soil texture, pH, M3soil texture, pH, M3--P, and M3P, and M3--CaCa

25. In comparison of OK and KSMD estimations
for soil texture and M3-Ca, imprecision index
values of KSMD are almost lower than those
of OK.
This could be referred to soil type effects are
significant on soil texture and M3-Ca and then
the KSMD estimations presented higher
precision than did the OK estimations.
Comparison of precisions of OK and KSMDComparison of precisions of OK and KSMD
estimationsestimations

26. OK
IP
KMSD
IP
Spatial assessment for estimation precisionsSpatial assessment for estimation precisions
of M3of M3--Ca with OK and KSMD (n=127)Ca with OK and KSMD (n=127)

27. In spatial assessment for estimation
precision of M3-Ca, the high-valued
imprecision indices of KSMD are obviously
lower than those of OK.
This indicates KSMD estimation is more
precise than OK estimation.
Spatial assessment for estimation precisions of M3Spatial assessment for estimation precisions of M3--CaCa
with OK and KSMDwith OK and KSMD (continued)(continued)

28. 100%
)(xIP
)(xIP)(xIP
DIP n
1i OKi
2
n
1i KMSDi
2n
1i OKi
2
×
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ −
=
∑
∑∑
=
==
pHSand Silt Clay M3-P M3-Ca
DIP (%) 34 40 4248 320
n=127
Decrease of estimation imprecision
of KSMD relative to OK (DIP):
Assessment for mapping quality of KSMDAssessment for mapping quality of KSMD

29. The decreases of estimation imprecision of
KSMD relative to OK (DIP) for soil texture and
M3-Ca are higher than 30%.
The mapping qualities with KSMD estimation
for soil texture and M3-Ca were obviously
improved.
Assessment for mapping quality of KSMDAssessment for mapping quality of KSMD
(continued)(continued)

30. ConclusionsConclusions
KSMD is a derived kriging approach with categorical
ancillary information. The estimation accuracy of
KSMD is similar to that of OK; However, compared with
OK, the estimation precision is raised by using KSMD.
The results suggested that soil map–delineation could
be used as auxiliary variables to improve the spatial
interpolation of soil properties.

31. Thank you for your attentionThank you for your attention