NRES Intro to Spatial Mapping Soil Sampling and Spatial Mapping by omahafunk

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									NRES 201 Intro to Spatial Mapping




                 Soil Sampling and Spatial Mapping

                   “A map is not a guess,
                    an estimation or a hunch,
                    a feeling or a foolish intuition,

                    A map is a dependable,
                    unwavering, inarguably accurate
                    portrayal of your position.”
                                                Rabbit
                        (From Winnie the Pooh’s Great Adventure)




                   Wise Management of Natural Resources




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                      Soil Sampling Strategies
                     and Precision Technologies

               Management Zone (soil type, yield
                 records, remote sensing, etc.)

               Grid-based Sampling  (compositing,
                 measurement “support”)

               Random




                The Influence of Composite Design on the Estimation
                       Variance for a Block Average Estimate

                        Random       Stratified Random    Grid




                       2  0, V       2  0, V        2  0, V 
                                               3                  3
                          N                    2                  2
                                           N             2.14 N
                        (assumes linear “variogram” within V)




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               Management with Limited Resources

                     Nutrient Application Rates

                     Resource Monitoring/Recovery

                     Risk Assessment/Hazard Delineation

                     Predicting grain protein, cellulose, etc.




                                    P Spatial Distribution




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                         Toolbox of Geostatistics

                                               Phosphorous Spatial Distribution


                  Provides BLUE for
                   Estimation

                  Provides Models of
                   Spatial Uncertainty




                    1937 Example of Soil pH
               Measured   variations in soil pH across
                 several counties at multiple spatial
                 scales.

               Observed        scale dependence in variance.

               Illustrates         concept of spatial variability
                 structure.




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                             measure”
                  How do we “measure” variability in a soil property?



               Two primary tools, the variogram and the histogram.

               • The variogram is a measure of the variability as
                 the distance between samples increases

               • The histogram is a measure of the relative
                 frequency of occurrence of certain values of the
                 property within the field.




                                                     Variogram
                                                     Williams Field P Variogram

                                     800
                                     700
                                     600
                        V a r ia n c e




                                     500
                                     400
                                     300
                                     200                               Variance
                                     100                               Model
                                       0
                                           0   100    200    300     400       500   600   700
                                                             Distance (m)




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                                    Histogram




                                    Mapping Soil Properties




                                Spatial Distribution of P (lbs/ac)




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                   Geostatistical Estimate of P Spatial Distribution (lbs/ac)




                          What is Sample Support?

              The geometry and orientation of the
              physical space associated with an
              observation.


                       3.
                       2.
                                                           1                   
                                               Z V ( xo )         
                       1.
                       0.
                                                                           Z ( x ) dx
                                   1 n                      V
                            Zv       Zi
                                   n i 1
                                                                V ( xo )




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                                                  Observed”
             Influence of Measurement Support on “Observed” P Distribution




                   Influence of Sample Support on Histograms

                       0.25                                        0.25
                                        Min = 19                                  Min = 10
                       0.20                                        0.20
                                        Max = 119                                 Max = 181
                       0.15                                        0.15

                       0.10               s2   = 358               0.10            s2 = 517
                       0.05                                        0.05

                       0.00                                        0.00
                              0.       100.       200.                    0.     100.       200.

                               100 m x 100 m                                   10 m x 10 m
                       0.25                                        0.25
                                        Min = 14                                  Min = 3
                       0.20                                        0.20
                                        Max = 143                                 Max = 219
                       0.15                                        0.15

                                          s2   = 442                                s2 = 740
                       0.10                                        0.10

                       0.05                                        0.05

                       0.00                                        0.00
                              0.       100.       200.                    0.     100.       200.


                                   50 m x 50 m                                   Point




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                                                                                   Sample Design Considerations



                                                                                                         L                                                 L                                       L
                                                                                                                                                                                                                                >=30

                                                                                                                                                                                                                                27.5




                                                                                                                                                                           130
                                      130




                                                                                                                      130
                                                                                                                                                                                                                                25




                                                                                                                                                                           120
                                      120




                                                                                                                      120
                                                                                                                                                                                                                                22.5

                                                                                                                                                                                                                                20




                                                                                                                                                                           110
                                      110




                                                                                                                      110
                                                                                                                                                                                                                                17.5




                                                                                                                                                                           100
                                                                                                                                                                                                                                15
                                      100




                                                                                                                      100
                                                                                                                                                                                                                                12.5




                                                                                                                                                                           90
                                      90




                                                                                                                      90
                                       90                                          100        110        120    130    90               100        110         120   130    90          100        110        120        130    <10
                                                                                                         MAP OF PREDICTION ERRORS




                                                                                                                                                                             0.6
                                            0.000 0.025 0.050 0.075 0.100 0.125




                                                                                                                            0.25




                                                                                                                                                                             0.5
                                                                                                                            0.20
                          Frequency




                                                                                                                                                                             0.4
                                                                                                                            0.15




                                                                                                                                                                             0.3
                                                                                                                            0.10




                                                                                                                                                                             0.2
                                                                                                                            0.05




                                                                                                                                                                             0.1
                                                                                                                            0.00




                                                                                                                                                                             0.0
                                                                                  10     15         20     25    30                10         15      20        25   30            10         15         20         25     30


                                                                                              SE (ppm)                                             SE (ppm)                                        SE (ppm)


                Prediction error at a 0.2 ha grid scale (1 composite sample/0.2 ha). Left and middle figures are 9 core
                composites with L = 8 and 30 m, respectively while figure on right is 7 core hexagon with optimal L.




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                  Estimates of Spatial Uncertainty




                                      F ( Z * )  Prob ( z  Z * )
                                1.0
                                                           Location 2
                  Probability




                                0.5



                                                  Location 1

                                      20    30     40    50    60
                                              P (lbs/acre)
                           Illustration of Local Uncertainty and Probability




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                                  Underestimation      Overestimation
                  Relative Loss




                                      -10   -5     0        5   10
                                        Estimation Error (lbs/ac)
                                   Figure 2. Example of Cost functions




                                            Summary
                 When using spatial data for management purposes, it is essential to
                  understand the data limitations (see attached appendix)

                 Optimal management of soil resources requires knowledge of the
                  spatial distributions of soil physical and chemical properties, and
                  knowledge of crop response functions to these factors.

                 The methods chosen for sampling, and also for mapping, of soil
                  properties results in different levels of spatial uncertainty.

                 Optimal management requires knowledge of uncertainty and map
                  quality.




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                    Appendix: Exploratory Analysis (FYI, not on exam)
                                                                               suggested
               The following are proposed steps for Exploratory Analysis (as suggested in the Data Analysis Project
                                                   Enschede,                 Geostatistics, 195-
               outlined by D. G. Rossiter @ ITC Enschede, and in Mining Geostatistics, p. 195-235, author A. Journel
                        Huijbregts,                                                        Goovaerts,
               and C. Huijbregts, Geostatistics for Natural Resources Evaluation, author Goovaerts, Chapters 2 and 4,
               and as summarized, added to, and modified by Tim Ellsworth)
                                         (NON-
               NATURE OF THE DATA (NON-SPATIAL ANALYSIS)
              Background
                      When and why were the data collected?
                      What questions are the data meant to answer?
                      Who will use the results and what will they do with them?
              Are there other studies of the same properties that would be of benefit to understanding this situation?
              Data Overview
                      How many samples are there, what was the sampling plan?
                      Is the sampling plan appropriate for the purposes of the study?
                      Can we request additional sampling if necessary?
                                                                   method/persons/equipment?
                       Was data collection performed by the same method/persons/equipment?
                      If not, can we identify who/what differs amongst the data?
                  What coordinate system are the data given in?
                                                                                 support”
                       What are the spatial locations of the data? What is the “support” of each measurement?
                                                                                           (geometric/coordinate
                       How were measurements made? Are there any systematic errors (geometric/coordinate
               precision).
              Attributes/Variables
                                                                                each
               What relevant information is available, What was measured at each observation point?
              For each variable:
                      What are the units? What is the measurement precision?
                      For categorical or classified data types, what are the classes?
              Statistical Analysis and Mapping
                    This should be performed by someone knowledgeable in the subject area.




                                           Typical Estimation Algorithm

                                                   n                    n
                                      Z j   wi Z i ;  wi  1
                                                  i 1                 i 1


                                           Prediction Error at location u.


                                      e(u )  Z * (u )  Z true (u )




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                  Loss Function, quantifying cost associated with a
                  specific error.


                 L[e(u )]  h ( e(u )); h  e(u ) 2 , e(u ) , etc.

                  Expected Loss, given probability associated with
                  a given error.

                                            
                      E [ L( e(u ))]   L( z  Z * ) f ( z )dz
                                           




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