1. Francisco Mauro, Vicente Monleon, and Hailemariam Temesgen
Univariate and Multivariate small area Estimation using LiDAR in SW OREGON
Francisco Mauro, Vicente Monleon, and Hailemariam Temesgen 1

2. 1 Provide estimates for different aggregation levels
OBJECTIVE:
Compare the performance of different methods for mapping and estimation at various resolutions (pixels, stands, compartments, strata, tracts)
1 Provide estimates for different aggregation levels
2 Provide specific measures of uncertainty of the estimates
Very briefly, the main objective of this study is analyzing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of LIDAR to predict the V might help to improve estimates of N. 2

3. Area Based Approach (Analogy)
Auxiliary information (DBH) +
Variables of Interest (V)
Sample Trees
Predictive models
Y=f(DBH)+ε
DBH Measurements
Volumes
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 3

4. Pixel Level predictions
Area Based Approach
Auxiliary information +
Variables of Interest
Sample plots
Predictive models
Y=f(LiDAR)+ε
Auxiliary information grid
Pixel Level predictions
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 4

5. Area Based Approach (Analogy)
Traditional inventory
LiDAR inventory
Unit=Tree
Unit=Pixel\plot
AUX INFO=LiDAR variables
AUX INFO=DBH
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 5

6. Area Based Approach (Analogy) Traditional inventory
LiDAR inventory
Field plots Volume and LiDAR known
Sample of Trees
Volume and DBH known
Tree level
predictions
Pixel level predictions
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 6

7. Area Based Approach (Analogy) Traditional inventory
LiDAR inventory
Parameter of Interest:
Sum of TREE Volumes for the total area
Parameter of interest:
Sum of PIXEL Volumes for the total area
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 7

8. Why does LiDAR works well in large areas? + Errors
Errors (+) (-) cancel out. Accurate estimates
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 8

9. Is this enough information for management?
No!!, We need disaggregation
Accurate Estimates for
Mean Volume
(Errors ~2%-7%) By
Spatial
units By
Size
classes
Typical set up of LIDAR based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 9

10. Area Based Approach (Analogy) Traditional inventory
LiDAR inventory
Stand estimates, parameter of interest: Sum of TREE Volumes in a stand
Stand estimates, parameter of interest: Sum of pixel Volumes in a stand
Tipical set up of lidar based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 10

11. Between spatial units variability
Scenario 1
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 11

12. Scenario 1 Within groups & Between groups variability
Between group variability small
Within group variability Large
Safe to use synthetic (general) models
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 12

13. Between spatial units variability
Scenario 2
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 13

14. Scenario 2 Within groups & Between groups variability
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N.
Between group variability Large
Within group variability Large
Need to account for between groups variability 14

15. SOLUTIONS TO BIAS PROBLEMS
stand groups?
SOLUTIONS TO BIAS PROBLEMS
Stratification (only) for large areas of interest (AOIs)
Smaller AOI → Smaller sample size
New methods called Small Area Estimation.
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 15

16. Small area estimation applied to Forest inventories
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N.
UNBIASED ESTIMATES
AOI SPECIFIC MEASURES OF UNCERTAINTY 16

17. Estimates for groups of stands
North fork of the Coquille river
Estimates for groups of stands
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 17

18. Estimates for groups of stands
North fork of the Coquille river
Estimates for groups of stands
Total BLM lands 36,812 ac
1,508 stands
146 Field plots (1/8 ac)
Average stand 24.4 ac
Average 1 plot every 10.3 stands
Average 1 plot every ac
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 18

19. Estimates for groups of stands
North fork of the Coquille river
Estimates for groups of stands
Type
Species
Age ni DF 20 11 40 4 50 6 60 9 70 5 80 7 90 1
100
150 2
190
240
270
420 3
440 17
MIX
BLM STANDS CLASSIFIED BASED ON:
SPECIES TYPE
AGE
HARWOODS & NON FOREST EXCLUDED
PURE CONIFERS AGE 320 EXCLUDED (47 PLOTS)
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. 19

20. Univariate small area modeling
OBJECTIVE:
Provide estimates for different aggregation levels
Provide specific measures of uncertainty of the estimates
For:
Volume, Basal Area, Dominant Height, Mean Height, Quadratic Mean Diameter, Stand density 20

21. Univariate Modeling Selection of candidates
Global measures of fit vs number of predictors
Univariate mixed effects models
Graphical assessment of residuals and random effects 21

22. Test for random effects
Not Significant (Scenario 1):
Dominant Height, Mean Height, Quadratic Mean Diameter,
Significant (Scenario 2):
Volume, Basal Area, Stand density 22

23. Watershed level predictions and measures of uncertainty
Variable
LiDAR Estimate
CV LiDAR
L95 LIDAR
U95 LIDAR
Field Only estimate
CV Field
Efficiency increase V
98044
5.5%
8737
10872
12364
9.1%
39% N
146
8.9%
120
172
137
6.1%
-47% BA
201
5.8%
178
224
250
8.2%
29%
Watershed level predictions and measures of uncertainty
Typical set up of LIDAR based inventories
All
Plots
Models
Grid
PIXEL LEVEL PREDICTIONS 23

24. Stand type level predictions and measures of uncertainty
Stand typology level
Stand type level predictions and measures of uncertainty 24

25. Stand type level predictions and measures of uncertainty
Stand typology level
Stand type level predictions and measures of uncertainty 25

26. Stand type level predictions and measures of uncertainty
Stand typology level
Stand type level predictions and measures of uncertainty 26

27. Pixel level predictions and measures of uncertainty
Study 2 Pixel level
Pixel level predictions and measures of uncertainty 27

28. Conclusions Some variables show among-stand type variability.
Small Area Methods allow a bias correction and improve efficiency when there is among-stand type variability.
Small Area Methods allow obtaining uncertainty measures for total area, stand typologies, and pixels. 28

29. Conclusions
Need of improved estimates for stand density. 29

30. Multivariate small area modelling
OBJECTIVE:
Improve areal estimates of stand density and volume for stand types by modeling both variables together 30

31. Advances in SAE theory to transfer to forest inventories
Mulivariate models.
Y=(Stand denstity and Volume)
Improved estimators that incorporate the correlation between random effects and/or residuals 31

32. Model fitting Selection of candidates Univariate mixed effects models
Global measures of fit vs number of predictors
Univariate mixed effects models
Graphical assessment of residuals and random effects
Multivariate mixed effects models
Same fixed effects. Correlation for residuals and random effect 32

33. Stand type predictions and measures of uncertainty
Model comparison
Stand type predictions and measures of uncertainty
EBLUPs and
MSE Naive estimator 33

34. Pixel level predictions and measures of uncertainty
Model comparison
Pixel level predictions and measures of uncertainty
MSE Naive estimator 34

35. Multivariate modeling conclusions
advantages
Smother predicted values for Stand density and volume
Important reduction of uncertainty at stand type level
Potential improvement considering more\other variables.
Disadvantages
Marginal improvements for global measures of uncertainty
Complicated modeling and unstable solutions.
Bias correction for MSE estimators are difficult to obtain. 35

36. Future Research Diameter distribution modeling:
Stems\Basal Area Volume by diameter classes
Multivariate prediction problem
As many variables as diameter classes
Additive parameter of interest
Compromise solution 36

37. Thanks for your attention!!37

38. To consider in future inventories
Field plot GPS positioning
Navigation to pre-selected locations using C\A code
Phase observations and coordinate refinement 38

39. To consider in future inventories
Navigation to pre-selected locations using C\A code
We are at the plot!!
10-15 m
10-15 m
Target plot location
10-15 m 39

40. To consider in future inventories
Phase differential GPS correction
Real plot location
1 m
Target plot location 40

41. To consider in future inventories11 12 13 21 22 23 31 32 33 41 42 43 51 52 53 61 62 63 71 72 73 81 82 83 91 92 93
101
102
103
(blank)
Grand Total 29 1 30 10 2 5 4 27 28 14 9 7 3 6 18 25 24 20 17 41

42. The importance of having measures of uncertainty
Internal or external quality assessment
Measures of reliability to consider when planning 42

43. Stand level ? ? ?
Typology X 43

44. to differentiate cases!!
Stand level ?
Replications in stands needed
to differentiate cases!! 44

45. To consider in future inventories
LiDAR density
National LiDAR flights point densities
0.5-1 pt/square meter Small reduction in predictive performance 45

46. Univariate MODELS
iStand Type jPixel
Heteroscedasticity 46

47. Same fixed effects as in the univariate models
Multivariate models
BASICALLY……GO TO
LONG FORMAT!
Fixed
EFFECTS
Random EFFECTS
RESIDUALS
Same fixed effects as in the univariate models 47

48. Fisher’s information matrix
Multivariate models
= 0 for REML
Fisher’s information matrix 48

49. Univariate MODEL SELECTION
V(units)
Selection of predictors (Fixed effects models)
5 best combinations of x variables. (Up to 4 predictors)
Graphical diagnostic
Standardized residuals (Patterns of heteroscedasticity)
Final modelling
Mixed models including patterns of heteroscedasticity for residuals.
Case Study 49

50. Within groups & Between groups variability
Mixed effects models
Within groups & Between groups variability
Between groups variability
Within group variability
Error cancelation ONLY for this part 50

51. What do you need to apply these techniques
Definition of Areas of Interest
Sample that allows to estimate between AOI Variability
Not all units have to have multiple sample but some units should 51

52. BLM LiDAR inventory Stand level? to differentiate cases!!
Replications in stands needed
to differentiate cases!! 52

53. Age\Species types for stand level estimation. (Problems)
Stand level estimation based on a reasonable assumption. All stands in the same group behave the same. But….
Stands might show high variability
We only see the between Age \Species type variability. 53

54. Estimates for non sampled stands
Our estimate is going to be the same as if we had used a synthetic estimator. But….
We know the between stand variability so we have information about how strong the stand effect can be 54

55. The importance of having measures of uncertainty
Internal or external quality assessment
Measure of reliability to consider planning 55

56. SOLUTIONS TO BIAS PROBLEMS
stand groups?
SOLUTIONS TO BIAS PROBLEMS
Stratification (only) for large areas of interest (AOIs)
Smaller AOI  smaller sample size
New methods called Small Area Estimation. 56

57. Study 1 Estimates of averages for Coos-Bay
Models to predict
Basal Area
Volume
Stand density
Quadratic mean diameter
Lorey’s height
Very briefly, the main objective of this study is analissing with a case study if areal estimates of stand density can be improved by developing multivariate models for V and N. The ability of lidar to predict the V might help to improve estimates of N. BA
VOL N
QMD
LorH 57