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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 252.1 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
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
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
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
Test for random effects Not Significant (Scenario 1): Dominant Height, Mean Height, Quadratic Mean Diameter, Significant (Scenario 2): Volume, Basal Area, Stand density 22
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
Stand type level predictions and measures of uncertainty Stand typology level Stand type level predictions and measures of uncertainty 24
Stand type level predictions and measures of uncertainty Stand typology level Stand type level predictions and measures of uncertainty 25
Stand type level predictions and measures of uncertainty Stand typology level Stand type level predictions and measures of uncertainty 26
Pixel level predictions and measures of uncertainty Study 2 Pixel level Pixel level predictions and measures of uncertainty 27
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
Conclusions Need of improved estimates for stand density. 29
Multivariate small area modelling OBJECTIVE: Improve areal estimates of stand density and volume for stand types by modeling both variables together 30
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
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
Stand type predictions and measures of uncertainty Model comparison Stand type predictions and measures of uncertainty EBLUPs and MSE Naive estimator 33
Pixel level predictions and measures of uncertainty Model comparison Pixel level predictions and measures of uncertainty MSE Naive estimator 34
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
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
Thanks for your attention!! 37
To consider in future inventories Field plot GPS positioning Navigation to pre-selected locations using C\A code Phase observations and coordinate refinement 38
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
To consider in future inventories Phase differential GPS correction Real plot location 1 m Target plot location 40
To consider in future inventories 11 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
The importance of having measures of uncertainty http://www.nwforestryservices.com Internal or external quality assessment Measures of reliability to consider when planning 42
Stand level ? ? ? Typology X 43
to differentiate cases!! Stand level ? Replications in stands needed to differentiate cases!! 44
To consider in future inventories LiDAR density National LiDAR flights point densities 0.5-1 pt/square meter Small reduction in predictive performance 45
Univariate MODELS iStand Type jPixel Heteroscedasticity 46
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
Fisher’s information matrix Multivariate models = 0 for REML Fisher’s information matrix 48
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
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
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
BLM LiDAR inventory Stand level? to differentiate cases!! Replications in stands needed to differentiate cases!! 52
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
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
The importance of having measures of uncertainty http://www.nwforestryservices.com Internal or external quality assessment Measure of reliability to consider planning 55
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
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