Heikkinen, Juha

Henttonen, Helena M.

Hyvönen, Pekka

Jukuri

© Natural Resources Institute Finland  t r l r  I tit t  i l  Juha Heikkinen, Pekka Hyvönen, and Helena M. Henttonen XXVIIIth International Biometric Conference. Victoria, Canada, July 10, 2016  Utilizing prior information in environmental inventory design - experiences from forest inventories © Natural Resources Institute Finland Natural Resources Institute Finland (Luke) 2 Heikkinen & al: Inventory design. IBC2016, Victoria Directorate 23 Scientists 669 Other experts 314 Research support personnel 431 December 2015 © Natural Resources Institute Finland Among Luke’s activities • National Forest Inventory (NFI) of Finland • Land use, land-use change and forestry (LULUCF) sector of national greenhouse gas inventory • International consultation in inventory design and related capacity building – Tanzania (Tomppo et al. Can. J. For. Res. 2014) – Vietnam – Nepal – Cambodia – Kenya 3 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Study areas Nakuru, Kenya: highly fragmented forests, 6% of area Lapland, Finland: borderline between taiga (Boreal forest) and tundra 4 Heikkinen & al: Inventory design. IBC2016, Victoria Kenya Lapland taiga tundra map source: Biome (Jun 21, 2016). Wikipedia © Natural Resources Institute Finland Inventories of natural resources and the environment • General aim: estimate total or mean of resource over (often administrative) region of intererst. • Example: mean tree biomass by species in forests of Kenya. • Unbiased, precise, and timely estimation: substantial amount of field measurements.  • Often fieldwork can be wisely targeted by using prior information. • Example: thematic maps from similar or related earlier inventories. 5 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Example of prior information Tree stem  volume in Northernmost Lapland (for methods, see Tomppo et al. Multi-Source National Forest Inventory. Springer 2008). 6 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland 7 Heikkinen & al: Inventory design. IBC2016, Victoria Power, K. & Gillis, M.D. 2006. Canada's forest inventory 2001. Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, Victoria, BC. Another example of prior information © Natural Resources Institute Finland 𝑌 =1𝐴 𝑦 𝑠 𝑑𝑠𝐴 where 𝐴R2 region and y response surface of interest, e.g. – 𝑦 𝑠 = 𝟏𝐹 s   𝑌 𝐴  area of F – 𝑦 𝑠  mean biomass in small plot around s   𝑌  mean biomass over A 𝑦 =1𝑛 𝑦𝑖𝑛𝑖=1 where 𝑦𝑖 = 𝑦(𝑠𝑖) field observations of y at n samle points si, how can we use prior information related to variability of y available at all sA, when choosing the sampling locations si. Question 8 Heikkinen & al: Inventory design. IBC2016, Victoria When estimating by © Natural Resources Institute Finland ~1km Common designs without prior information Systematic plot sampling: e.g., square grid of sample plot centers for field measurements • “regularly spaced design points are optimal for a variety of reasonable spatial correlation functions” (Stevens and Olsen, J. Amer. Statist. Assoc. 2004). Systematic cluster sampling (sys1): e.g., square grid of sample plot clusters • Large-scale inventory: one grid location/day. • Distribute one day’s work between plots in different neighbouring forest stands rather than measure a large number of similar trees from one stand. 9 Heikkinen & al: Inventory design. IBC2016, Victoria ~10km © Natural Resources Institute Finland Stratified sampling and Neyman allocation Example (unrealistically simplified setting for illustration): Use prior information to • divide inventory region A into two strata Ah so that variation of y high in A1 and low in A2, (e.g. map of forest types) and to • estimate variances Sh2 of y within strata h = 1, 2 (e.g. biomass map from earlier inventory). Neyman allocation: sampling densities  ph = nh  /  |Ah| determined by p1 / p2 = S1 / S2, where • nh is the sample size and  • |Ah| the area of stratum h. 10 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Example: mean tree biomass in Kenya 11 Heikkinen & al: Inventory design. IBC2016, Victoria Vegetation classes (left)  stratification (middle):  • Stratum 1: plantations (high mean biomass -> high variability), 2: other forests and non-forest Biomass in forest (right)  Stratum variances Sh2 Note: if stratum h non-forests, then Sh = 0 © Natural Resources Institute Finland Stratified systematic plot sampling  Two grids with densities dh, such that d1/d2 = S1/S2. Sample from stratum h: dh  Ah  p1/p2  S1/S2 12 Heikkinen & al: Inventory design. IBC2016, Victoria Stratum 1: plantation forests (high mean biomass, high variability) Stratum 2:        other forests and non-forest (low mean biomass, low variability) © Natural Resources Institute Finland Stratified systematic cluster sampling 13 Heikkinen & al: Inventory design. IBC2016, Victoria Variable number of plots / cluster   idea of one day per cluster is lost.    Example: one cluster from stratum 1 grid; only 2 plots within stratum 1 included in the sample.  © Natural Resources Institute Finland Two-phase (double) sampling Instead of single points, stratify whole clusters. 14 Heikkinen & al: Inventory design. IBC2016, Victoria Stratum 1: clusters with 2 or more forest plots Stratum 2: clusters with 0 or 1 forest plots Note: No need to specify high/low-biomass forests © Natural Resources Institute Finland In simple (one-phase) stratified sampling • exact stratum weights for stratified estimation from |Ah| • and variances Sh between clusters for Neyman allocation from auxiliary data at population level. In double sampling (of clusters) weights and variances are estimated from 1st-phase sample, e.g., dense systematic grid. 2nd-phase sample, measured in field. Often, but not necessarily, subsample of 1st-phase sample.    First phase sample must be dense 15 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Three strategies for 2nd-phase sampling  ran2: simple random subsamples of nh clusters from       1st-phase sample • dense 1st phase for good weights & to enable uneven allocation       low sampling fraction, esp. in stratum 2  spatial balance lost • fixed sample size possible  exact Neyman allocation sys2: as earlier for stratified systematic plot sampling • new grids with densities according to Neyman allocation • optimal spatial balance within strata • random nh: only approximate Neyman allocation bal2: Grafström & Tillé (Environmetrics 2012) • stratified spatially balanced subsampling from 1st-phase sample • fixed sample size possible for each h  exact Neyman allocation • spatial balance also across strata, but sub-optimal (within strata) in comparison to systematic sampling   16 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Stratified two-phase cluster samples 17 Heikkinen & al: Inventory design. IBC2016, Victoria Target allocation  Stratum 1: 21 clusters  Stratum 2: 4 clusters         ran2 sys2 bal2 gray grid: 1st-phase sample © Natural Resources Institute Finland Comparison of designs: sampling simulation Anticipated variance of inventory estimator by • simulating replications of each design  • comparing sample means to known population mean of biomass map • estimating variance by MSE over replications This will typically underestimate the variance of the actual inventory estimator, because some of the natural variation is smoothed out in multi-source maps. However, if spatial structure of biomass map reflects true spatial structure in scales that determine cluster-to-cluster variation, then such sampling simulation should be useful in comparison of different sampling designs.  18 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Sampling simulator developed at Metla/Luke Also allows comparison of different cluster forms and can take into account transfer time between sample plots – digital terrain model, vegetation type etc. and measurement time – biomass or vegetation type Has been applied in  – Vietnam 2012-2013 – Cambodia 2014 – Kenya 2015 More information: pekka.hyvonen@luke.fi kari.t.korhonen@luke.fi  19 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Case studies on three test areas       Qualitative differences • Forests more concentrated in Lapland (SE),        scattered in  Nakuru • Less plots/cluster in Nakuru due to more measurements/plot, more difficult movement, shorter day • Variability of y different in all three areas Target: 10% relative sampling error by sys1 20 Heikkinen & al: Inventory design. IBC2016, Victoria 𝐴  km2 % forest 𝑆 𝑦   𝑛 clusters plots/ cluster Lapland 28,140 0.99 1.0 42 9 Nakuru, arid 9,270 0.16 3.2 376 5 Nakuru, humid 13,590 0.23 2.6 374 5 © Natural Resources Institute Finland Stratified two-phase bal2-design: Nakuru 21 Heikkinen & al: Inventory design. IBC2016, Victoria arid humid © Natural Resources Institute Finland Stratified two-phase bal2-design: Lapland 22 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Preliminary results 23 Heikkinen & al: Inventory design. IBC2016, Victoria   ran1 sys1 ran2 sys2 bal2 Lapland 424 196 158 124 100 Nakuru, arid 379 217 121 110 100 Nakuru, humid 485 225 127 116 100 ran1: 1-phase simple random sampling Why RSE2? Ratio between two designs gives the ratio between n yielding same precision. Below: Equivalent sample sizes within each row. © Natural Resources Institute Finland Conclusions • Clustered designs practical in large-scale inventories. • Double sampling for stratification simple and efficient way to utilize prior information. • Method of Grafström & Tillé simple and apparently efficient way to balance 2nd-phase sample spatially. • Very much work in progress; interesting to see – how bal2 fares, when prior info not so good – effect of number of strata: effect of random sample size of sys2 pronounced with more strata                  smaller samples within some strata Use prior information!  24 Heikkinen & al: Inventory design. IBC2016, Victoria © Natural Resources Institute Finland Thank you! Heikkinen & al: Inventory design. IBC2016, Victoria 25 

Utilizing prior information in environmental inventory design - experiences from forest inventories

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