FIA Technical Context for API Documentation Enhancement¶

Overview¶

This document compiles authoritative FIA technical information gathered from official USDA Forest Service sources to enhance pyFIA's API documentation.

Key References¶

Primary Methodological Reference¶

Bechtold, W.A. and Patterson, P.L. (Editors). 2005. The enhanced forest inventory and analysis program - national sampling design and estimation procedures. General Technical Report SRS-80. U.S. Department of Agriculture, Forest Service, Southern Research Station, Asheville, NC. 85 p.

Foundational document for FIA's enhanced program methodology
Describes transition to annual inventory system
Details three-phase sampling design
Presents core estimators for National Information Management System (NIMS)
Available at: https://www.srs.fs.usda.gov/pubs/gtr/gtr_srs080/gtr_srs080.pdf
DOI: 10.2737/SRS-GTR-80

Key Chapters (with page references)¶

Chapter	Title	Authors	Pages
3	The Forest Inventory and Analysis Plot Design	Bechtold, W.A.; Scott, C.T.	27-52
4	Sample-based estimators used by FIA NIMS	Scott, C.T.; Bechtold, W.A.; Reams, G.A.; Smith, W.D.; Westfall, J.A.; Hansen, M.H.; Moisen, G.G.	53-77

Critical Equations (Chapter 4)¶

Equation	Page	Description
Eq. 4.1	47	Domain indicator function (Φ_hid) for condition attributes
Eq. 4.2	49	Adjustment factor (1/p_mh) for non-sampled plots
Eq. 4.8	53	Tree attribute estimation (y_hid)
Section 4.2	55-60	Stratification and EXPNS expansion factor

Key Sections¶

Section 3.4.3 (pg. 40-42): Nonsampled Plots and Plot Replacement - handling inaccessible plots
Section 4.2 (pg. 55-60): Post-stratified estimation procedures and variance formulas

Additional Key References¶

Woudenberg, S.W. et al. 2010. The Forest Inventory and Analysis Database: Database description and users manual version 4.0 for Phase 2. Gen. Tech. Rep. RMRS-GTR-245. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station.
Westfall, J.A. et al. 2023. National scale volume and biomass (NSVB) estimators. Adopted by FIA program September 2023.

FIA Sampling Design¶

Three-Phase Design¶

Phase 1: Remote sensing for stratification and identification of forested land
Phase 2: Field plots - one per 6,000 acres of forest land
Forest type, site attributes, tree species, tree size, tree condition
Spatially explicit tree compositional data
Phase 3: Subset of Phase 2 plots with expanded measurements
Tree crown conditions, lichen composition, understory vegetation
Down woody debris, soil attributes

Plot Configuration¶

FIA uses a nested plot design with specific radii:

Plot Components and Sizes¶

Microplot:
Radius: 2.073 m (6.8 ft)
Trees measured: DBH < 12.446 cm (4.9 in)
Area: 13.5 m² (145 ft²)
Subplot:
Radius: 7.315 m (24.0 ft)
Trees measured: DBH ≥ 12.446 cm (4.9 in)
Area: 168.3 m² (1,809 ft²)
Macroplot:
Radius: 17.953 m (58.9 ft)
Trees measured: Large trees based on regional breakpoint diameter
Area: 1,012 m² (10,890 ft²)

Total Sample Area¶

Each plot represents approximately 2.47 acres
Data extrapolated to represent ~6,000 acres

Evaluation System (EVALID)¶

EVALID Structure¶

Format: SSYYTT (6-digit code) - SS: State FIPS code (e.g., 48 for Texas) - YY: Evaluation year (last 2 digits, e.g., 23 for 2023) - TT: Evaluation type code

Evaluation Types (EVAL_TYP)¶

EXPALL (typically TT=00): All area estimation plots - most comprehensive
EXPVOL (typically TT=01): Volume/biomass plots with tree measurements
EXPGROW: Growth estimation plots
EXPMORT: Mortality estimation plots
EXPREMV: Removal estimation plots
EXPCHNG (typically TT=03): Change estimation plots
EXPDWM (typically TT=07): Down woody materials plots
EXPINV (typically TT=09): Inventory plots

Critical Rules¶

Never mix EVALIDs - use only ONE per estimation
EXPALL required for unbiased area estimates
Evaluation year represents complete statistical estimate, not individual plot measurements

Volume Calculations¶

Volume Variables in FIA Database¶

VOLCFNET (Net Cubic-Foot Volume)¶

Net volume after deducting defects and cull
Used for growing stock calculations
Formula: TPACURR × VOLCFNET × EXPVOL

VOLCFGRS (Gross Cubic-Foot Volume)¶

Total stem volume (1-ft stump to 4-in top)
Trees ≥ 5.0 inches DBH
No deductions for defects

VOLCFSND (Sound Cubic-Foot Volume)¶

Volume excluding rotten or missing cull
Used for merchantable bole biomass when available

VOLBFNET (Net Board-Foot Volume)¶

Sawlog volume in board feet
Different size thresholds:
Softwoods: ≥9" DBH, 1-ft stump to 6" top
Hardwoods: ≥11" DBH, 1-ft stump to 8" top

Growing Stock Definition¶

Live trees ≥5" DBH
Tree class code (TREECLCD) = 2
No serious defects affecting merchantability
Volume: 1-ft stump to 4-inch top diameter

Expansion Factors and Adjustments¶

Tree-Level Expansion¶

TPA_UNADJ (Trees Per Acre Unadjusted) - Base expansion factor before plot-level adjustments - Varies by plot component: - Microplot: 74.965282 trees/acre - Subplot: 6.018046 trees/acre - Macroplot: Varies by region

Plot-Level Adjustments¶

ADJ_FACTOR_MICR, ADJ_FACTOR_SUBP, ADJ_FACTOR_MACR - Adjustment factors from POP_STRATUM table - Applied based on tree diameter: - DIA < 5.0": ADJ_FACTOR_MICR - 5.0" ≤ DIA < MACRO_BREAKPOINT_DIA: ADJ_FACTOR_SUBP - DIA ≥ MACRO_BREAKPOINT_DIA: ADJ_FACTOR_MACR

Stratum-Level Expansion¶

EXPNS (Expansion Factor) - From POP_STRATUM table - Expands plot to population level - Accounts for stratification design

Complete Expansion Formula¶

Per-acre value = Σ(Tree measurement × TPA_UNADJ × ADJ_FACTOR × EXPNS × CONDPROP_UNADJ)

Biomass and Carbon¶

Biomass Variables (DRYBIO_*)¶

DRYBIO_AG: Aboveground biomass (pounds)
DRYBIO_BG: Belowground biomass (coarse roots)
DRYBIO_BOLE: Main stem wood and bark
DRYBIO_STUMP: Stump biomass
DRYBIO_SAPLING: Sapling biomass
DRYBIO_TOP: Top and branches above merchantable height

Carbon Calculation¶

Standard factor: 47% of dry biomass (IPCC guidelines)
Formula: Carbon = Biomass × 0.47

Unit Conversions¶

Pounds to tons: Divide by 2,000
Cubic feet to cords: Divide by 79

Land Classification¶

Forest Land (COND_STATUS_CD = 1)¶

At least 10% stocked with forest trees
At least 1 acre in size
At least 120 feet wide

Timberland¶

Forest land that is:
Not reserved (RESERVCD = 0)
Capable of producing ≥20 ft³/acre/year (SITECLCD < 7)
Available for timber harvest

Growth-Removal-Mortality (GRM) Tables¶

Key GRM Tables¶

TREE_GRM_COMPONENT: Component-level data for each tree
TREE_GRM_MIDPT: Tree measurements at remeasurement midpoint

Component Types¶

SURVIVOR: Trees alive at both measurements
MORTALITY1, MORTALITY2: Trees that died between measurements
CUT: Trees removed through harvest
INGROWTH: New trees growing into measurable size

GRM Column Naming Pattern¶

SUBP_{METRIC}_{TREE_TYPE}_{LAND_TYPE}
Example: SUBP_TPAMORT_UNADJ_GS_FOREST

- Metrics: TPAMORT_UNADJ, TPAREMV_UNADJ, TPAGROW_UNADJ - Tree types: GS (growing stock), AL (all live) - Land types: FOREST, TIMBER

Annual vs. Periodic Inventory¶

Rotating Panel Design¶

Each state divided into panels (typically 5-7)
One panel measured annually
Complete cycle every 5-7 years (10 years in western states)

Evaluation vs. Inventory Years¶

INVYR: Year individual plot was measured
EVALID Year: Reference year for complete statistical estimate
Example: EVALID 482300 represents Texas 2023 conditions, though includes plots from 2019-2023

Common Grouping Variables¶

Ownership (OWNGRPCD)¶

10: National Forest
20: Other Federal
30: State and Local Government
40: Private

Stand Size Class (STDSZCD)¶

1: Large diameter
2: Medium diameter
3: Small diameter
4: Seedling/sapling
5: Nonstocked

Site Productivity Class (SITECLCD)¶

1: 225+ cu ft/ac/yr
2: 165-224 cu ft/ac/yr
3: 120-164 cu ft/ac/yr
4: 85-119 cu ft/ac/yr
5: 50-84 cu ft/ac/yr
6: 20-49 cu ft/ac/yr
7: 0-19 cu ft/ac/yr

Tree Status (STATUSCD)¶

1: Live tree
2: Dead tree
3: Removed (cut or dead)

Statistical Considerations¶

Design-Based Estimation¶

Post-stratified estimation for improved precision
Finite population correction factors
Ratio-of-means estimators for per-acre values

Variance Calculation¶

Following Bechtold & Patterson (2005), Chapter 4, Section 4.2 (pp. 55-60):

Domain Total Variance Formula¶

For tree-based estimates (volume, biomass, tree count, growth, mortality, removals), pyFIA uses the stratified domain total variance formula:

V(Ŷ) = Σ_h w_h² × s²_yh × n_h

Where: - Ŷ = estimated population total for the domain - w_h = EXPNS (expansion factor = acres/plot in stratum h) - s²_yh = sample variance of Y in stratum h (with ddof=1) - n_h = number of plots in stratum h

This formula matches EVALIDator's variance calculation methodology and produces SE estimates within 1-3% of official USFS estimates.

Key Implementation Details¶

All plots included: Variance calculations must include ALL plots in the evaluation, not just those with non-zero values. Plots without trees in the domain contribute zeros, which affects the variance calculation.
Per-acre SE derivation: SE per acre is calculated by dividing total SE by total area:
```
SE_per_acre = SE_total / total_area
```
Single-plot strata: Strata with only one plot are excluded from variance calculation (variance is undefined with n=1).
Ratio vs. Domain Total: EVALIDator uses domain total variance (shown above) rather than ratio-of-means variance with covariance terms. The simpler formula is appropriate because tree attribute values (y_i) already incorporate the expansion to plot-level totals.

Area Variance¶

For area estimates, a slightly different approach is used that accounts for post-stratification variance components (V1/V2). pyFIA SE estimates for area are typically within 2-3% of EVALIDator.

Validation Results¶

pyFIA variance calculations have been validated against EVALIDator for Georgia (EVALID 132301, 132303):

Estimator	pyFIA SE	EVALIDator SE	Difference
Forest Area	138,928	136,048	2.1%
Volume (GS)	545,617,192	549,272,904	0.67%
Biomass (AG)	14,204,093	14,256,973	0.37%
TPA (Live)	204,196,873	199,352,867	2.4%
Growth	35,406,501	35,445,004	0.11%
Mortality	18,549,971	18,517,419	0.18%
Removals	58,202,325	58,906,897	1.2%

Temporal Methods (FIA Methodology)¶

FIA supports multiple temporal estimation methods, though pyFIA currently implements only TI:

TI: Temporally Indifferent (all available data) - implemented in pyFIA, matches EVALIDator default
Annual: Single year estimates - not implemented
SMA: Simple Moving Average - not implemented
LMA: Linear Moving Average - not implemented
EMA: Exponential Moving Average - not implemented

Data Quality Notes¶

Pre-1999 Periodic Inventories¶

Variable plot designs by region/state
Some attributes may not be populated
Different calculation methods possible

NULL Value Handling¶

Common in certain fields (e.g., PHYSCLCD ~18% NULL)
Handle safely in grouping operations
May appear as separate group in results

Implementation Recommendations for pyFIA¶

Documentation Enhancements¶

Add Bechtold & Patterson (2005) as primary reference
Include plot configuration details in Notes sections
Document expansion factor hierarchy
Explain EVALID vs INVYR distinction
Add volume type definitions
Include standard grouping variable descriptions

Code Improvements¶

Validate EVALID selection to prevent overcounting
Implement proper diameter-based adjustment factor selection
Add warnings for pre-1999 data limitations
Include unit conversion helpers
Document GRM table requirements

User Guidance¶

Emphasize single EVALID rule
Explain land type classifications
Provide grouping variable recommendations
Include expansion factor examples
Document regional variations