Chapter 8: Uncertainty and Risk

Learning Objectives

After reading this chapter, you should be able to:

Identify sources of uncertainty in wood supply models
Use scenario analysis to explore uncertain outcomes
Understand the limitations of deterministic models
Apply basic risk assessment techniques to forest management plans

Why Does Uncertainty Matter?

Forest management operates in a world of uncertainty:

Growth uncertainty: Trees don’t grow exactly as predicted
Market uncertainty: Timber prices fluctuate
Disturbance uncertainty: Fire, insects, windthrow
Policy uncertainty: Regulations may change
Climate uncertainty: Future climate may differ from historical

Ignoring uncertainty can lead to:

Over-optimistic harvest plans
Inadequate buffer stocks
Financial losses
Ecological damage

Sources of Uncertainty

Source	Description
Growth	Actual growth may differ from predicted curves
Prices	Timber prices change over time
Disturbances	Fire, insects, windthrow reduce inventory
Policy	New regulations may restrict harvest
Climate	Future climate may alter growth patterns

Scenario Analysis

Scenario analysis explores how outcomes change under different assumptions. Instead of a single “best estimate,” you examine multiple scenarios:

from ws3.forest import ForestModel
from ws3.core import Curve

# Scenario analysis in ws3 is done by comparing outcomes from
# different model configurations. The typical workflow:
#
#   1. Build model with optimistic growth curves:
#      model = ForestModel("optimistic", "/path/to/optimistic_data",
#                          2024, horizon=20, period_length=10)
#      model.import_areas_section()
#      model.import_yields_section()  # uses optimistic curves
#      model.import_actions_section()
#      model.import_transitions_section()
#      model.reset_actions()
#      model.grow(start_period=1)
#
#   2. Build model with pessimistic growth curves:
#      model = ForestModel("pessimistic", "/path/to/pessimistic_data",
#                          2024, horizon=20, period_length=10)
#      # ... same import steps with pessimistic data ...
#
#   3. Compare results by querying area/volume at each period:
#      for period in model.periods:
#          for dtype in model.dtypes.values():
#              area = dtype.area(period)
#              # query yield curves for volume at current age
#
# Curve construction uses points=[(x,y)] format:
#   optimistic_curve = Curve(label="optimistic_vol",
#       points=[(0,0),(10,8),(20,35),(30,90),...,(100,640)],
#       is_volume=True)

# Example: define curves for scenario comparison
optimistic_curve = Curve(
    label="optimistic_vol",
    is_volume=True,
    points=[(0, 0), (10, 8), (20, 35), (30, 90), (40, 160),
            (50, 260), (60, 380), (70, 500), (80, 580),
            (90, 620), (100, 640)]
)

pessimistic_curve = Curve(
    label="pessimistic_vol",
    is_volume=True,
    points=[(0, 0), (10, 3), (20, 15), (30, 40), (40, 75),
            (50, 130), (60, 200), (70, 280), (80, 350),
            (90, 400), (100, 420)]
)

# Compare by running separate models with different curve data
# and querying dtype.area(period) and yield curve values for each period

Monte Carlo Simulation

Monte Carlo simulation generates many random scenarios to estimate the probability distribution of outcomes:

import numpy as np

# Define growth curve parameters
mean_volume = 500  # m³/ha
std_volume = 100   # m³/ha

# Generate 1000 random scenarios
n_scenarios = 1000
volumes = np.random.normal(mean_volume, std_volume, n_scenarios)

# Calculate NPV for each scenario
npvs = []
for vol in volumes:
    revenue = vol * 50  # $/m³
    npv = revenue / (1.05 ** 40) - 10000  # Discount to present
    npvs.append(npv)

# Summarize results
print(f"Mean NPV: ${np.mean(npvs):,.0f}")
print(f"Std dev: ${np.std(npvs):,.0f}")
print(f"P(NPV > 0): {np.mean(npvs > 0)*100:.1f}%")
print(f"95th percentile: ${np.percentile(npvs, 95):,.0f}")

Risk Assessment

Risk assessment evaluates the likelihood and impact of adverse events:

# Define disturbance probabilities
fire_prob = 0.02  # 2% chance per year
insect_prob = 0.05  # 5% chance per year

# Calculate probability of no disturbance over 100 years
no_disturb_prob = (1 - fire_prob) ** 100 * (1 - insect_prob) ** 100
print(f"Probability of no disturbance in 100 years: {no_disturb_prob*100:.1f}%")

# Calculate expected volume loss
expected_loss = 1 - no_disturb_prob
print(f"Expected volume loss: {expected_loss*100:.1f}%")

Adaptive Management

Adaptive management acknowledges uncertainty and adjusts plans as new information becomes available:

        graph TD
  PLAN["Plan"] --> IMPLEMENT["Implement"]
  IMPLEMENT --> MONITOR["Monitor outcomes"]
  MONITOR --> LEARN["Learn from results"]
  LEARN --> ADJUST["Adjust plan"]
  ADJUST --> IMPLEMENT

Benefits of Adaptive Management:

Reduces regret: Plans can be adjusted based on actual outcomes
Improves learning: Monitoring generates new knowledge
Builds resilience: Flexible plans handle uncertainty better
Increases stakeholder confidence: Transparent process

Limitations of Deterministic Models

Deterministic wood supply models (like basic ws3 models) have limitations:

Single outcome: Only one “best” plan, no probability distribution
Fixed parameters: Growth curves, prices, costs are fixed
No feedback: Cannot learn from monitoring results
Ignores tail risks: Rare but severe events are not modeled

To address these limitations:

Use scenario analysis to explore multiple futures
Apply sensitivity analysis to identify key drivers
Incorporate adaptive management principles
Consider stochastic optimization for risk-aware decisions

Exercises

Exercise 1 (Easy): Run a scenario analysis with optimistic and pessimistic growth curves. Compare the total harvest volumes.

Exercise 2 (Medium): Perform a Monte Carlo simulation with 1000 scenarios to estimate the probability of NPV > 0.

Exercise 3 (Hard): Design an adaptive management plan that includes monitoring triggers and adjustment rules.