Isaac Held's Vision for Model Hierarchies and the Future of Climate Science
Isaac Held's 2005 essay presents a fundamental tension in climate science that resonates across all complex systems modeling. On one hand, we strive to simulate by capturing as much dynamics as possible in comprehensive numerical models. On the other hand, we try to understand by simplifying and capturing the essence of phenomena in idealized models.
High resolution
Many processes
Realistic simulations
Difficult to understand
Simple structures
Few processes
Easy to understand
Hard to apply
This gap threatens the health of climate theory. Without a way to connect these two extremes, we risk accumulating simulation results we cannot fully understand or interpret. Held's solution: model hierarchies.
Held points to molecular biology's dramatic success in deciphering the human genome and protein interactions. The key? Nature provided a ready-made hierarchy:
Evolution ensures that insights from simpler organisms apply to complex ones. Biologists didn't need to design this hierarchy—they just studied what nature provided!
Unfortunately, Nature has not provided us with simpler climate systems. We have only one Earth. Planetary atmospheres (Venus, Mars, Jupiter) provide some insights, but they're few and idiosyncratic. Laboratory simulations help but can't address our most complex problems.
We must construct our own hierarchies. This is theoretical science, not experimental science. We must both design the hierarchy AND convince the community to focus on specific models—a much harder task than biologists face!
| Aspect | Physics/Chemistry | Climate Science | Implication for Modeling |
|---|---|---|---|
| Fundamental Laws | Well-established (Newton, Maxwell, Schrödinger) | Emergent from multiple interacting systems | Climate models must be constructed bottom-up from component processes |
| Experimental Control | Can isolate systems, vary parameters | One Earth, no control experiments | Must rely on paleoclimate, regional variations, models |
| Natural Hierarchies | Atoms → Molecules → Materials (chemistry) Particles → Fields (physics) |
None provided by nature | Must deliberately construct model hierarchies |
| Time Scales | Often separable (fast/slow) | Multiple interacting scales | Parameterizations necessary, introducing uncertainty |
| Predictability | Often deterministic at fundamental level | Inherently chaotic and probabilistic | Ensemble approaches, probabilistic forecasts |
| Validation | Direct comparison with controlled experiments | Comparison with historical observations | Extrapolation (future climate) hard to validate |
| Model Purpose | Usually for understanding | Must balance understanding and prediction | Tension between elegance and comprehensiveness |
The Goal: Map out how dynamics change as key sources of complexity are added or subtracted
Held describes an idealized model designed to study moist convection and large-scale circulation:
This model is intermediate—simpler than comprehensive GCMs but more complex than dry models. It allows systematic study of how convection schemes affect tropical convergence zones.
Climate models, at their core, are stock-flow models tracking the movement and transformation of quantities through Earth system compartments. Held's hierarchy concept maps beautifully onto the stock-flow framework:
| Model Level | Stocks (Compartments) | Flows (Processes) | Conservation Laws |
|---|---|---|---|
| Simple Energy Balance | 1 stock: Global temperature | Solar in, IR out | Energy conservation |
| Box Model | Few stocks: Tropics, mid-lat, poles | Heat transport, radiation | Energy + momentum |
| Held's Moist Model | 3D atmosphere, latent heat, no condensate | Convection, radiation, dynamics | Energy + mass + moisture |
| Full GCM | 3D atmosphere, ocean, ice, biosphere, chemistry | All physical/chemical processes | All conservation laws (approximate) |
Moving up Held's hierarchy means:
The art of hierarchy construction is knowing which stocks and flows to include at each level to isolate specific mechanisms while maintaining essential physics.
Held argues that understanding comprehensive models as dynamical systems is not just academic—it has practical value for improving simulations:
When we understand which aspects of a convection scheme cause the "double ITCZ problem," our fixes are informed rather than random. Development becomes less like tinkering and more like engineering.
Understanding why one model performs better than another without laboriously morphing one into the other. We can learn from other groups' successes more efficiently.
Model intercomparison projects (like CMIP for IPCC) show which results are robust and which aren't. But without hierarchies, we can't understand WHY models differ.
Simple, elegant models provide lasting understanding that survives beyond the obsolescence of today's comprehensive models. They form the foundation for future work.
Held contrasts two types of model components:
| Component Type | Example | Development Approach | Status |
|---|---|---|---|
| Well-Understood | Atmospheric radiation (clear sky) | Systematic bottom-up: Broadband codes tested against line-by-line calculations from laboratory data | ✓ Mature, reliable |
| Poorly-Understood | Deep moist convection | Trial and error, "tinkering" based on wisdom and prejudice, serendipitous improvements | ⚠️ Little consensus, ongoing research |
For poorly-understood components, holistic understanding through hierarchies is essential. We can't yet build convection schemes from first principles, so we need to understand how different schemes affect the full system.
Held identifies a critical problem: Many idealized climate models are more elaborate than necessary. This happens because:
For understanding: Include only the stocks and flows necessary to capture the mechanism you're studying. Remove everything else.
For prediction: Include all stocks and flows that significantly affect outcomes, even if they obscure individual mechanisms.
The tension: An elegant model for understanding the hydrological cycle might have 4 compartments (atmosphere, surface, soil, groundwater). A predictive model for a real watershed might need 40 compartments (multiple soil layers, vegetation types, aquifers, etc.). Both are valid—the question is purpose.
Held makes a provocative distinction:
| Model Type | Primary Goal | Lifespan | Value |
|---|---|---|---|
| Comprehensive GCMs | Practical prediction | Temporary—will be obsolete as computing power increases | Immediate practical importance, but historical interest only in future |
| Elegant Hierarchies | Understanding mechanisms | Lasting—fundamental insights remain valid | Foundation for future generations' understanding |
This is analogous to physics: Newton's laws are still taught 300 years later (lasting value), while the best calculations of planetary orbits from the 1800s are obsolete (practical but temporary).
Held distinguishes two modes of modeling:
Value: Flexible, exploratory, generates ideas
Value: Builds cumulative understanding, community resource
Held argues we need both, but hierarchy development has been neglected. Without shared reference models, we face a "babel of modeling results" that we cannot relate to one another.
Held nominates Phillips' 1956 two-layer quasi-geostrophic model as the climate equivalent of E. coli—a model simple enough to understand deeply but complex enough to exhibit key phenomena (baroclinic instability, jet streams).
Just as molecular biologists focused intensively on E. coli rather than each studying their own favorite bacterium, climate scientists should focus on a few canonical models at each hierarchy level.
The challenge: In biology, nature provided E. coli. In climate, we must convince the community to adopt specific models—much harder!
The stock-flow framework provides a natural language for constructing Held's hierarchies:
Stock: Global mean temperature T
Flows:
Conservation: dT/dt = [S(1-α) - σT⁴] / heat_capacity
Purpose: Understand basic greenhouse effect, ice-albedo feedback
Stocks: Tropical temperature T₁, Polar temperature T₂
Flows:
Conservation: Energy conserved, but can move between boxes
Purpose: Understand meridional heat transport, polar amplification
Stocks: Temperature, velocity, pressure fields; water vapor; latent heat
Flows:
Conservation: Energy, mass, moisture, momentum
Purpose: Understand how convection schemes affect ITCZ, tropical storms
Stocks: Temperature, winds, moisture (multiple phases), tracers, ocean T and circulation, sea ice, land surface states, vegetation, etc.
Flows: All physical, chemical, biological processes
Conservation: All conservation laws (approximately, with parameterizations)
Purpose: Realistic simulation for policy, regional predictions
Our earlier hydrological model (4 compartments: atmosphere, surface, soil, groundwater) sits at Level 2 of a climate hierarchy:
Each level isolates different mechanisms: Level 1 for global water balance, Level 2 for partitioning between reservoirs, Level 3 for spatial patterns, Level 4 for realistic prediction.
When building intermediate models, resist the urge to add every realistic detail. Include only what's needed to study your target mechanism. This makes your model more likely to be adopted by others.
If you want your model to have lasting value, make it fully reproducible. Specify every parameter, every algorithm choice, every boundary condition. Others should be able to rebuild your model from your documentation.
Don't just create isolated models. Show how your intermediate model connects to simpler models below and comprehensive models above. Map out what changes as you add complexity.
The community should coordinate to study a few canonical models intensively (like biologists with E. coli), rather than each researcher creating their own variant. This requires consensus-building—difficult but essential.
Held argues we need all three modes of research:
| Research Mode | Purpose | Products | Current Status |
|---|---|---|---|
| 1. Comprehensive Simulation | Practical prediction for policy, applications | IPCC-class models, regional climate projections | ✓ Well-funded, high priority |
| 2. Conceptual Research | Explore ideas, test hypotheses, generate insights | Papers with new concepts, feedback analyses | ✓ Active, creative |
| 3. Hierarchy Development | Build lasting understanding, connect levels | Canonical intermediate models, systematic analyses | ⚠️ Underfunded, fragmented |
The gap between simulation and understanding persists because hierarchy development is neglected. We need to:
Held's essay is fundamentally about the purpose of scientific modeling. Should models be temporary tools (obsolete as computing power grows) or lasting frameworks for understanding?
His answer: Both are needed, but we've overemphasized the former. Comprehensive climate models serve immediate practical needs but will be replaced. Elegant model hierarchies provide lasting understanding that transcends individual simulations.
The stock-flow framework provides a natural language for Held's vision:
Our hydrological cycle model exemplifies this: 4 stocks, 8 flows, capturing essential water movement while remaining simple enough to understand. It could be a stepping stone in a hierarchy from 1-box global models to comprehensive land-surface schemes.
"Should we strive to construct climate models of lasting value? Or should we accept as inevitable the obsolescence of our models as computer power increases?"
Held's Answer: We must do both—but we've neglected the former.
The health of climate science depends on building hierarchies that last.