Mathematical Representation of this model

Precipitation = Evapotranspiration + Change in Storage

P = ET + ΔS

(at global scales ΔS includes streamflow since that water is still “stored” in the earth)

Water balance can tell you a lot

Model Goals

Because models are only approximations of reality - the most important part of the modelling process is knowing why you want to build a model

Some broad types of goals

Understanding (how does something work, what are key drivers of responses, how do different drivers interact)

Estimation/Scenario (what might be the consequences of decisions we make about the environment, what might the environment look like if something changes)

Communication - contribute to education and broader understanding

Actual goal(s) needs to be more precisely defined

Models for understanding(big #’s, little #’s as controls on phenomena)

The is often the role of inverse inference models - for example using a GCM to assess whether CO2 emissions can explain trends in warming temperature

This application of models is often in the form of a question

In a particular place (Baltimore Harbor), would temperature often be a limiting factor in eutrophication? At what times of year, would N-export matter more or less?

US EPA Source

Models for estimation and what if scenarios

IPCCC Projections

Estimate of global temperatures over the next 100 years

Models for estimation

Estimate of energy savings from LED adoption

Modeling for Problem Solving in Environmental Science

• There is something you need to know in order to solve the problem

  • Answer to a question

    • What if?
    • How Much?
    • Which Alternative?
    • Why is this happening?

  • Test a Hypothesis

Modeling for Problem Solving in Environmental Science

• Always start by clearly defining your goal as a questions (or hypothesis to be tested)

• Examples?

Models can also be for communication Example:Glaciers

Goal: Help public understand why, even if temperature warms - glaciers might grow (due to increasing snowfall) - but a threshold temperature might be reached where glacier will shrink

Glacier model

Model Goals

Understanding (how does something work, what are key drivers of responses, how do different drivers interact)

Estimation/Scenario (what might be the consequences of decisions we make about the environment)

Communication - contribute to education and broader understanding

Conceptual Models

• models are always simplifications of reality - they help us to make sense of reality by focusing on specific aspects that are most relevant to your goal

• always start a modeling project by diagramming your conceptual model - how to you see the system;

  • from here you design or choose your ‘actual’ model

• in a project, dialogue it is critical to dialogue to agree on the conceptual model

• “all models are wrong but some are useful” - British Statistician George Box

Pair and Share

Share your conceptual model with a partner…Ask each other

• how would this model help “understand” why an observed pattern occurs; is there something you could have done to make this inverse inference more clear

• are the mechanisms that translate inputs to outputs clear; are there multiple mechanisms involved

• what are some applications of this model - what would be the goal in that application

• what are the core assumptions in the model

• are there changes you would suggest to your partner’s model

Basic components of models

Inputs : Varying; think x of a x vs. y regression

Parameters : single values that influence relationships in the model

Outputs : what you want to estimate

Simple model

Input : Change in unemployment rate

Output : Change in GDP

Parameters : Slope and intercept of the line

The US “changes in unemployment – GDP growth” regression with the 95% confidence bands.

STEPS: Modeling for Problem Solving in ES

Clearly define your goal (a question you want to answer, hypothesis you want to test, prediction you want to make) - as precisely as possible

• Design or Select your model

• Implement the model

• Evaluate the model and quantify uncertainty

• Apply the model to the goal

• Communicate model results

Goals

The goal will help you to define the core pieces of a model

Often helpful to start at the end: Outputs

Problem: which piece of land should be purchased to maximize biodiversity?

Outputs: monetary costs and benefits of different options in 2015 dollars, including “non-market” benefits

Goals

The goal will help you to define the core pieces of a model

Often helpful to start at the end: Outputs

Problem: how will forest carbon sequestration change if fire frequency increases with warming

Outputs carbon sequestration for different fire frequencies

For Next Class

1. Fill out Help us get to know you survey on Canvas

2. Listen to only timestap 26:27 to 31:22 (basically 5 minutes) of the following blog by Lisa Felman Barrett - a highly cited psychologist

   • blog 26:27 to 31:22

   • if you are interested you can learn More about Lisa Felman Barrett

   • Think about what an inverse inference problem might be in the context of the environment

3. Listen to this podcast on climate models - Pay particular attention to how Gavin Schmidt talks about the design, goal and skill of models

   • The emergent pattersn of climate change

   • If you are interested you can learn More about Gavid Schmidt

4. After listening to these podcast, do the following

   1. Think of a conceptual model that you or someone else might use to understand some pattern that they observe in the environment (in other words a model that might help them to solve an inverse inference problem to understand the mechanisms that causes the observation)?