1. Introduction to Modeling Unit V, Module 21A

2. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s2 Module 21 Introduction to Modeling  This module has three main goals. It will help you:  Understand how models help environmental scientists:  Learn about natural systems  Predict how natural systems will behave under different conditions  Evaluate different management scenarios  Learn about different approaches to modeling natural systems  See and use examples of watershed, lake, stream, and biotic models

3. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s3 Lecture 1 Understanding Models  What is a model?  A model is a simplified representation of the real world  There are two types of models  Conceptual  Mathematical Fishing Effort Equilibrium Yield Surplus Yield Model (Lackey and Hubert 1978)

4. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s4 Conceptual Models  What are they?  Qualitative, usually based on graphs  Represent important system:  components  processes  linkages  Interactions

5. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s5 Conceptual Models  When should they be used?  As an initial step –  For hypothesis testing  For mathematical model development  As a framework –  For future monitoring, research, and management actions at a site

6. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s6 Conceptual Models  How can they be used?  Design field sampling and monitoring programs  Ensure that all important system attributes are measured  Determine causes of environmental problems  Identify system linkages and possible cause and effect relationships  Identify potential conflicts among management objectives  Anticipate the full range of possible system responses to management actions  Including potential negative effects

7. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s7 Conceptual Model Example Macrophytes Zooplankton refuges Nutrient release due to anoxia + - + + + - - - Fish cover Mean zooplankton size Grazing impact + Sedimentation rate Hypolimnetic oxygen depletion + Algal biomass + + + Increased nutrient loading Primary productivity Increased pH % blue-green algae + + + Transparency + +

8. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s8 Mathematical Models  What are they?  Mathematical equations that translate a conceptual understanding of a system or process into quantitative terms (Reckhow and Chapra 1983)  How are they used?  Diagnosis  E.g., What is the cause of reduced water clarity in a lake?  Prediction  E.g., How long will it take for lake water quality to improve, once controls are in place?

9. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s9 Categories of Mathematical Models Type Empirical Based on data analysis Mechanistic Mathematical descriptions based on theory Time Factor Static or steady-state Time-independent Dynamic Describe or predict system behavior over time Treatment of Data Uncertainty and Variability Deterministic Do not address data variability Stochastic Address variability/uncertainty

10. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s10 Mathematical Models  When should you not use a model?  If you do not understand the problem or system well enough to express it in concise, quantitative terms  If the model has not been tested and verified for situations and conditions similar to your resource  It is important to understand model:  Structure  Assumptions  Limitations

11. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s11 Remember!  Models do not substitute for logical thinking or other types of data collection and analysis  Models should not be more complicated than is necessary for the task at hand

12. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s12 Selecting or Developing a Model  Important first steps  Define the question or problem to be addressed with the model  Determine appropriate spatial and temporal scales  Identify important ecosystem components and processes that must be considered to answer the management questions

13. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s13 Selecting or Developing a Model  Some specific questions to ask  Temporal scale  Do I need to predict changes over time or are steady-state conditions adequate?  If time is important, do I need to look at  Short-term change (e.g., daily, seasonal) or  Long-term change (e.g., trends over years)?  Spatial scale  Is my question best addressed:  On a regional scale (e.g., compare streams in a region) or  By modeling specific processes within an individual system?

14. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s14 Lake Models  Most are based on mass balance* calculations * All fluxes of mass to and from specific compartments in the environment must be accounted for over time Annual Water Load to Lake Atmosphere Tributary Groundwater Runoff 40% 22% 17% 21%

15. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s15 Use Lake Models to Ask:  What is the lake’s present water quality?  Development:  What was the lake’s water quality before development?  How will future watershed development affect water quality?  Nutrients:  What are the most important sources of nutrients to the lake?  What level of nutrient loading can the lake tolerate before it develops algae problems?

16. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s16 Use Lake Models to Ask:  Nutrient management:  How much must nutrients be reduced to eliminate nuisance algal blooms?  How long will it take for lake water quality to improve once controls are in place?  How successful will restoration be, based on water quality management goals?  Are proposed lake management goals realistic and cost effective?

17. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s17 Eutrophication Modeling  Excessive nutrients that promote algal growth were identified as the most important problem in 44% of all U.S. lakes surveyed in 1998 (U.S. EPA 2000) e.g., Lake Onondaga, NY

18. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s18 Phosphorus Dynamics in Temperate Lakes – Observations  Algal growth is usually limited by the supply of phosphorus (P)  An increase (or decrease) in P entering the lake over a year or season will increase (or decrease) the average concentrations of P and algae  A lake’s capacity to absorb increased P loading without consequent algal blooms increases with:  Volume  Depth  Flushing  Sedimentation rates

19. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s19 Mass Balance Loading Models  Assumptions  Water quality is degraded by excess phosphorus in the lake  Phosphorus comes in from the watershed (including sewage outfalls)  Phosphorus leaves the lake via outflows and by sedimentation

20. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s20 Conceptual Model of Nutrient Effects on Water Quality  Natural phosphorus loading  Geology/land use  Precipitation  Hydrology  Lake morphometry

21. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s21 Model Goals  Estimate how much phosphorus is entering the lake in order to estimate the lake water concentration under different scenarios  Once you can predict the lake phosphorus concentration, use empirical relationships to deduce other water quality parameters such as:  Chlorophyll-a (algae)  Secchi depth (clarity)  Dissolved oxygen in the hypolimnion (bottom layer)

22. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s22 Model Assumptions  Algal growth is limited by phosphorus  Not limited by nitrogen, light, grazers or other factors  The whole lake volume is well-mixed  Water inflow equals water outflow  Phosphorus obeys mass balance principles

23. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s23 Model Steps 1. Develop hydrological and nutrient budgets 2. Calculate lake phosphorus concentrations from external and internal phosphorus loading 3. Predict water quality from lake phosphorus concentration 4. Verify the model 5. Forecast and track changes in water quality

24. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s24 Step 1 – Hydrologic Budget Inflow + precipitation = outflow + evaporation + change in storage

25. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s25 Step 1 – Phosphorus Budget External load = outflow load + sedimentation – internal load + change in storage

26. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s26 Step 2 – Predicting Phosphorus Concentrations Four variables are calculated:  Ave. input P concentration = external P load / outflow  Ave. water residence time = lake volume / outflow  Mean depth = lake volume / lake surface area  Net P retention = (sedimentation – internal load) / external load Annual Water Load Atmosphere Tributary Groundwater Runoff 40% 22% 17% 21% Annual P Load Internal 64% Runoff 22% Groundwater 3% Tributary 3% Atmospheric 8%

27. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s27 Step 3 – Relationships Between P and Other Water Quality Variables Log chla Log Total P Total P Secchi Transparency (m)

28. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s28 Step 4 – Model Verification  Water quality models must be tested with real field data under baseline conditions to ensure that they work!  Field sampling must consider several dimensions:  Depth  Sampling location  Seasonality  Annual variation  Analytical error and natural variability must be considered

29. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s29 Step 5 – Forecasting and Tracking Changes in Water Quality Reducing inflow P led to reduced in-lake P concentrations

30. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s30 Example – Lake Washington, WA  Urbanized lake east of Seattle  Sewage was diverted from the lake into Puget Sound  Eutrophic lake recovered to meso-oligotrophic

31. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s31 Example – Lake Washington

32. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s32 Example – Shagawa Lake, MN  Adjacent to the Boundary Waters Canoe Area Wilderness  Moderate size, shallow  Eutrophic from Ely, MN sewage  Recovery slower than expected after new Advanced Wastewater Treatment System put in  Slow recovery due to long- term sediment phosphorus release

33. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s33 Example – Shagawa Lake Annual temperature and dissolved oxygen data

34. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s34 References  Reckhow and Chapra  Terrene Institute

35. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s35 End of Lecture One

36. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s36 Watershed Models  This section has three main purposes. It should help you to:  Understand when and how modeling can contribute to watershed assessment  Learn approaches and tools that are useful for watershed modeling  Note: watershed assessment can require different tools and approaches from traditional point source modeling  Understand the considerations in choosing models for watershed assessments