Introduction to Modeling Unit V, Module 21A. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s2...

Introduction to Modeling

Unit V, Module 21A

Developed by: Hagley Updated: May 30, 2004 U5-m21a-s2

Module 21Introduction to Modeling This module has three main goals. It will help

you: Understand how models help environmental

scientists:Learn about natural systemsPredict 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


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

Equ

ilibr

ium

Yie

ld

Surplus Yield Model (Lackey and Hubert 1978)


Conceptual Models

What are they? Qualitative, usually based on graphs Represent important system:

componentsprocesses linkages Interactions


Conceptual Models

When should they be used? As an initial step –

For hypothesis testingFor mathematical model development

As a framework – For future monitoring, research, and management actions at a site


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


Conceptual Model Example

Macrophytes

Zooplankton refugesNutrient 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

+

+


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?


Categories of Mathematical Models

TypeEmpirical

Based on data analysisMechanistic

Mathematical descriptions based on theory

Time FactorStatic or steady-state

Time-independentDynamic

Describe or predict system behavior over time

Treatment of Data Uncertainty and VariabilityDeterministic

Do not address data variabilityStochastic

Address variability/uncertainty


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


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


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


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?


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

Runoff40%

22% 17%21%


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?


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?


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


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


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


Conceptual Model of Nutrient Effects on Water Quality

Natural phosphorus loading Geology/land use Precipitation Hydrology Lake morphometry


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)


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


Model Steps

1. Develop hydrological and nutrient budgets2. Calculate lake phosphorus concentrations

from external and internal phosphorus loading

3. Predict water quality from lake phosphorus concentration

4. Verify the model5. Forecast and track changes in water quality


Step 1 – Hydrologic Budget

Inflow + precipitation = outflow + evaporation + change in storage


Step 1 – Phosphorus Budget

External load = outflow load + sedimentation – internal load + change in storage


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

Runoff40%

22% 17%21%

Annual P Load

Internal 64% Runoff 22%

Groundwater 3% Tributary 3%Atmospheric

8%


Step 3 – Relationships Between P and Other Water Quality Variables

Log

chla

Log Total P

Total PSecc

hi T

rans

pare

ncy

(m)


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


Step 5 – Forecasting and Tracking Changes in Water Quality

• Reducing inflow P led to reduced

in-lake P concentrations


Example – Lake Washington, WA

Urbanized lake east of Seattle

Sewage was diverted from the lake into Puget Sound

Eutrophic lake recovered to meso-oligotrophic


Example – Lake Washington


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


Example – Shagawa Lake

• Annual temperature and dissolved oxygen data


References

Reckhow and Chapra Terrene Institute


End of Lecture One


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

Introduction to Modeling Unit V, Module 21A. Developed by: Hagley Updated: May 30, 2004 U5-m21a-s2...

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