Lesson 3b Environmental Models...Lesson 3b – Environmental Models Spatial and temporal simulations...

Lesson 3b – Environmental Models Spatial and temporal simulations to inform sensor system design

• Environmental scientists and engineers often use models to simulate environmental systems

• Short-term questions to help with specific tasks: – What will the fate of chemical X

be if it is released into the river? – How rapidly will fertilizer be

transported through the soil zone to the groundwater?

• Long-term questions related to bigger issues – How do we expect reservoir

conditions change with climate change forecasts?

– How will releases from a waste treatment facility affect long-term fishery conditions?

IITR-UCM-NI Water Sustainbility & Sensor Networks Course

Environmental model terminology

State variables: Quantities or properties of the environmental system which change in time and space Examples: chemical concentration, water temperature

External forces or drivers: Processes (constant or time-variable) which influence the state variables without being influenced by them Examples: sunlight forcing a photoreaction in water, wind mixing a

chemical in a lake Input: (special case of external driver) Mass flux into the environmental system

Example: Chemicals flowing from a pipe into a river Internal processes: Transport or reaction processes that affect one or more

state variables Examples: Decay of a chemical, heating of water by solar radiation Model parameters: define the types and rates of the internal process

Examples: Reaction rate constant, water-to-air flux rate Output: (special type of internal process) Mass flux out of the environmental

system Examples: Canal flowing from a reservoir, volatile chemical leaving a lake

for the atmosphere IITR-UCM-NI Water Sustainbility & Sensor

Networks Course

Environmental Models and Sensor System Design

• The models are in effect quantitative hypotheses about how we believe the environment will behave

• Good news: we understand the physical processes well, and the chemical and biological processes to some extent

• Bad news: the “geometry” of the problem (spatially variable properties) complicates the physical processes – This forces us to “tune” the models

(formally known as model calibration or inverse modeling)

• Sensor systems are helping to help to address the bad news – More data in time and space

– Better model testing

Calibrated model Observed temperature


Model Calibration/Inverse Modeling

• Model calibration is an important area and large and active research field

• It is closely related to sensor network design

• There are two aspects to our design: 1. (Environmental) Number and

location observations needed to validate the model sufficiently

2. (Technical) Number and locations of data acquisition and communication systems, and power management

• IMPORTANT: We are not trying to create the “perfect” simulation; instead, we are trying to create simulations adequate to address our problem


Model Validation

• Model validation follows the calibration process, and is the true test of the model

• The validation process uses the calibrated model to simulate new data (data not used during the calibration)

• Reasons for poor validation results: o Calibration data did not cover a broad

range of forcing conditions o Model processes are incorrect or

incomplete (calibration was somewhat lucky)

• Often, the calibration and validation process is iterative, with the model continuously being improved o This iterative process can include adding

new sensors, changing locations and sampling frequencies

o We relate our choices here quantitatively to the model error

07/16/1994 - 12/31/2000 calibration period

01/01/2001 - 12/31/2001 verification period

Again, we typically have a acceptable level of error summarized statistically (RMS, for example), and we check that the errors are random (unbiased)


Simple environmental models: “box” models

These models focus on mass input, outputs, and mass reaction or transfer rates

The environmental system is assumed to be homogeneous (all properties are the same throughout the medium)

Take the following simple example: 2 chemicals i and j enter a lake and react with each other:

Ii , Ij

YCCX ji

Oi , Oj

Volume, V

Materials balance (focused in i): Change in concentration of i with time = input – output – reactions removing i + reaction producing i

iiiii PROI

dt

dCV


Example Lake Model (adapted from Schwarzenbach et al. (2003) Environmental Organic Chemistry , 2nd edition, Wiley Interscience)

Lake volume

o Total volume, V

o Epilimnion, VE

o Hypolimnion, VH

Area

o Lake surface, Ao

o At thermocline, Ath

Inflow = outflow = Q

Chemical i concentration = C

Mass input (chemical i) = QCi

Ave. windspeed @ 10m above the lake, u10

Ave. incident solar radiation

Air-water exchange velocity, vaw

Epi-hypo exchange velocity, vth

Chemical decay rate, kd

Simple profile view of a lake

Epilimnion

Hypolimnion

Benthos (sediments)

input output

Note: the “thermocline” is the temperature gradient between the (warm) epilimnion and (cold) hypolimnion; it is typically narrow in depth compared to the two lake regions


Chemical pollution in a small lake

Problem: Observations reveal that the lake has a relatively constant concentration of the pollutant X. The river input and output for the lake is known. Analyze the dynamic behavior of pollutant X in this lake, assuming that it is nonvolatile (no flux to the atmosphere) and that it decays at a reaction rate proportional to its concentration (first-order decay rate, units time-1).

Let’s discuss the assumptions in the model as shown here

0 CVkQCQCdt

dCV din



Solution: Given our assumptions, and the fact that the observed concentration is relatively constant, we can easily solve the equation.

0 CVkQCQCdt

dCV din

So, a steady state (constant with time) observation here is a function of the balance between dilution (Q/V term) and decay rate (kd term).

d

in

VkQ

QCC

d

in

kVQ

CVQC

/

/or


Sensor system for monitoring this example

We place a sensor and communication system on the lake (an instrumented buoy)

According to our model, the location is not important

Measurements may be made perhaps every day; more frequently is not necessary

output input

Question: What if we were interested in knowing about algae concentrations in the lake? - Algae need sunlight to grow - Algae can sink to the hypolimnion where

they stop reproducing (no light) How might our sensor system change?



Different Solution: What if the input concentration became zero (for example, if we stopped putting X in the river)? Now, we have a transient case:

0 CVkQCQCdt

dCV din

Here, we have an exponential reduction of the concentration where the overall reduction rate is a function of outflow and decay. Now, we may wish to measure more frequently to observe the reduction rate

CkVQdt

dCd / or

0

dtkVQC

dCd /

tkVQCC do /exp


Additional model complexity is possible, depending on the problem(s) under investigation

Lake model approach from Global Lake Ecological Observation Network (GLEON) see: http://cdi.gleon.org/models/numerical-model/


http://cdi.gleon.org/models/numerical-model/




Distributed parameter numerical models

• As we increase complexity, it will typically become difficult to assess natural systems using analytical solutions

• Finite difference or finite element “grid” models solve for hydrodynamic and reactive transport in smaller, interconnected pieces – The environmental

parameters can then be assigned locally

• Many such modeling systems exist for soil, groundwater, rivers, lakes, oceans, and the globe (Global Circulation Models, GCMs)

Example software packages: Proprietary: MIKE software by DHI - http://mikebydhi.com/ Proprietary: EMSI software - http://www.ems-i.com/ U.S. Geological Survey (typically freeware) - http://water.usgs.gov/software/


http://mikebydhi.com/

http://mikebydhi.com/

http://www.ems-i.com/




http://water.usgs.gov/software/

http://water.usgs.gov/software/

Other environmental models: Soils and Groundwater

• Soil and groundwater models simulate the movement of water and chemicals in the subsurface (porous media)

• Soil models are more complicated: soil, air, water

• Groundwater models less complicate: soil, water

• Geospatial statistical approaches are important here – Largest challenge here: soil

properties vary greatly with soil type, and soil type changes spatially and can be difficult to assess (particularly deep in the subsurface)


Sensor systems in Soils and Groundwater

• Installation of sensors in soils and groundwater requires digging or drilling in the soil

• For shallow applications (agriculture) this is not difficult

• For deeper, groundwater applications, observation wells are needed and this can be difficult and expensive – Best to use existing wells as much as

possible, but sometimes these are not available


Other environmental models: Watershed models

• Simulates hydrology and surface water flows

• More recently, these models have been integrated with soil and groundwater models: Integrated Watershed Management models

• These complex models were made to be supported by data from sensor systems!

Chesapeake Bay watershed (east coast U.S.) US Geological Survey study: http://md.water.usgs.gov/publications/ofr-2004-1433/sparv3.htm#seg


http://md.water.usgs.gov/publications/ofr-2004-1433/sparv3.htm







Simple example: Laboratory sandbox

• Water flows from left to right through uniform sand (a very simple groundwater model)

• Thermocouples are placed in the sand and a warm water source is introduced

• We use the resulting data to (1) calibrate a model, and (2) test the model for locating the source with a varying number of sensors Details in provided paper (Day 3 folder):

Kim, Park and Harmon (2005). Real-Time Parameter Estimation for Analyzing Transport in Porous Media, Ground Water Monitoring & Remediation, 25(2), 78-86.


Example (continued)

• The software flow chart at right shows how we collected, analyzed and interpret the data in near real-time

• Below, is the LabView™ interface for visualizing the results


Example (continued)

• A simple 3D heat transfer model was used to simulate the water temperature in the sand

• The key parameters are (1) the heat dispersion parameters (kx, ky, kz) and (2) the heat source location and temperature

• Equation (5) is the analytical solution to this problem (it is applicable only for homogeneous systems, such as this one)


Example (continued)

• The sampling network design problem was posed as an optimization problem:

• (6) was solved using a gradient search algorithm (Levenberg-Marquardt)

• Results at right (top) show the best simulations after the key model mixing parameters (thermal dispersion coefficients) were auto-calibrated

• (bottom) These results tries to find the heat source using incrementally increasing numbers of sensors (more sensors, better chance to find the source)


Summary

Environmental simulation models are used to assess and forecast conditions between observation points (we cannot measure everywhere) This will depend on the sensor quality and the quality of the

calibration work done by the sensor user, and power management A wide variety of models are available for soil (irrigation), groundwater,

surface water (lakes, rivers), and integrated watersheds These models required estimate of environmental parameters (mixing,

reactions, etc.) which often vary in space and sometimes temporally as well Model calibration: Identifying model parameters by “tuning” the

model to historical data Model validation or verification: Testing the calibrated model

against new data or previously unused historical data It is wise to use an environmental model to help inform the sensor

system design (in addition to technical considerations such as data communication, power management, and budget)


Lesson 3b Environmental Models...Lesson 3b – Environmental Models Spatial and temporal simulations...

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