Developing a Graphical User Interface to Improve Learning of Stochastic Theory for Water Resources in the

Classroom

Faisal Hossain, Jonathan Schwenk and David Huddleston

Department of Civil and Environmental EngineeringTennessee Technological University

What is Stochastic Theory?

• Probability Theory

• Stochastic Processes

• Random Variables – Random Processes (that can be described by a probability distribution)

• Each time the process ‘acts’ it yields a different realization in time and space

• Repeatability is ‘probabilistic’

Why Stochastic Theory for Water Resources Engineering?

1. Uncertainty is omni-present in natural or man-made water resources systems.

2. Need understanding of Random functions, Probability, Distributions, Time series, Spatial trends – to model/predict the variability.

3. Hydrologic models – inherently uncertain (uncertain data, model assumptions, scale issues).

4. ABET requires some concepts of Probability and Statistics as part of CE curriculum.

Nothing stays the same FOREVER in Water Resources

Examples of Application of Stochastic Theory in Water Resources

1. Reservoir systems analysis – forecasting upstream inflow, power demand, navigation (optimization)

2. Flood Forecasting; Rainfall forecasting (time series analysis)

3. Data assimilation in adaptive schemes for real-time decision making (kalman filtering)

4. Improving model structure through reduction of uncertainty

5. Spatial Interpolation of groundwater contamination (kriging)

6. Flood frequency analysis (extreme value distribution)

ExamplesSYSTEM

SPATIAL

TEMPORAL

Emerging Needs related to Stochastic Theory in Water Resources

• More and more research conducted at graduate level involving stochastic theory applications

• Bloom’s learning level of entering graduate students should be ‘understanding’ or ‘application’

• Major demand raised on admission criterion for graduate applicants

• Graduate students should be prepared a priori on the application of stochastic theory

Questions we should ask

1. Are we doing a good job with instruction of stochastic theory in CE/Water resources?

2. What do statisticians think?

3. Are entering graduate students adequately prepared to conduct research involving this stochastic aspect in water resources?

4. What could we do to improve learning of students in classroom?

5. Could computer assisted schemes help? (e.g. GUI tools)

Instruction of Stochastic Theory(What do Statisticians Think?)

“For too long we in the statistics profession have tolerated poor statistics teaching, which produces courses that are often rated as the worst course or the most useless course that graduates in other fields claim they have ever taken. We too often teach what appears to the students a collection of unrelated methods illustrated by examples taken from coin-tossing, card-playing and dice-rolling. And then we expect the students to be able to translate this wide variety of methods with simple gambling examples to complex industrial problems involving the application of a large number of methods".

Godfrey, B. 1986. Future Directions in Statistics. Report 10 Center for Quality and Productivity Improvement, University of Madison, WI, 34-39.

OBJECTIVES

• 1. Gauge the current state of instruction of Stochastic Theory in Civil Engineering curriculum (survey courses).

• 2. Proof of Concept of a GUI-based instruction tool for teaching stochastic theory in the classroom.

Stochastic Theory in Civil Engineering Curriculum

• Survey conducted using the world wide web only.Survey method – search for ‘keywords’ from course title and description.Keywords – ‘Stochastic’, ‘Probability’, ‘Numerical’, ‘Systems’ etc.

ASSUMPTIONS:• Information posted by university course catalog or

instructor’s website on the world wide web is accurate and up to date.

• All relevant course content information is available from the world wide web.

• All courses are actively offered on a routine basis by instructors.

• The course has a significant amount of stochastic theory component (or a nearest relative discipline) delivered as course content.

Stochastic Theory in Civil Engineering Curriculum

Total Number of Universities Surveyed 67

Number of Universities with www listing of relevant courses 57

Total number of courses identified (having the generic terms ‘stochastic’, ‘statistics’, ‘numerical’ etc in CE curricula)

241

% Graduate(Dual listed) and Undergraduate 84(4.5)11.5

Number of schools with integrated courses on Stochastic Theory 40

Number of courses on Stochastic Theory 84

Number of courses on Stochastic Theory in Water Resources and Environmental Engineering

27 (11.2%)

Number of courses on Stochastic Theory in Water Resources only 23 (9.2%)

% is calculated by dividing the absolute number by the total number of courses surveyed (i.e. 241).

Preliminary Synopsis on Survey of Curricula on Stochastic Theory in the Nation

Current overwhelming representation of graduate courses perhaps underscores a current need to rethink strategies and strive for a more equitable distribution that would facilitate a smoother learning experience. For example, creating more undergraduate variants of these graduate courses and offering them early in a student’s CE education experience are likely to further strengthen the appreciation of the concepts on stochastic methods by the CE student.

Solution?Popularize Stochastic Theory using Graphical

User Interface (GUI) and Active Learning

1. A picture is worth a thousand words - Confucius

2. A picture is worth a million words if you can rapidly visualize the ‘words’ – Anonymous

3. GUIs can rapidly visualize ‘any way’ desired – Ideal for active learning

4. GUIs give full interactive control to manipulate and alter concepts and see the effect graphically almost immediately

5. A lot of GUIs in mathematics education – none exists (to the best of our knowledge) for stochastic theory in water resources education

STEVE – Stochastic Theory Education through Visualization Environment

Proof-of-Concept – Can it work in a classroom environment?

Core program is a Stochastic Model – Two Dimensional Satellite Rainfall Error Model – SREM2D

SREM2D corrupts true rainfall using various concepts of Stochastic Theory to simulate satellite rainfall

SREM2D

STEVE – Stochastic Theory Education through Visualization Environment

Screen Shot of STEVE 1.0

Entity Dependence Diagram for STEVE GUI

Coded in Java Native Interfacing – No O/S and compiler requirement!

Using GUI to improve student learningOne example – Geostatistics, Correlation lengths, spatial clustering1. Teach the theory – concept of variograms, lag distance, spatial correlation, modeling variograms, correlation lengths, interpolation (say kriging)

2. Next, allow students to use STEVE GUI:

• Alter parameters on variogram model type (exponential)

• Alter correlation lengths (high, low, medium)

• Observe – the effect on rainfall visualization

• Pose questions – seek answers – reconcile actual observation with expected observation through theory

• Improve learning through trial and error (rapid visualization is key to multiple iteration)

Using GUI to improve student learning

High Correlation Length

Medium Correlation Length

Low Correlation Length

CORRELATION LENGTHS IN RAINFALL

Using GUI to improve student learning

High Probability of Precipitation

Medium Probability of Precipitation

Low Probability of Precipitation

Conclusions

1. Survey of current curriculum on Stochastic Theory in Civil Engineering reveals a dominance of graduate courses (84%)

2. GUI for rapid visualization of stochastic theory concepts to ‘pictures’ has merit in improving student learning.

3. GUI educational tools for Stochastic Theory in Water Resources engineering is absent.

4. Technical and Software issues on GUI development need to be addressed.

Future Directions

1. Improve GUI’s computational aspect – visualization, portability, software

2. Survey (surveymonkey.com) of instructors on demand for such instructional tool.

3. Prototype testing in summer research camps using a group of control and test students

This work was funded by the Department of Civil and Environmental Engineering’s DMF Project

Support received from Dr. Ambareen Siraj on the development of STEVE GUI is greatly appreciated.

Derek Parsons of Computer Science Department led the development of STEVE

ACKNOWLEDGEMENTS