water environmental model

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Water Environmental Model and Inverse Problem

1Dr. Xiaodong LiuHohai University 1Outline of the Lecture Introduction to WEM A personal perspective on WEM Mixing in Rivers Inverse Problem of WEM

2Outline of the Lecture Introduction to WEM A personal perspective on WEM Mixing in Rivers Inverse Problem of WEM



5Methods for studying water environmentObservation is often the first step in asking environmental questions.

Questions may form the first step in designing experiments and models.

61Methodsfield observation

Field work at Lake Tai 20037

TaihuOctober 20078Lake TaiorLake Taihu is a largefreshwaterlakein theYangtze Deltaplain nearShanghai,China. The lake belongs toJiangsuprovince With an area of 2,250 square kilometers and an average depth of 2 meters (6.6ft), it is the third-largest freshwater lake inChina, afterPoyangandDongting. In recent years, Lake Tai has been plagued by pollution as a result of rapid economic growth in the surrounding region.

Lake TaihuTaihuYangtze River

Location9Taihu Sensors

Vaisala WXT 510Air T, WD, WS, Rain, AP

Apogee Solar RadiationSeaPoint Turbidity and Chlorophyll a

Instrument NorthwestpHZebra-TechDO

NexSensTemp Chain

iQuestDatalogger and GPRS

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Lake water quality monitoring!high tech of field observation

1Real time monitoring 2Remote Sensor11

Remote Sensing

122ExperimentationExperiments can be used to test hypotheses.

An ecologist may set up an artificial environment in a laboratory or greenhouse, or carefully alter conditions in selected parts of natural ecosystems.13Methods lab experiments

Sediment flumeSediment flume

Phytoplankton growth143ModelingMany environmental events occur over such long periods of time or over such large distances that they are difficult to study directly.

Ecologists make models to help them understand these phenomena.1516Advantages of Environmental ModelingA good model can reveal more about a environmental processes and responses than we might otherwise learn through conventional (i.e., limited number) sampling techniques. Spatio-temporal continuity & large-scale.Modeling can predict how water quality might behave before any pollution occurs. Prediction.Modeling can be used to simulate different mitigative measures to minimize potential impacts from development activities. Scenario. What is a model? - All models are wrong, but some are useful.George Edward Pelham Box FRS (born 18 October 1919) is a statistician, who has made important contributions in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference. Box famously wrote that "essentially, all models are wrong, but some are useful" in his book on response surface methodology with NormanR. Draper.

17Understanding ModelsWhat is a model?A model is a simplified representation of the real worldThere are two types of modelsConceptualMathematicalFishing EffortEquilibrium YieldSurplus Yield Model (Lackey and Hubert 1978)Developed by: Hagley Updated: May 30, 2004 U5-m21a-s#18Reckhow, K.H., and S.C. Chapra. 1983. Engineering Approaches for Lake Management. Vol. 1: Data Analysis and Empirical Modeling. Butterworth Publ., Boston, MA. A model is a simplified representation of a real object, process, concept, or system (Reckhow and Chapra 1983)Conceptual ModelsWhat are they?Qualitative, usually based on graphsRepresent important system: componentsprocesseslinkagesInteractionsDeveloped by: Hagley Updated: May 30, 2004 U5-m21a-s#Conceptual ModelsWhen should they be used?As an initial step For hypothesis testingFor mathematical model developmentAs a framework For future monitoring, research, and management actions at a site

Developed by: Hagley Updated: May 30, 2004 U5-m21a-s#Conceptual ModelsHow can they be used?Design field sampling and monitoring programs Ensure that all important system attributes are measuredDetermine causes of environmental problems Identify system linkages and possible cause and effect relationshipsIdentify potential conflicts among management objectivesAnticipate the full range of possible system responses to management actionsIncluding potential negative effectsDeveloped by: Hagley Updated: May 30, 2004 U5-m21a-s#Conceptual Model ExampleMacrophytesZooplankton refugesNutrient release due to anoxia+-+++---Fish coverMean zooplankton sizeGrazing impact+Sedimentation rateHypolimnetic oxygen depletion+Algal biomass+++Increased nutrient loadingPrimary productivityIncreased pH% blue-green algae+++Transparency++Developed by: Hagley Updated: May 30, 2004 U5-m21a-s#22This is a conceptual model of the biotic and chemical interactions involved in the food web and their influence on eutrophication. A plus sign indicates a positive influence and a minus sign indicates a negative influence. The conceptual model in this slide represents biotic interactions and nutrient cycling in a lake or reservoir ecosystem. Biota in one trophic level affect those in another trophic level in many ways directly through predation or changes in the physical or chemical characteristics of the water, or indirectly through nutrient cycling pathways. Holdren et al. 2001.

Holdren, C., W. Jones, and J. Taggart. 2001. Managing Lakes and Reservoirs. N. Am. Lake Manage. Soc. and Terrene Inst., in coop. with Off. Water Assess. Watershed Prot. Div. U.S. Environ. Prot. Agency, Madison, WI.Mathematical ModelsWhat 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?DiagnosisE.g., What is the cause of reduced water quality in a lake?PredictionE.g., How long will it take for lake water quality to improve, once controls are in place?Developed by: Hagley Updated: May 30, 2004 U5-m21a-s#23A mathematical model is a mathematical equation or set of equations that translates a conceptual understanding of a system or process into quantitative terms (Reckhow and Chapra 1983).

Categories of Mathematical ModelsTypeEmpiricalBased on data analysisMechanisticMathematical descriptions based on theoryTime FactorStatic or steady-stateTime-independentDynamicDescribe or predict system behavior over timeTreatment of Data Uncertainty and VariabilityDeterministicDo not address data variabilityStochasticAddress variability/uncertaintyDeveloped by: Hagley Updated: May 30, 2004 U5-m21a-s#Mathematical ModelsWhen should you not use a model?If you do not understand the problem or system well enough to express it in concise, quantitative termsIf the model has not been tested and verified for situations and conditions similar to your resourceIt is important to understand model:StructureAssumptionsLimitations

Developed by: Hagley Updated: May 30, 2004 U5-m21a-s#Mathematical modeling .

Mathematical modeling involves teamwork2626 Mathematical Modeling Process

2727Emphasize the various approximations involved in the modeling process:RWP WM MMMM CMCM R/C

Development & application

28Teamwork!!!

29 Common used Environmental model

1EFDC (EPA) 2CAEDYM (CWR) 3WASP (EPA) 4ECOPATH () 5MIKE (DHI) 6QUAL2E (EPA) 7Delft3D (Netherlands)30Outline of the Lecture Introduction to WEM A personal perspective on WEM Mixing in Rivers Inverse Problem of WEM

31WASP 7 CourseBasic Principle of Mechanistic ModelsLaws of ConservationConservative properties are those that are not gained or lost through ordinary reactions. Therefore we can account for any change by simply keeping track of all those processes that can cause changeExamples of conservative propertiesMass (water mass, constituent mass)MomentumHeat Model Equations N-S equation

33HYDRODYNAMIC EQUATIONSThe equation of continuity, based on the conservation of water mass, predicts water heights (heads) and velocitiesMethodsmodel

34CASE-Lake Tai wind-driven circulation Control VolumezyxConservation of constituent massWater Quality Model36

Three Dimensional Pollutants Transport Equation

Typical waste materialsNatural Inorganic Salts and SedimentsWaste HeatOrganic WastesTrace MetalsSynthetic Organic ChemicalsRadioactive MaterialsChemical and Biological Warfare Agents37WEM38SolversOutputCategories of WEM39

Outline of the Lecture Introduction to WEM A personal perspective on WEM Mixing in Rivers Inverse Problem of WEM

40What is Mixing ProcessHydrologic Transport ProcessesAdvectionDiffusion (molecular)Diffusion (Turbulent)DispersionMixingEvaporationParticle Settling

41Hydrologic Transport ProcessesAdvection: Transport by an imposed current system, as in a river waters.42

Diffusion (molecular): The scattering of particles by random molecular motions,which may be described by Ficks law.

Hydrologic Transport ProcessesDiffusion (Turbulent):The random scattering of particles by turbulent motion. (which are much larger than molecular diffusion.)43Straight lineLaminar flow pattern Turbulence flow patternReynolds test Hydrologic Transport Processes44

Hydrologic Transport ProcessesDispersion: The scattering of particles by the combined effects of shear and transverse diffusion.45

uniform flow shear flow Consider flow between two paralllel plates of infinite extentOXOXuuUniformShear46ut0 ut0

20155215647DispersionOXuyyyhu(y)u(y)OXc(y)yyhc(y)47Hydrologic Transport ProcessesMixing: Diffusion of dispersion as described above; any process which causes one parcel of water to be mingled with or diluted by another. 48

AdvectionDiffutionDiffusion Coefficients49

49Mixing in Rivers

Consider a stream of effluent discharged into a river, as sketched in the figure.Three stages in the mixing of an effluent into a river Stage 1Vertical Mixing

Effluent ~ Vertical mixing uniform section Mixing: The initial momentum of the discharge determine the rate of waste dilution. 3D model shouid be applied to simulate the mixing process of pollutants.

2D model shouid be applied to simulate the mixing process of pollutants.Stage 2Transverse MixingVertical mixing uniform section ~ Transverse mixing uniform section

To simulate the mixing process of pollutants, 1D model should be applied.

Stage 3longitudinal MixingTransverse mixing uniform section ~Stage 1Stage 3Up streamQeffluentStage 2Outline of the Lecture Introduction to WEM A personal perspective on WEM Mixing in Rivers Inverse Problem of WEM

54WEM55Output C(x,y,z,t)Inverse Problems of WEM56Output C(x,y,z,t)Determination of Ex57The one-dimensional dispersion equation

MVoxxo

Under the conditions of instantaneous source andsteady flow, the concentration in downstream can be obtained.Determination of Ex58

Inverse ModelEx=?CASE STUDY...59

1Case Study: Lake Chao Water Diversion

1 D river modelWater Environmental Model

3D Lake Model2DYangziRivermodel

Model VerificationWater quality models must be tested with real field data under baseline conditions to ensure that they work!Field sampling must consider several dimensions:DepthSampling locationSeasonalityAnnual variationAnalytical error and natural variability must be considered

Sampling location

Mesh xy150m3Model Verification63Model Verification TN

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The development of Management System

ThanksLake Hamilton, NZ66

water environmental model

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