The “Modeling” Environment - Importance of model calibration and confirmation (prior to management decision)

Water Quality Modeling Process

1. Problem specification: start Clarification of the customers’ objectives (what you’re dealing with) Two information sources - Management objectives, control options, and constraints (physical, legal, regulatory, economic) - Collection of data (or pre-existing data) – physics, chemistry, biology of the target water body  Acknowledging problem objectives, water quality variables, and basic structure of the target systems (temporal, spatial, and kinetic mechanisms of the systems)

Water Quality Modeling Process 2. Model Selection - Use of existing models - Development of new model Theoretical development – critical issue → model complexity,  “as simple as possible, but not too simple“ Numerical specification and validation – numerical solution and test for its mathematical expressions (mass balances, simple solutions, range of conditions, graphical evaluation, benchmarking-  testing)

Water Quality Modeling Process 3. Preliminary Application - Useful for identifying data deficiencies and theoretical gaps - Useful for identifying the most important model parameters (e.g., Sensitivity analysis) 4. Calibration – Tuning the model - Varying the model parameters to obtain an optimal agreement between the model calculations and data set in a systematic way: a) Forcing functions and physical parameters: initial and boundary conditions, loadings, physics) b) Calibration parameters (kinetics) - Adjustment of model parameters a) Fix the system parameters measured with sufficient precision b) Adjust the estimated parameters in reasonable ranges until a best fit

Water Quality Modeling Process 5. Confirmation and Robustness (verification) -Applying the newly developed model for new several data sets: varying forcing functions and physical parameters to reflect new conditions, but no change in kinetic parameters No match? → additional mechanism characterization, model refinement, fine tune - The actual goal of confirmation → robustness using more and diverse confirmation processes

Water Quality Modeling Process 6. Management Application - Predicting the effects of the environmental improvement (remedial action) by changing model parameters and forcing functions → 7. Post-Audit - Lessons from the implementation of models in remedial actions (before and after)

QUAL Model Comprehensive and versatile stream water quality model History of QUAL model QUAL-I (1970) – Texas Water Development Board QUAL-II (1972) – Water Resources Engineers, Inc. QUAL2E (1987) – USEPA, Center for Water Quality Modeling (Brown and Barnwell) QUAL2K (2003) – USEPA, Center for Exposure Assessment Modeling (Chapra and Pelletier)

QUAL 2K Model One dimensional simulation – complete vertical and lateral mixing in the channel Steady and nonuniform flow Backward-time/backward-space (BTBS) difference (implicit) approach Simulation of steady or quasi-steady state – model runs until it reaches steady state → long-term prediction (for the period during which flows and loadings are constant) Simulation of unsteady state (time-variable) – only for diurnal variations in water quality variables, heat budget, and temperature → simulated on a diurnal time scale Software environment and interface – MS Excel (Visual Basic) Model segment – unequally-spaced reaches, multiple loadings/abstractions can be allocated to each reach

QUAL 2K Model CBOD (carbonaceous BOD) speciation – slowly oxidizing BOD (slow CBOD) and rapidly oxidizing BOD (fast BOD) Anoxia – at low oxygen levels, oxidation reaction is reduced to “0”. Denitrification (1st- order reaction) at low oxygen levels becomes significant. Sediment-water interactions – sediment-water fluxes of DO and nutrients are simulated internally (oxygen (SOD) and nutrient fluxes are simulated as a function of settling particulate OM, reactions within the sediments, and the conc. of soluble OM in the overlying water. Light extinction – simulated as a function of algae, detritus, and inorganic solids. pH – alkalinity and total inorganic carbon are simulated, and then pH is simulated based on these quantities. Pathogens – A generic pathogen is simulated (pathogen removal = f (temperature, light, and settling))

QUAL 2K Model Simulation constituents - Temperature, conductivity, inorganic suspended solids, total suspended solids, DO, slowly CBOD, fast CBOD, ultimate CBOD(=slow CBOD + fast CBOD + phytoplankton biomass+ detritus), detritus (particulate organic matter), TOC, dissolved org.-N, NH 4 + /NH 3, NO 3 -, TN, TKN, dissolved org.-P, inorg.-P, TP, floating algae (phytoplankton), bottom algae, pathogen, pH, Alkalinity

QUAL 2K Model 1. Conceptual representation CSTRs (reaches) in series (variable length reaches) Advection, Dispersion, Reaction in each reach 2. Functional representation for each reach Hydraulic balance equation (dQ/dt, inflow, outflow, external sources or withdrawals) Heat balance equation (dT/dt, inflow, outflow, surface heat exchange, heat exchange with sediment) Mass balance equation (dc/dt, advection, dispersion(diffusion), reactions, external sources and sinks) 3. Strings of reaches Same system parameters (hydrogeometric parameters-velocity, area, depth, Manning’s parameters, etc.-QUAL 2 model assumes a trapezoidal cross- section)

Conceptual representation Stream i+1 x ixix i-1 x Computational reach i xx Q xi QiQi Q i-1 FLOW BALANCE

Conceptual representation MASS BALANCE (Q x C x ) i (QC) i (QC) i-1 “S i ” DL CDL C  x  x A i DL CDL C A AccumulationDispersionAdvectionReactionsExternal sources / sinks Transport

Flow balance Flow balance at steady state for each reach

Hydraulic characteristics Water velocity and depth determined by one of the following methods – choose one of them 1. Weirs

2. Manning’s equation – trapezoidal cross-section Manning’s n value Generally, n increases with decreasing depth Typical values = ~ 0.15 for rough natural channels for the bankfull stream (for the stream under bankfull conditions, n could be higher than these values

3. Rating curves Power equations for the determination of mean velocity and depth of a stream a, b, , and  can be determined from velocity-discharge and stage-discharge rating curves (intercept → a, , slope →b,  ). Discharge, Q (m 3 /s) velocity, U (m 2 /s) Discharge, Q (m 3 /s) stage, H (m)

Travel time The residence time for each reach The travel time from the headwater to the downstream end of reach i Dispersion The longitudinal dispersion for each reach, E p,i – determined by Fisher’s eqn. or measured value entered, Numerical dispersion Note:

Heat budgets Significant impacts on water quality - Physical processes (thermal stratification), chemical and biological transformations of matters in water - Diurnal temperature variations: ammonia toxicity - Effects on biota Relationship btw. Temp and Heat  Water has a very high value of specific heat T = temperature ( o C or K)  = density (kg/m 3 or g/cm 3 ) H = heat (J or cal) C p = specific heat (J kg -1 o C -1 or cal g -1 o C -1 ) substanceDensity (kg/m 3 ) at 20 o CSpecific heat (J kg -1 o C -1 ) Dry air Water Common brick Cast iron

Heat balance Governing equation Accumulation = inflow – outflow  surface heat exchange  heat exchange with sediment Accumulation: Inflow: Outflow: Surface heat exchange: Heat exchange with sediment: Total balance Surface heat exchange InflowOutflow Heat exchange with sediment

Surface heat exchange The components of surface heat exchange Radiation – energy that transmitted in the form of electromagnetic waves and does not depend on matter for its transmission Non-radiation – depends on the motion of molecules of matter Net absorbed radiation – independent of water temperature Water-dependent components – affected by water temperature

Surface heat exchange The total surface heat flux J sn = net solar shortwave radiation J an = net atmospheric longwave radiation J br = longwave back radiation from the water J c = conduction J e = evaporation Net absorbed radiation Solar shortwave radiation = f (solar altitude, scattering, absorption, reflection, shading) J 0 = extraterrestrial radiation a t = atmospheric attenuation (Bras’ method = f (turbidity) or Ryan/Stolzenbach’s method = f (elevation, solar altitude) a c = cloud attenuation 1-R s = reflection, R s = albedo (fraction reflected) 1-S f = shading, S f = effective shade (fraction blocked by vegetation and topography) Atmospheric longwave radiation – longwave radiation emitted by the atmosphere itself  = the Stefan-Boltzmann constant T air = air temp. ( o C)  sky = effective emissivity of the atmosphere 1-R L = reflection, R L = longwave reflection coeff. (  0.03)  sky can be determined by one of three methods: Brutsaert’s, Brunt’s, and Koberg’s (QUAL2K manual - Brutsaert’s method-physically-based, good for intermeidate latitude- is broadly used)

Surface heat exchange Water-dependent components Water longwave radiation – back radiation from the water surface  = emissivity of water (  0.97) T s = water surface temp. Conduction (transfer of heat from molecule to molecule when matter of different temperatures come into contact) and convection (heat transfer that occurs due to mass movement of fluids) c 1 = Bowen’s coeff. (  0.47 mmHg/ o C) f(Uw) = wind velocity term, determined by one of three methods: Brady-Graves-Geyer’s, Adams 1’s, and Adams 2’s (QUAL2K manual) Evaporation and condensation – heat loss represented by Dalton’s law e s = saturation vapor pressure at the water surface (mmHg) e air = vapor pressure in the overlying air (mmHg) Wind speed conversion – to enter the equivalent wind velocity value in QUAL 2K (wind speed at 7 meters above the water surface) U wz = wind speed measured at a height z w (m/s) z = 7 m, z w = height at wind speeds measured (m)

Sediment-water heat exchange Heat flux btw. bottom sediment and overlying water Total heat flux Net solar radiation Atmospheric longwave radiation Water longwave radiation Conduction/ convection Evaporation/ condensation Sediment-water heat exchange  s = sediment density (g/cm 3 ) C ps = specific heat for the sediment (0.7 cal g -1 o C -1 in QUAL 2K)  s = sediment thermal diffusivity (0.005 cm 2 /s in QUAL 2K) H sedi = effective thickness of the sediment layer (cm) T sedi = temp. of the bottom sediment

Atmospheric moisture Relative humidity e air = vapor pressure of the air (mmHg) e sat = saturation vapor pressure (mmHg) T d = dew-point temperature Ex 30.3 calculation of relative humidity, dew point and air temp. Air temp = 25 o C, relative humidity = 60%, and water temp. = 35 o C (a) Air vapor pressure and dew-point temp. (b) Evaporation takes place?

Temperature simulation in QUAL 2K Heat balance for a reach I, Bulk dispersion coefficient, Net heat loads from point/nonpoint sources,