Assumptions

This page provides a complete overview of the assumptions made by the gwtransport package. Understanding these assumptions helps practitioners determine when gwtransport is appropriate for their application and how to validate results.

Module Reference

Module	Primary Functions
advection	gamma_infiltration_to_extraction(), infiltration_to_extraction(), infiltration_to_extraction_front_tracking()
residence_time	residence_time(), residence_time_mean(), freundlich_retardation()
deposition	deposition_to_extraction(), extraction_to_deposition()
logremoval	residence_time_to_log_removal(), gamma_mean(), parallel_mean()
diffusion_fast	infiltration_to_extraction()
gamma	bins(), mean_std_to_alpha_beta()

Physical/Hydrogeological Assumptions

1. Advection-Dominated Transport

Assumption: Microdispersion (mechanical dispersion) and molecular diffusion are negligible compared to macrodispersion (advective spreading from aquifer heterogeneity captured by the APVD).

Applies to: advection module (all functions), residence_time, deposition, logremoval

Does NOT apply when using: diffusion_fast or diffusion modules (which explicitly add diffusive spreading)

What this means: The spreading of solute plumes is dominated by macrodispersion (variation in flow path lengths — different streamlines have different travel times), not by microdispersion and molecular diffusion (processes within individual streamlines).

When it holds:

• Heterogeneous aquifers with significant pore volume variability

• Moderate to high flow velocities

• Short to moderate flow path lengths

When it fails:

• Homogeneous aquifers (low advective spreading)

• Very long flow paths (diffusion accumulates)

• Low flow velocities (more time for diffusion)

• High diffusivity materials

Testable: Yes - variance ratio test

\[\frac{\sigma^2_{\text{diffusion}}}{\sigma^2_{\text{advection}}} < 0.1 \implies \text{Diffusion negligible}\]

Understanding the scale-dependence:

What appears as “dispersion” at one scale becomes “advection through heterogeneity” at a finer observation scale. The APVD captures macrodispersion (velocity variations at the aquifer scale); \(\alpha_L\) captures microdispersion (velocity variations at the pore scale). These are the same physical phenomenon at different resolutions. See Macrodispersion and Microdispersion as Scale-Dependent Heterogeneity for details and Macrodispersion and Microdispersion for background.

Relationship to the diffusion module:

When using the advection module alone, only macrodispersion (spreading from the pore volume distribution) is modeled. To add microdispersion and molecular diffusion, use:

• gwtransport.diffusion_fast for approximate but fast Gaussian smoothing

• gwtransport.diffusion for analytical advection-dispersion solutions

Alternatively, use the “equivalent APVD std” approach described in Macrodispersion and Microdispersion in Solute Transport to convert microdispersion to equivalent APVD spreading, allowing continued use of the fast advection module.

2. Steady Streamlines

Assumption: The geometry of flow paths (streamlines) remains fixed over time; only flow rates vary.

Applies to: All modules (advection, residence_time, deposition, logremoval, diffusion)

What this means: When pumping rate doubles, water moves twice as fast along the same paths—the paths themselves don’t change. The pore volume distribution (see The Central Concept: Pore Volume Distribution) is only well-defined and time-invariant under this assumption: it is a property of the aquifer for a given streamline configuration. If boundary conditions change in a way that redirects flow, the streamlines rearrange and the APVD itself changes.

When it holds:

• Uniform scaling of flow field with pumping rate

• Stable boundary conditions (river stage, recharge patterns)

• No significant changes in aquifer properties

When it fails:

• Changing boundary conditions that redirect flow

• Multiple pumping wells with varying schedules

• Seasonal changes in recharge distribution

• Density-dependent flow (saltwater intrusion)

Testable: Yes - cross-validation across flow regimes. Calibrate on high-flow periods, validate on low-flow periods (or vice versa). If the same pore volume distribution works across flow regimes, the assumption holds.

3. Saturated Flow

Assumption: The aquifer is fully saturated; there is no vadose (unsaturated) zone transport.

Applies to: All modules

What this means: All pore space is filled with water. The package does not model variably saturated conditions, capillary effects, or air-water interfaces.

When it holds:

• Confined aquifers

• Unconfined aquifers below the water table

• Bank filtration systems with permanent saturation

When it fails:

• Vadose zone transport

• Perched aquifers

• Intermittently saturated zones

• Artificial recharge through unsaturated zone

Testable: No - this defines the domain of applicability. If your system includes significant unsaturated zone transport, gwtransport is not the appropriate tool.

4. Single Porosity

Assumption: All water flows through a single connected pore network; there is no matrix diffusion or dual-porosity behavior.

Applies to: All modules

What this means: Water in the aquifer is mobile and participates in flow. There are no stagnant zones where solutes can diffuse in and out, causing tailing.

When it holds:

• Granular aquifers (sand, gravel)

• Well-connected pore networks

• Systems where matrix diffusion timescales >> residence times

When it fails:

• Fractured rock aquifers

• Karst systems

• Clay-rich aquitards with diffusive exchange

• Dual-porosity media

Testable: No - this defines the domain of applicability. Characteristic signature of dual-porosity: extended tailing in breakthrough curves that cannot be explained by pore volume heterogeneity alone.

5. No Reactions or Decay

Assumption: Transport is conservative (no mass loss or gain). The package models only physical transport processes (advection, sorption), not chemical or biological reactions.

Applies to: advection, residence_time, deposition, diffusion

Partially relaxed in: logremoval module, which applies empirical decay coefficients as post-processing to residence times

What this means: What infiltrates will eventually be extracted (accounting for retardation). There is no:

• First-order decay (pathogens, radionuclides)

• Biodegradation

• Chemical reactions (precipitation, dissolution, redox)

• Volatilization

When it holds:

• Conservative tracers (chloride, bromide)

• Temperature (thermal transport)

• Solutes that are stable over residence time scales

• Short residence times where decay is minimal

When it fails:

• Pathogen transport (die-off occurs)

• Biodegradable contaminants

• Redox-sensitive species

• Radionuclides with significant decay

Testable: Partially - compare mass balance between infiltration and extraction. If extracted mass << infiltrated mass (after accounting for retardation and mixing), reactions/decay are significant.

Note

The log-removal calculations in the Pathogen Removal in Bank Filtration Systems example use an empirical rate coefficient to represent pathogen inactivation. This is a post-processing step, not part of the core transport model. For reactive transport, gwtransport predictions are conservative (over-predict concentrations).

6. No Transverse Mixing

Assumption: Each streamtube transports independently; there is no mixing or dispersion between adjacent streamlines.

Applies to: All modules (fundamental to the streamtube approach)

What this means: A parcel of water stays on its streamline from infiltration to extraction. Concentration differences between streamlines are preserved.

When it holds:

• Stratified aquifers

• Laminar flow conditions

• Short to moderate travel distances

When it fails:

• Highly heterogeneous aquifers with tortuous flow

• Long travel distances allowing transverse dispersion

• Turbulent flow (rare in porous media)

Testable: Difficult - requires spatially distributed concentration data. Indirect test: if model systematically over-predicts peak concentrations and under-predicts tails, transverse mixing may be significant.

7. Incompressible Flow

Assumption: Water is incompressible; mass is conserved; flow in equals flow out.

Applies to: All modules (fundamental assumption)

What this means: There is no storage change in the aquifer over the timescales of interest. The flow rate measured at extraction represents the flow through the entire system.

When it holds:

• Steady-state or quasi-steady flow

• Confined aquifers with minimal storage

• Timescales longer than aquifer response time

When it fails:

• Rapid transients (pumping tests)

• Significant aquifer storage effects

• Compressible aquifer materials

Testable: No - this is a fundamental assumption of the streamtube approach.

Model Parameterization Assumptions

8. Gamma Distribution Adequacy

Assumption: The two-parameter gamma distribution adequately represents the actual pore volume heterogeneity.

Applies to: Functions with gamma_ prefix only:

• gamma_infiltration_to_extraction()

• gamma_extraction_to_infiltration()

• gamma_mean(), gamma_pdf(), gamma_cdf(), gamma_find_flow_for_target_mean()

Does NOT apply to:

• infiltration_to_extraction() — accepts explicit pore volumes

• infiltration_to_extraction_front_tracking() — accepts explicit pore volumes

What this means: The shape of the pore volume distribution can be captured by specifying only mean and standard deviation. The gamma distribution is unimodal and right-skewed. See Gamma Distribution Model for background on this parameterization.

When it holds:

• Moderately heterogeneous aquifers

• Unimodal pore volume distributions

• When detailed pore volume data are not available

When it fails:

• Multi-modal distributions (e.g., multiple aquifer layers)

• Extreme heterogeneity

• When streamline analysis provides actual pore volumes

Testable: Yes

• If pore volumes are known: Kolmogorov-Smirnov test, Q-Q plot

• If only time series available: Check residuals for systematic patterns suggesting distribution mismatch

Alternative: Use infiltration_to_extraction() with explicit pore volumes from streamline analysis instead of gamma_infiltration_to_extraction().

9. Linear Retardation

Assumption: The retardation factor R is constant and does not depend on concentration.

Applies to: Most functions that accept a retardation_factor parameter:

• gamma_infiltration_to_extraction(), infiltration_to_extraction()

• gamma_extraction_to_infiltration(), extraction_to_infiltration()

• residence_time(), residence_time_mean()

• deposition_to_extraction(), extraction_to_deposition()

• infiltration_to_extraction()

Does NOT apply to:

• infiltration_to_extraction_front_tracking() — supports Freundlich (non-linear) sorption

• freundlich_retardation() — computes concentration-dependent R

What this means: All concentrations travel at the same retarded velocity. The sorption isotherm is linear. See Retardation Factor for background on retardation.

When it holds:

• Conservative tracers (R = 1)

• Temperature (R ≈ 2, constant)

• Linear sorption isotherms

• Low concentration ranges where isotherms are approximately linear

When it fails:

• Non-linear (Freundlich, Langmuir) sorption

• High concentrations approaching sorption capacity

• Concentration-dependent retardation

Testable: Yes - compare predictions with constant R vs. concentration-dependent R (Freundlich). The package supports non-linear sorption via infiltration_to_extraction_front_tracking().

Note

gwtransport provides exact solutions for Freundlich sorption using front-tracking. If non-linear sorption is suspected, use the front-tracking functions instead of assuming linear retardation.

10. Thermal Retardation Factor

Assumption: For temperature transport, the retardation factor R ≈ 2.0 (or another specified value) is appropriate.

Applies to: Any module when used for temperature transport (user must specify appropriate R)

What this means: Heat exchanges with the aquifer matrix, causing temperature signals to travel slower than water. The retardation factor depends on the ratio of heat capacities:

\[R = 1 + \frac{(1-n) \rho_s c_s}{n \rho_w c_w}\]

where n is porosity, ρ is density, and c is specific heat capacity.

When it holds:

• Known or typical aquifer thermal properties

• Uniform thermal properties along flow path

When it fails:

• Highly variable thermal properties

• Aquifers with unusual mineralogy

• Very high or low porosity

Testable: Yes - calibrate R as a free parameter and check if:

1. The optimized value is physically plausible (typically 1.5-3.0)

2. The confidence interval is reasonable

3. The value is consistent with known thermal properties

Data and Input Assumptions

11. Representative Input Signal

Assumption: The measured infiltration concentration/temperature represents the actual input to the aquifer system.

Applies to: All modules that take cin (infiltration concentration) as input:

• advection module (all forward functions)

• infiltration_to_extraction()

• deposition_to_extraction() (for deposition rates)

What this means: The monitoring point captures the true input signal without significant bias, lag, or spatial averaging issues.

When it holds:

• Monitoring point is at or near infiltration location

• Infiltration zone is spatially uniform

• No significant lag between surface water and infiltration

When it fails:

• Monitoring distant from actual infiltration

• Spatially heterogeneous infiltration zone

• Significant travel time through riverbed/bank

• Multiple infiltration sources with different signals

Testable: Yes - sensitivity analysis. Perturb input signal timing (shift by days) and magnitude (scale by %) and assess impact on predictions.

12. Well-Mixed Extraction

Assumption: All streamlines contribute to extracted water simultaneously as a flow-weighted average.

Applies to: All modules that compute extraction concentrations:

• advection module (all functions computing cout)

• infiltration_to_extraction()

• deposition_to_extraction()

• logremoval module (log-removal averaged across flow paths)

What this means: The extraction well integrates flow from all contributing streamlines. There is no vertical stratification or preferential flow to specific screen intervals.

When it holds:

• Fully screened wells

• Long well screens relative to aquifer thickness

• Vertically uniform aquifer properties

When it fails:

• Partially penetrating wells

• Short screens in thick aquifers

• Vertically stratified aquifers

• Point extraction (e.g., piezometers)

Testable: Difficult - requires multi-depth sampling or flow profiling. Compare predictions for different assumed screen configurations if data available.

13. Adequate Time Resolution

Assumption: The input data time resolution captures the relevant dynamics of the system.

Applies to: All modules that use tedges for temporal discretization

What this means: Temporal discretization (tedges) is fine enough that sub-interval variations don’t significantly affect results.

When it holds:

• Daily data for systems with residence times >> days

• High-frequency data for rapid transients

When it fails:

• Coarse temporal resolution relative to residence time

• Rapidly varying input signals

• Short residence times with sub-daily dynamics

Testable: Yes - resample input data to coarser resolution and compare results. If results change significantly, finer resolution may be needed.

Numerical Implementation

14. Adequate Discretization

Assumption: The number of bins (n_bins) used to discretize the gamma distribution is sufficient for accurate results.

Applies to: Functions with gamma_ prefix that use n_bins parameter:

• gamma_infiltration_to_extraction()

• gamma_extraction_to_infiltration()

• bins()

Does NOT apply to:

• Functions using explicit pore volume arrays (already discretized by user)

• logremoval.gamma_* functions (use analytical formulas, not discretization)

What this means: The continuous gamma distribution is approximated by discrete bins. Too few bins may cause numerical artifacts; too many is computationally wasteful.

When it holds:

• n_bins ≥ 50 for most applications

• Default n_bins = 100 is usually adequate

When it fails:

• Very narrow distributions (high precision needed)

• Very wide distributions (need coverage of tails)

• Sharp input signals requiring fine temporal resolution

Testable: Yes - convergence test. Run with n_bins = 50, 100, 200, 500 and check that results converge. If results change significantly between 100 and 200, use more bins.

Summary: When is gwtransport Appropriate?

Good Candidates

• Bank filtration systems

• Managed aquifer recharge in granular aquifers

• Alluvial aquifers with moderate heterogeneity

• Systems where advection dominates dispersion

• Conservative tracer or temperature transport

• Preliminary assessment before detailed modeling

Poor Candidates

• Fractured rock or karst systems

• Vadose zone transport

• Reactive contaminants with significant decay

• Highly transient flow with changing streamline geometry

• Dual-porosity systems with matrix diffusion

When in Doubt

1. Start with gwtransport as a first assessment

2. Test key assumptions (especially advection dominance and gamma adequacy)

3. If assumptions fail or predictions don’t match observations, consider more complex models

4. Use gwtransport results to identify which additional complexity is needed

Testing Framework

The assumptions can be organized into testable categories:

Category	Assumptions	Modules Affected	Test Methods
Domain Applicability	Saturated flow, Single porosity, No reactions	All	Not testable - defines when to use gwtransport
Transport Physics	Advection-dominated	All except diffusion	Variance ratio
Transport Physics	Steady streamlines, No transverse mixing, Incompressible	All	Cross-validation, Residual analysis
Parameterization	Gamma adequate	gamma_* functions only	Goodness-of-fit, Q-Q plot
Parameterization	Linear retardation	All except front_tracking	Compare with non-linear model
Parameterization	Thermal R	Temperature applications	Sensitivity analysis, Physical bounds
Data Quality	Representative input, Well-mixed extraction, Time resolution	All	Sensitivity analysis, Resampling
Numerical	Adequate discretization	gamma_* functions only	Convergence tests

Quick Reference: Assumptions by Module

Module	Key Assumptions	Can Be Relaxed By
advection (gamma functions)	Gamma distribution, Linear R, Advection-dominated	Use explicit pore volumes, front-tracking
advection (explicit pore volumes)	Linear R, Advection-dominated	Use front-tracking for non-linear R
advection (front-tracking)	Advection-dominated	— (supports non-linear sorption)
residence_time	Steady streamlines, Linear R	Use freundlich_retardation() for non-linear
deposition	Steady streamlines, Linear R, No decay	—
logremoval	Steady streamlines	— (adds empirical decay)
diffusion_fast	Steady streamlines	— (fast approximation, relaxes advection-only assumption)
diffusion	Steady streamlines	— (analytical solution, relaxes advection-only assumption)