Types Of Models

Question 1

What is a physical based model?

Answer 1

also called process-based or mechanistic; based
on physical laws; purely driven by imitating processes
ex: 10% of rainfall will be intercepted by canopy, another 10% will
be held in depressions, 70% will infiltrate into the soil, and the
last 10% will runoff

Question 2

What is an empirical model?

Answer 2

based on observation or experience rather than
theory or logic; purely driven by cause and effect
ex: about 10% of rainfall will runoff

Question 3

Lumped vs. Distributed

Answer 3

lumped – put in an indiscriminate mass or group; treat as alike
without regard for particulars
ex: representing an area or object with a scalar mean value
distributed – shared or spread out
ex: representing an area or object with an array of values

Question 4

Point vs. Nonpoint

Answer 4

point – a source which has negligible dimensions
ex: a pipe discharging in a river
nonpoint – also called diffuse; a source which has significant
dimensions
ex: runoff from a field flowing into a river
Q: When are animals point and/or nonpoint pollution sources?

Question 5

Source vs. Receiving

Answer 5

source – primarily concerned with the origination (and
transport) of a target substance or thing
ex: the target is generally an output
receiving – primarily concerned with the fate (and transport) of a
target substance or thing
ex: the target is generally an input

Question 6

Analytical vs. Numerical

Answer 6

analytical – has a well-understood problem with a set of
logical steps to follow to calculate an exact outcome
ex: for x – 1 = 0, what is x? (solution: add one to both sides)
numerical – has a difficult problem whose solution is
approximated through guessing and testing
ex: for x – 1 = 0, what is x? (solution: guess and test)

Question 7

Vectorized vs. Rasterized

Answer 7

vectorized – data represented
as points, lines, or polygons
rasterized – also called gridded
or mesh; data represented as a
matrix of cells

Question 8

Uniform vs. Nonuniform

Answer 8

uniform – having the same condition throughout
ex: a field with no BMPs
nonuniform – having varying conditions throughout
ex: a field with BMPs
Q: Is this the same as lumped vs. distributed and why?

Question 9

Deterministic vs. Stochastic

Answer 9

deterministic – there exists only one unique set of output for a
given set of input
ex: mean or median of a given distribution
stochastic – there exists multiple possible sets of output for a
given set of input; not the same as ‘statistical’
ex: random sample of a given distribution

Question 10

Stationary vs. Nonstationary

Answer 10

stationary – has statistical properties or moments that do not
change through time
nonstationary – has statistical properties or moments that do
change through time

Question 11

Parametric vs. Nonparametric

Answer 11

parametric – distribution parameters are known
ex: normal, logistic, uniform, poisson, or other distributions
nonparametric – distribution parameters are not known
ex: no distribution assumed
Q: Can I apply nonparametric analyses to data which is normal?

Question 12

What are some mathematical models?

Answer 12

Deterministic, stochastic, statistical, empirical, mechanistic, and simulation models

Question 13

What are some examples of deterministic models?

Answer 13

Landlab, CUSP (Cohesive Uniform Slope Processes), USLE, RUSLE, WEPP, SIBERIA, Caesar-lisflood, CASCADE (CAtchment Simulation Model for Channel and Drainage Evolution)

Question 14

What are some example of stochastic models?

Answer 14

Stochastic models incorporate randomness and probabilistic elements to simulate processes such as hillslope evolution, erosion, tillage, and morphology. These models are used to capture the inherent variability and uncertainty in natural processes. Here are some commonly used stochastic models in these areas:

Hillslope Evolution

1.	Cellular Automata Models: These models simulate hillslope processes using a grid of cells, each of which evolves according to probabilistic rules based on the states of neighboring cells. Examples include models developed for simulating soil creep and landslide dynamics.

Erosion

1.	WATEM/SEDEM (Water and Tillage Erosion Model/ Sediment Delivery Model): A stochastic model that simulates soil erosion and sediment delivery by water and tillage. It includes probabilistic elements to account for variability in rainfall and land management practices.
2.	MMF (Morgan-Morgan-Finney): While primarily a deterministic model, MMF can include stochastic components to account for variability in rainfall and soil properties, influencing erosion rates.

Tillage

1.	STIR (Soil Tillage Intensity Rating) with Stochastic Elements: When incorporating stochastic elements, the STIR model can simulate variability in tillage practices and their effects on soil erosion over time.
2.	ALMANAC (Agricultural Land Management Alternatives with Numerical Assessment Criteria): This model includes stochastic components to simulate the effects of different tillage practices on soil properties and crop yields.

Morphology

1.	CASCADE (CAtchment Simulation Model for Channel and Drainage Evolution) with Stochastic Elements: By incorporating stochastic elements, this model can simulate the probabilistic nature of channel network development and drainage basin evolution.

Landscape Evolution

1.	LAPSUS (Landscape Process Modelling at Multi-dimensions and Scales): A stochastic model that simulates landscape evolution processes such as soil erosion, sediment transport, and deposition. It incorporates randomness in rainfall events and soil properties.
2.	GOLEM (Geomorphic Landscape Evolution Model): A stochastic model that simulates landscape evolution by incorporating probabilistic rules for processes such as erosion, sediment transport, and deposition.

Probabilistic Soil-Landslide Models

1.	TRIGRS (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model): A stochastic model that simulates the probability of landslides triggered by rainfall infiltration. It incorporates variability in soil properties and rainfall intensity.
2.	SHALSTAB (Shallow Landsliding Stability Model): A stochastic model used to predict the spatial distribution of shallow landslides. It includes probabilistic elements to account for variability in soil strength and hydrologic conditions.

Hybrid Models

1.	Landlab with Stochastic Components: The Landlab toolkit can incorporate stochastic elements in its various components to simulate the probabilistic nature of hillslope and landscape evolution processes.

These stochastic models are valuable for understanding and predicting the behavior of natural systems under uncertain conditions. They provide insights into the range of possible outcomes and help quantify the uncertainty associated with predictions of hillslope evolution, erosion, tillage effects, and landscape morphology.

Question 15

What are some examples of statistical models?

Answer 15

Statistical models use empirical data to identify relationships between variables and predict outcomes. They are valuable for understanding and quantifying processes related to hillslope evolution, erosion, tillage, and morphology. Here are some common statistical models used in these fields:

Hillslope Evolution

1.	Regression Models: These models use statistical techniques to relate hillslope characteristics (e.g., slope gradient, soil properties) to rates of soil erosion and deposition. Multiple linear regression and logistic regression are common approaches.
2.	Principal Component Analysis (PCA): PCA is used to reduce the dimensionality of data and identify key factors influencing hillslope evolution. It helps in understanding the main drivers of hillslope processes.

Erosion

1.	RUSLE (Revised Universal Soil Loss Equation): Though primarily deterministic, RUSLE can be enhanced with statistical methods to estimate parameters from empirical data. It uses regression equations to predict soil loss based on rainfall, soil type, topography, crop system, and management practices.
2.	G2 (Generalized Geographical Model for Soil Erosion Prediction): This model incorporates statistical techniques to estimate soil erosion risk using geographical and environmental data.
3.	Statistical Downscaling: Used to relate large-scale climate data to local soil erosion patterns, helping predict erosion under different climate scenarios.

Tillage

1.	ANOVA (Analysis of Variance): ANOVA is used to assess the impact of different tillage practices on soil properties and crop yields by comparing means across multiple groups.
2.	Mixed-Effects Models: These models account for both fixed and random effects, making them suitable for analyzing the impact of tillage practices on soil erosion across different fields and conditions.

Morphology

1.	Geostatistical Models: Kriging and other geostatistical techniques are used to interpolate and predict soil and landscape properties from spatially correlated data. These methods help in understanding the spatial variability of morphological features.
2.	Cluster Analysis: Used to classify and group similar landforms or soil types based on their morphological characteristics. It helps in identifying patterns and relationships in landscape data.

Landscape Evolution

1.	Multivariate Statistical Models: These models analyze the relationships between multiple variables influencing landscape evolution, such as climate, vegetation, and soil properties.
2.	Time Series Analysis: Statistical methods like autoregressive integrated moving average (ARIMA) models are used to analyze and predict temporal changes in landscape features.

Predictive Models

1.	Random Forests: An ensemble learning method that uses multiple decision trees to predict soil erosion and landscape changes based on input variables. It provides a robust way to handle non-linear relationships and interactions.
2.	Support Vector Machines (SVM): Used for classification and regression tasks in soil erosion prediction and landscape classification. SVMs help in identifying patterns in complex datasets.

Bayesian Models

1.	Bayesian Networks: These models use probabilistic relationships between variables to predict outcomes and assess the uncertainty in predictions. They are useful for modeling complex environmental systems with multiple interacting factors.
2.	Bayesian Hierarchical Models: These models account for variability at different levels (e.g., site-specific, regional) and incorporate prior knowledge to improve predictions of hillslope processes and erosion rates.

Question 16

What are some examples of empirical models?

Answer 16

Empirical models rely on observed data and established relationships between variables to predict outcomes and understand processes. They are particularly useful when detailed mechanistic understanding is limited but sufficient observational data is available. Here are some common empirical models used for hillslope evolution, erosion, tillage, and morphology:

Hillslope Evolution

1.	Empirical Soil Creep Models: These models use empirical relationships to estimate soil movement down slopes based on factors like slope angle and soil properties. An example is the soil creep equation that relates creep rate to slope gradient.
2.	Sediment Transport Equations: Empirical formulas, such as those developed by Meyer-Peter and Müller or Bagnold, estimate sediment transport rates on hillslopes based on slope and flow conditions.

Erosion

1.	USLE (Universal Soil Loss Equation): A well-known empirical model that predicts average annual soil loss from agricultural fields based on rainfall pattern, soil type, topography, crop system, and management practices.
2.	RUSLE (Revised Universal Soil Loss Equation): An updated version of USLE that incorporates improved empirical relationships to estimate soil loss with more accuracy.
3.	MUSLE (Modified Universal Soil Loss Equation): Extends USLE by incorporating sediment yield from individual storm events, using runoff volume and peak flow rate as additional factors.

Tillage

1.	Empirical Tillage Erosion Models: These models estimate soil displacement due to tillage operations based on factors like implement type, tillage depth, and slope gradient. Examples include models developed by Govers et al. and Van Oost et al.
2.	STIR (Soil Tillage Intensity Rating): Quantifies the impact of different tillage practices on soil erosion by using empirical data on tillage frequency and intensity.

Morphology

1.	Empirical Channel Evolution Models: Models that predict changes in channel morphology based on observed relationships between flow characteristics, sediment load, and channel shape. Examples include models developed by Schumm and Simon.
2.	Bank Erosion Models: Empirical models that estimate bank erosion rates using observed relationships between factors like bank height, soil type, vegetation cover, and flow conditions.

Landscape Evolution

1.	SIBERIA: A landscape evolution model that combines empirical and mechanistic approaches to simulate long-term landform development. It uses empirical relationships to parameterize processes like erosion and sediment transport.
2.	G2 (Generalized Geographical Model for Soil Erosion Prediction): Uses empirical data to estimate soil erosion risk and sediment delivery, combining factors like topography, land use, and soil properties.

Predictive Models

1.	Regression-Based Models: Use empirical relationships derived from observed data to predict soil erosion, sediment transport, and landscape changes. Examples include multiple linear regression and logistic regression models.
2.	Factorial ANOVA Models: Analyze the effects of multiple factors on erosion rates or landscape features by using empirical data from field experiments or observations.

Vegetation and Climate Impact Models

1.	Empirical Vegetation Models: Estimate the impact of vegetation cover on soil erosion and hillslope stability based on observed relationships between vegetation type, cover density, and erosion rates.
2.	Empirical Climate Models: Predict the impact of climate variables (e.g., rainfall intensity, temperature) on erosion and landscape evolution using historical climate data and observed erosion patterns.

Hydrological Models

1.	Empirical Runoff Models: Estimate surface runoff and its contribution to soil erosion using observed relationships between rainfall, soil characteristics, and land cover. Examples include the Curve Number method developed by the USDA.

Empirical models provide valuable insights into hillslope processes, erosion, tillage effects, and landscape morphology by leveraging observational data. They are often easier to apply than mechanistic models and can be particularly useful for large-scale or data-rich studies where detailed process understanding is not feasible.

Question 17

What are some examples of mechanistic models?

Answer 17

Mechanistic models, also known as process-based models, simulate physical processes based on fundamental principles and laws of nature. These models are designed to provide a detailed and realistic representation of the physical mechanisms driving hillslope evolution, erosion, tillage, and morphology. Here are some common mechanistic models used in these areas:

Hillslope Evolution

1.	CSDMS (Community Surface Dynamics Modeling System): A suite of mechanistic models that simulate landscape and hillslope evolution by integrating processes like weathering, erosion, and sediment transport.
2.	Geomorphic Transport Laws: Mechanistic formulations that describe soil and sediment transport on hillslopes, such as the diffusion equation for soil creep and the advection-diffusion equation for sediment transport.

Erosion

1.	WEPP (Water Erosion Prediction Project): A process-based model developed by the USDA to predict soil erosion by water. It includes detailed simulations of hydrology, plant growth, soil erosion, and sediment transport.
2.	KINEROS2 (Kinematic Runoff and Erosion Model): A mechanistic model that simulates surface runoff and erosion processes using kinematic wave theory and sediment transport equations.
3.	SWAT (Soil and Water Assessment Tool): A comprehensive model that integrates hydrology, weather, erosion, plant growth, nutrients, and land management practices to predict the impact of land use on water, sediment, and agricultural chemical yields.

Tillage

1.	CTEM (Conservation Tillage Erosion Model): A mechanistic model that simulates soil displacement due to tillage operations based on the physical interactions between tillage implements and soil.
2.	TillTM: A model that simulates the mechanical processes of tillage, including soil loosening, mixing, and movement caused by different tillage tools.

Morphology

1.	CAESAR-Lisflood: A process-based model that simulates river and landscape evolution, including detailed representations of erosion, sediment transport, and deposition processes.
2.	SIBERIA: A landscape evolution model that uses process-based equations to simulate long-term changes in landform development, including the interactions between hydrology, erosion, and sediment transport.

Landscape Evolution

1.	CASCADE (CAtchment Simulation Model for Channel and Drainage Evolution): A mechanistic model that simulates the evolution of channel networks and drainage basins by incorporating fluvial processes, hillslope processes, and sediment transport.
2.	GOLEM (Geomorphic Landscape Evolution Model): A mechanistic model that simulates landscape evolution using principles of geomorphology, hydrology, and sediment transport.
3.	CHILD (Channel-Hillslope Integrated Landscape Development): A model that simulates the coupled evolution of channels and hillslopes using process-based equations for erosion, sediment transport, and deposition.

Soil and Sediment Transport

1.	Erosion-Deposition Models: Mechanistic models that simulate the transport of soil and sediment based on physical principles such as the continuity equation, sediment transport capacity, and flow velocity. Examples include the Exner equation for sediment continuity.
2.	Hairsine-Rose Model: A process-based model that describes the erosion, deposition, and transport of sediment particles on hillslopes and in channels.

Hydrological Processes

1.	Hortonian Overland Flow Models: These models simulate the generation of overland flow based on infiltration-excess runoff, using principles of soil infiltration and surface flow dynamics.
2.	Subsurface Flow Models: Mechanistic models that simulate groundwater flow and its interaction with surface processes, such as the Richards equation for variably saturated flow.

Vegetation and Climate Impact Models

1.	Vegetation Dynamics Models: These models simulate the interactions between vegetation cover and soil erosion based on mechanistic principles of plant growth, root reinforcement, and soil-vegetation feedbacks.
2.	Climate Impact Models: Mechanistic models that simulate the impact of climate variables (e.g., rainfall intensity, temperature) on erosion and landscape evolution, incorporating climate-driven changes in hydrology and vegetation.

Mechanistic models provide a detailed and realistic representation of physical processes, making them valuable for understanding complex interactions in natural systems. They are often used for in-depth studies, scenario analysis, and to inform management practices and policy decisions related to land use and conservation.

Question 18

What are some examples of simulation models?

Answer 18

Simulation models are computational frameworks designed to replicate the behavior of complex systems over time. They can incorporate elements from deterministic, stochastic, statistical, empirical, and mechanistic models, providing a comprehensive tool for studying hillslope evolution, erosion, tillage, and morphology. Here are some common simulation models used in these areas:

Hillslope Evolution

1.	Landlab: A Python toolkit for building, running, and analyzing numerical models of earth-surface dynamics. It includes components for simulating hillslope diffusion, soil production, and hydrology processes.
2.	GOLEM (Geomorphic Landscape Evolution Model): Simulates the long-term evolution of landscapes by incorporating processes like weathering, erosion, and sediment transport. It can be used to study how hillslopes evolve over geological timescales.

Erosion

1.	WEPP (Water Erosion Prediction Project): Simulates soil erosion by water using detailed hydrological and sediment transport processes. It can model the impact of different land management practices on erosion rates.
2.	SWAT (Soil and Water Assessment Tool): A comprehensive model that simulates the impact of land use, management practices, and climate on water, sediment, and agricultural chemical yields. It integrates hydrology, plant growth, erosion, and nutrient cycling.
3.	KINEROS2 (Kinematic Runoff and Erosion Model): Simulates surface runoff and erosion using kinematic wave theory and sediment transport equations. It is suitable for small watersheds and event-based simulations.

Tillage

1.	CTEM (Conservation Tillage Erosion Model): Simulates the mechanical processes of soil movement due to tillage operations, incorporating the effects of different tillage implements and practices.
2.	APSIM (Agricultural Production Systems sIMulator): Includes modules for simulating the impact of tillage on soil properties, erosion, and crop growth. It uses detailed process-based equations to represent tillage effects.

Morphology

1.	CAESAR-Lisflood: A simulation model that combines cellular automata and hydrodynamic modeling to simulate river and landscape evolution, including erosion, sediment transport, and deposition processes.
2.	CASCADE (CAtchment Simulation Model for Channel and Drainage Evolution): Simulates the evolution of channel networks and drainage basins by incorporating fluvial and hillslope processes.

Landscape Evolution

1.	CHILD (Channel-Hillslope Integrated Landscape Development): A simulation model that integrates the evolution of channels and hillslopes using process-based equations for erosion, sediment transport, and deposition.
2.	SIBERIA: Simulates long-term landscape evolution by integrating processes like hydrology, erosion, and sediment transport, using both mechanistic and empirical approaches.

Soil and Sediment Transport

1.	SedFlow: Simulates sediment transport and deposition in river systems based on hydraulic and sediment transport equations.
2.	Hairsine-Rose Model: Simulates the erosion, deposition, and transport of sediment particles on hillslopes and in channels using process-based equations.

Hydrological Processes

1.	Hortonian Overland Flow Models: Simulate the generation of overland flow based on infiltration-excess runoff, using principles of soil infiltration and surface flow dynamics.
2.	Richards Equation Models: Simulate variably saturated groundwater flow and its interaction with surface processes, such as soil moisture dynamics and subsurface flow.

Vegetation and Climate Impact Models

1.	DLEM (Dynamic Land Ecosystem Model): Simulates the interactions between vegetation, soil, and climate to study the impact of climate change on ecosystem processes, including erosion and sediment transport.
2.	CLM (Community Land Model): Integrates vegetation dynamics, hydrology, and land surface processes to simulate the impact of climate and land use on erosion and landscape evolution.

Integrated Models

1.	MIKE SHE: A fully integrated hydrological modeling system that simulates surface water, groundwater, and sediment transport processes, incorporating detailed representations of hydrology, vegetation, and land management practices.
2.	HydroGeoSphere: A coupled surface-subsurface flow and transport model that simulates the integrated hydrological processes, including erosion and sediment transport.

Simulation models are powerful tools for understanding and predicting the behavior of complex environmental systems. They provide a framework for integrating various processes and data, allowing researchers to explore different scenarios, test hypotheses, and inform management and policy decisions.

Question 19

Linear diffusion equation and non-linear diffusion equation