Chapter 3 Classifying model structure - Lecture only (0 pts)

Throughout the rest of the course, we will gather data and create models to explore how environmental factors, such as snowmelt, land cover, evapotranspiration (ET), and topography, impact runoff. To discuss these methods, we should review some modeling terminology describing model complexity and type.

Environmental models, including hydrological models, are built around simplifying assumptions of natural systems. The complexity of the model may depend on its application. Effective hydrological models share key traits: they are simple, parsimonious, and robust across various watersheds. In other words, they are easy to understand and streamlined and consistently perform well across different basins or even geographical areas. Therefore, more complex is only sometimes better.

3.1 Spatial Complexity

There are general terms that classify the spatial complexity of hydrological models:

A lumped system is one in which the dependent variables of interest are a function of time alone, and the study basin is spatially ‘lumped’ or assumed to be spatially homogeneous across the basin. So far in this course, we have focused mainly on lumped models. You may remember the figure below from the transfer functions module. It represents the lumped watershed as a bucket with a single input, outlet output, and storage volume for each timestep.

A distributed system is one in which all dependent variables are functions of time and one or more spatial variables. Modeling a distributed system means partitioning our basins into raster cells (grids) and assigning inputs, outputs, and the spatial variables that affect inputs and outputs across these cells. We then calculate the processes at the cell level and route them downstream. These models allow us to represent the spatial complexity of physically based processes. They can simulate or forecast parameters other than streamflow, such as soil moisture, evapotranspiration, and groundwater recharge.

A semi-distributed system is an intermediate approach that combines elements of both lumped and distributed systems. Certain variables may be spatially distributed, while others are treated as lumped. Alternatively, we can divide the watershed into sub-basins and treat each sub-basin as a lumped basin. Outputs from each sub-basin are then linked together and routed downstream. Semi-distribution allows for a more nuanced representation of the basin’s characteristics, acknowledging spatial variability where needed while maintaining some simplifications for computation efficiency.

In small-scale studies, we can design a model structure that fits the specific situation well. However, when we are dealing with larger areas, model design may be challenging. Our data might differ across regions with variable climate and landscape features. Sometimes, it is best to use a complex model to capture all the different processes happening over a big area. However, it could be better to stick with a simpler model because we might have limited data or the number of calculations is very computationally expensive. It is up to the modeler to determine the simplest model that meets the desired application.

3.2 Modeling Approaches

Empirical Models are based on empirical analysis of observed inputs (e.g., rainfall) or outputs (ET, discharge). These simple models may not be transferable to other watersheds. Also, they may not reveal much about the physical processes influencing runoff. Therefore, these types of models may not be valid if the study area experiences land use or climate change.

Conceptual Models describe processes with simple mathematical equations. For example, we might use a simple linear equation to interpolate precipitation inputs over a watershed with a high elevation gradient using precipitation measurements from two points (high and low). This represents the basic relationship between precipitation and elevation, but does not capture all features that affect precipitation patterns (e.g. aspect, prevailing winds). The combined impact of these factors is probably negligible compared to the substantial amount of data required to accurately model them.

Physically Based Models These models offer deep insights into the processes governing runoff generation by relying on fundamental physical equations like mass conservation. However, they come with drawbacks. Their implementation often demands complex numerical solving methods and a significant volume of input data. Without empirical data to validate these techniques, there is a risk of introducing substantial uncertainty into our models, reducing their reliability and effectiveness

When modeling watersheds, we often use a mix of empirical, conceptual, and physically based models. The choice of model type depends on factors like the data we have, the time or computing resources we can allocate, and how we plan to use the model.