Skip to main content

Hole and Boundary

We sometimes do not understand well enough of what we are dealing with in our daily life.
I was lucky enough to attend a seminar by Achille C. Varzi a few years ago, which inspired me on this topic: looking at hole and boundary from a different perspective.

This post is a mixture of both philosophy and Earth Science (but which discipline isn't driven by philosophy anyway?) The topic of this post is about hole and boundary, which are very common objects in our daily life.

By the definition from Wikipedia: A hole is a hollow place, an opening in/through a solid body, or an excavation in the ground. In another word, a hole exists because there is a closed Boundary between two different types of materials (often one of them is air). For example, a donut has a hole.

Now the question is how should we define boundary, which is not an easy task if you look closer.
For example, where is the boundary between a lake and its surrounding land? If you draw a polygon around the lake, you will soon realize that you cannot find a perfect location where the line should be. This is similar to the case you cannot find the right rule to measure the total length of the coastal line. The scale matters in these cases.

We haven't touched time yet. As time passes on, the water level in a lake is very likely to change.

There are many more interesting examples. Here are a few:
  1. When do we consider the food/drink is part of our body, the moment they enter into our mouth or they are actually digested?
  2. When do we call a baby is born?
  3. When do we call a person is dead?
The list goes on but I will now focus on the boundary in Earth Science.

First, when we look at the map of any Earth image, there is a boundary because computer/photo must has one. But in fact the boundary of Earth is very unclear to us, the land surface? near surface atmosphere? outer space? This is critical because you have to consider these differences in different scenarios. For example, if you are to simulate or analyze the formation and impact of volcano eruption, you might have to consider deep geology features and all the way to the atmosphere.

If you look "horizontally" (even though Earth is not flat), what boundary should we use? Land-Ocean-Sea Ice? They are changing constantly. On land, we are more familiar with political boundaries, the so called "nations" or "states", etc. These artificial boundaries are somewhat senseless in some cases. For example, the shape of states in USA and the boulder between USA and Canada.

Then there is a problem, we cannot accurately simulate some processes without crossing boundaries. It is like we cannot estimate the stream discharge in Columbia River, WA, without knowing the snow conditions from Canada. Another example is the water data sharing between China and India (see here).

Recognizing the issues brought out by boundaries, we need to understand most of our Earth science activities do not have clear boundaries. This field itself is an interdisciplinary. As we are talking about scales, no matter in time or in spatial, there are lots of factors are involved. For example, if we are using watershed as a boundary for a land surface modeling, we have to consider whether the boundary applies to groundwater system. Also, the watershed delineation itself is DEM resolution dependent. So how can we justify the watershed is accurate enough for the application.

Because linking different processes from different components implies a "mapping" process, we are basically mapping the boundaries. For example, a mapping from atmosphere to ocean suggests we need to make sure the boundaries have overlap.

While not all mappings are perfect, there some approaches might be better than the others. I think a better understanding of boundary and how we should define boundary can help us to design a better Earth system modeling framework.



Popular posts from this blog

Spatial datasets operations: mask raster using region of interest

Climate change related studies usually involve spatial datasets extraction from a larger domain.
In this article, I will briefly discuss some potential issues and solutions.

In the most common scenario, we need to extract a raster file using a polygon based shapefile. And I will focus as an example.

In a typical desktop application such as ArcMap or ENVI, this is usually done with a tool called clip or extract using mask or ROI.

Before any analysis can be done, it is the best practice to project all datasets into the same projection.

If you are lucky enough, you may find that the polygon you will use actually matches up with the raster grid perfectly. But it rarely happens unless you created the shapefile using "fishnet" or other approaches.

What if luck is not with you? The algorithm within these tool usually will make the best estimate of the value based on the location. The nearest re-sample, but not limited to, will be used to calculate the value. But what about the outp…

Numerical simulation: ode/pde solver and spin-up

For Earth Science model development, I inevitably have to deal with ODE and PDE equations. I also have come across some discussion related to this topic, i.e.,

In an attempt to answer this question, as well as redefine the problem I am dealing with, I decided to organize some materials to illustrate our current state on this topic.

Models are essentially equations. In Earth Science, these equations are usually ODE or PDE. So I want to discuss this from a mathematical perspective.

Ideally, we want to solve these ODE/PDE with initial condition (IC) and boundary condition (BC) using various numerical methods.

Because of the nature of geology, everything is similar to its neighbors. So we can construct a system of equations which may have multiple equation for each single grid cell. Now we have an array of equation…

Watershed Delineation On A Hexagonal Mesh Grid: Part A

One of our recent publications is "Watershed Delineation On A Hexagonal Mesh Grid" published on Environmental Modeling and Software (link).
Here I want to provide some behind the scene details of this study.

(The figures are high resolution, you might need to zoom in to view.)

First, I'd like to introduce the motivation of this work. Many of us including me have done lots of watershed/catchment hydrology modeling. For example, one of my recent publications is a three-dimensional carbon-water cycle modeling work (link), which uses lots of watershed hydrology algorithms.
In principle, watershed hydrology should be applied to large spatial domain, even global scale. But why no one is doing it?  I will use the popular USDA SWAT model as an example. Why no one is setting up a SWAT model globally? 
There are several reasons we cannot use SWAT at global scale: We cannot produce a global DEM with a desired map projection. SWAT model relies on stream network, which depends on DEM.…