### Spatial datasets operations: a hexagon-based discrete grid systems for global simulation

After finished my three-dimensional coupled water and carbon cycle model, I have been thinking whether I can apply this approach at large spatial domain or even global scale.
During this process, I realized that most (or all) global scale land surface modeling work are based on the square grid system, which is widely used in Earth science. This grid is also common recognized as pixel, grid cell.

Can we still use grid in global scale land surface model simulation?
Yes and no. If you do not consider lateral flow, then interactions between grid cells are omitted. In this scenario, grid cell might be the easiest approach to do so.
However, if horizontal interactions are considered. Then the grid-based structure will fail. This is because latitude/longitude based structure will create singularity in polar regions like this.

And due to the distortion, it is impossible to calculate interactions within this area across polar regions.

Most maps of various variables at global scale express the polar regions as lines instead of points due to current limitation in map projections.

So what is the solution?
As I mentioned in my previous post, a hexagon-based discrete grid system can be used to address this issue. To get it start easily, image Earth as a football, specifically, a soccer, then no place on this surface will be distorted and they all will have nearly the same area.
Using technics in geometry, we can further divide the "faces" into smaller "faces". Without getting into some details we can produce a discrete grid system like this:

Create a structure like this requires some program like this
http://www.discreteglobalgrids.org/software/
There is also an online service similar:
https://www.pyxisglobe.com/view/Explore

After this grid system is built, another problem is how we can index all the grids. Traditional cartesian coordinate system will not work well in this scenario.

In DGGRID, a Central Place Index (CPI) system is introduced to address this issue, but not implemented at all resolutions, which however provides an effective approach.

Besides, we also need to consider the relationship between grids, specifically, we need to know the neighbors of each grid in global simulation. So far I haven't got a decent solution for the indexing problem but will update when available.

I want to thank Dr. Kevin for his help in DGGRID program and Perry Peterson on Q&A related to Pyxis.

### 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.,

https://www.researchgate.net/post/What_does_one_mean_by_Model_Spin_Up_Time

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.
https://en.wikipedia.org/wiki/Initial_value_problem
https://en.wikipedia.org/wiki/Boundary_value_problem

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.…