### Paper discussion special issue the ECO3D model

Recently we have published a paper on Journal of Advanced Modeling of Earth System.
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019MS001792

This is also a personal milestone because it is the last chapter of my PhD thesis. Below I will provide some details of this work.

In many of my earlier posts, I have discussed that our Earth system is always evolving in a three dimensional domain. The water flows, the atmosphere flows as well.

However, in our numerical simulations, we do not always use 3D method. Sometimes we just don’t felt it necessary. For example, we always assume rain drops on land surface in vertical direction even though rain can attack our windows with an angel.

In some other scenarios, we don’t use 3D because of computational resources. We can build a fully 3D model. But it is not useable if we don’t have the computer power to run it.

Land surface model is an important component in ESM. But current generation of LSM is 1D instead of 3D. There are many reasons for this design, which I plan not to cover here. Instead, I will focus on why 3D makes sense and what is the challenge.

From 1D to 3D means that each grid is aware of its neighborhood. More importantly, it talks to its neighborhood and exchanges maybe gifts.

To put it in the model language, traditionally, each grid is isolated from others, so water and carbon budget are calculated in each grid independently. In 3D, a grid can send or receive some water and carbon from neighborhood. It’s like a grid at mountain valley can receive water from mountain ridge. Isn’t that making much more sense?
On land, each grid cell can connect to its 4/6/8 neighbors:
They can also connect with river:

Water can carry lots of stuff, including carbon in the dissolved mode. Water can also carry other stuff such as sediment and debris.

So without 3D, we cannot actually calculate how much stuff are carried by water from one grid to another.

How to implement a 3D approach is another story, in ECO3D, we used a method widely used in the hydrology community, an explicit forward Euler method. There are several advantages of this method. I personally think that it’s suitable for parallel computing and does not require expensive matrix solvers.

We also introduced a brand new DOC model, DOC is one of the carbon that flows with water, apparently. This is currently the only litter DOC model that considers lateral flow.
Currently we haven’t consider the DOC in the groundwater system.

Other solutes including particles can also be added and modeled by ECO3D in the near future.

As we have more solutes in the water flow, it’s natural to have biogeochemistry and reactive transport as well.

There are many scientific questions we can answer with this model. But my time is limited so I will slowly try them out in the near future.

### 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.…