### Ecosystem modeling: a review on spatial resolution and lateral flow

We all agree that lateral flow is important in hydrology, but why most ecosystem models do not consider lateral flow?

The answer is usually related to spatial resolution. In a large scale or global scale GCM model simulation, the spatial resolution is usually $0.5^{\circ} \times 0.5^{\circ}$. At this resolution, lateral flow is usually negligible compared with vertical fluxes.

However, this procedure usually causes problems in mass balance. First, without lateral flow, freshwater into the ocean cannot be estimated accurately. Second, dissolved nutrients into the oceanic systems cannot be estimated.

So the question is at what resolution do we actually MUST consider lateral flow?

The answer depends on the fluxes you are looking into. For example, if you are looking into water flow, it it more than likely you have to always consider it, especially at regional scale. If you are looking into carbon/nitrogen fluxes, the problem will become slightly complicated.

First, we will need to evaluate what lateral fluxes are expressed in equations.
For water flow in a simplified grid cell:

\begin{align}\frac{\partial Water}{\partial t} & = Rain + Snowmelt - Evaportranspiration \\ & + Groundwater_{upwelling} - Groundwater_{recharge} \\ & + Runoff_{in} - Runoff_{out} \end{align}

For carbon fluxes:

\begin{align}\frac{\partial C_{pool}}{\partial t} & = Photosynthesis\\ & - Resipiration_{autotrophic} - Resipiration_{heterotrophic} \\ & + Carbon_{in} - Carbon_{out} \end{align}

Due to the fact that terms on the right hand side are often associated with water condition, it is therefore difficult to determine how sensitive these processes are affected by lateral flow. For example, if photosynthesis algorithm is based on soil moisture, it is likely Photosynthesis maybe affected by lateral flow, but the uncertainty range could be within $5\%$ or more. Or dissolved carbon that flows through water flow is about $1\%$ of the other terms.

Therefore, it is our responsibility to check how sensitive our models/algorithms are to the lateral flow. So far, I have not seen much work conducted in this direction. I am planning to conduct some research using my three-dimensional ecosystem modeling.

### 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…

### Lessons I have learnt during E3SM development

I have been involved with the E3SM development since I joined PNNL as a postdoc. Over the course of time, I have learnt a lot from the E3SM model. I also found many issues within the model, which reflects lots of similar struggles in the lifespan of software engineering.

Here I list a few major ones that we all dislike but they are around in almost every project we have worked on.

Excessive usage of existing framework even it is not meant to Working in a large project means that you should NOT re-invent the wheels if they are already there. But more often, developers tend to use existing data types and functions even when they were not designed to do so. The reason is simple: it is easier to use existing ones than to create new ones. For example, in E3SM, there was not a data type to transfer data between river and land. Instead, developers use the data type designed for atmosphere and land to do the job. While it is ok to do so, it added unnecessary confusion for future development a…