### Numerical simulation: unit system

Unit is always one of the most important factors in science. Most of the time, a number without unit is useless.
For numerical simulation, a good design of unit system can be critical.
Recently, I have written a short script/program to prepare climate data for my groundwater/surface water hydrology simulation. I downloaded some data from the National Climatic Data Center(NCDC) separately, and I did NOT notice the changes in unit system. In the end, I have to do everything over again.

So the question is: what kind of unit system should we use to improve our efficiency, and how do we actually implement it?

First of all, we need to identify the unit system used in the data obtained from third party. This is usually done through reading the meta data in the documentation. Never directly use the data without reading the documentation!
A lot of time we don't usually have choices of the unit system provided. In this case, the best practice might be stick with the original unit system.

However,  we should use the SI unit system whenever possible. They are apparently a few benefits from it. For example, NCDC climate data online usually provide standard unit and metric unit system. In this scenario, I would prefer to use metric. And you can always convert them into other units without much efforts.

When we implement related numerical simulation program, using SI unit system for data I/O is also very straightforward. For some type of data, a scale factor can easily preserve the precision without losing efficiency. In modern programming language, the double floating data type can handle almost all type of data without memory issues.

Even when you are dealing with old algorithms which use standard unit system, you can always convert the units before actual calculations, and convert them back to SI afterwards.

Below is the unit system used in one of my recent projects:
Data Unit Note
Temperature Fahrenheit It could be reproduced in Kelvin
Precipitation Millimeter
Dewpoint temperature Fahrenheit

### 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.…