### 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…

### 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…

### A modern way of automate calibration of a hydrologic model

Calibration of hydrologic model can be tedious, that is why we spent great efforts to automate this process. And sometimes we need some tool that is universal, reusable, so that we don't have to re-invent the wheel again and again.

Today I want to introduce a very effective framework to conduct a hydrologic model calibration. I call it framework because you can apply this method to any model and use any of your preferred language in some steps.

Here is the framework:
Let me explain what is going on:
PEST generate new parameter file based on a simple template;PEST call Python interface to start model simulation;Python interface translates parameter file to model input files;Python interface launches SWAT simulation;Python interface extracts results; andPEST analyzes result and updates parameters.
A few highlights here:
This is an example for a SWAT model, and you can change it to any model you are calibrating;I used Python, but you can also use any other language such as C/C++ or eve…