### Evaluate the stream networks from watershed delineation

Recently I asked a question on the GIS Exchange site:
https://gis.stackexchange.com/questions/315910/quantitatively-evaluating-quality-of-watershed-delineation-stream-line-results

I also asked the question on Research Gate:
https://www.researchgate.net/post/How_to_quantitatively_evaluate_the_quality_of_the_watershed_delineation_stream_line_results

The reason is that we have developed a watershed delineation model and we need to evaluate whether our model performs better or not than the previous method.

So we set out trying to find ways to evaluate the results.
The first thing as a watershed hydrologist will usually do is to look at the stream segments. If they match up with actual stream lines then it means the model is not bad.

However, both our method and the previous method can produce similar stream segment results. The the question is how can we say which one is better than the other one.

So we did some research online, and most publications used visual results as proof. Basically,  we literally "see" the differences between different models.

Then there are also a few papers include slope, length for comparison, which still does not actually show which one is better effectively.

Among them, there is one paper proposed that by calculating distance between simulated stream and actual stream, we can determine how close the model is away from the truth. And I think this might be the closest we can find.

However, the idea of distance between two line vectors is not as intuitive as it looks.

So we kept researching.
Then we realized that if we place two stream line vectors together, we can get a polygon created by them. And if the two vectors are very close, then the area of the polygon should be small.
This is illustrated by the figure:
Figure 1. The stream line vector with the true stream lines.

The new question becomes:
How can we calculate the area of this "intersected area"?
There is no existing tool can do this task in GIS. Because we are intersecting polylines and we need to create multiple polygons. It would be possible if we have the mathematical formula of each line and the locations of each intersection. By any means, it is a challenge in precise GIS.

So instead of thinking in the vector domain, we decided to try the raster domain. Luckily, we can easily convert these vectors into raster and do raster calculation. TLDR, the new question is similar to calculating the area of a closed domain.

And there are several related questions. For example this one:
https://stackoverflow.com/questions/21816562/finding-holes-in-2d-point-sets

If you have ever used Photoshop, you probably have used the magic tool, which actually solves the problem we have here.

In one sentence, in order to calculate the area of the closed holes, we need to fill the rest of the raster.
Since I did not use any advanced fill algorithm at the time of solving the problem, a brutal algorithm was used. Basically it fills the raster from boundary towards inside. And it took a long time to run.

Figure 2. The fill algorithm. The x-axis is step, and the y-axis the remaining pixel count.

Of course, if flood filling algorithm will significantly reduce the computational time.
And the result shows that our method performs better under coarse resolution.

The take away message: I was surprised that a watershed delineation evaluation process will lead to flood filling algorithm, which is already used in the depression filling process!

For those who is not familiar with flood filling algorithm, here is more information:

Let me know if you have any question.

### 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…

### 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…

### Surface water hydrology modeling: deal with different types of precipitation

In surface water hydrology, precipitation is one of the most important components.
However, withing most hydrology models, it is unclear of how precipitation is actually represented.
For example, in a typical water cycle illustration from Wiki, precipitation is described as
Here is the question, what form does precipitation actually take when it falls to land surface? Water can be in either liquid (water, rain), solid(ice, snow) or gas(water vapor) forms. How about precipitation? Surely most of time precipitation is either rain of snow. In some cases, it takes form in hail, etc.
Since the physical proprieties of water and snow are significantly different, it is necessary to distinguish them within surface water hydrology models. In some scenarios, rain and snow may co-exist in a mixed precipitation event. In this case, surface water hydrology models need to deal with both of them. The difficulty is how to manage the two-phase mass and energy balance. A complete comparison of how differ…