Quantifying the role of permafrost distribution in groundwater and surface water interactions using a three-dimensional hydrological model

Following my earlier post on promoting my research, this is the second study that I conducted in an attempt to understand the hydrology processes in high latitudes.

You are encouraged to read the first post for a background understanding of this study.

Let's cut to the chase, the title of this study is "Quantifying the role of permafrost distribution in groundwater and surface water interactions using a three-dimensional hydrological model", and you can access the paper through here or this.

In Arctic, snow and glacier are not the only players in the hydrology processes. Permafrost, the so called frozen soil is also an important player in both hydrology and carbon cycles.

There are several reasons for that:
1. It is frozen, so it could potentially release a lot of water in the warming climate;
2. Permafrost degradation can change the landscape, then both the carbon and water cycles will be affected;
3. Permafrost is like a barrier, it blocks interactions. Therefore, permafrost degradation will change the interactions between surface processes and deep processes.
While there are many aspects we can look into, we decided to look into the groundwater and surface water (GW-SW) interactions. Part of the reason is that we now consider permafrost in a three-dimensional domain and GW-SW interaction in directly affected by the spatial distribution of permafrost.

So we started with the standard groundwater flow model, this model is again from USGS, and it is called MODFLOW. More details can be found at here (https://water.usgs.gov/ogw/modflow/).

I would not get into details of how MODFLOW works. I do want to highlight a few important things.
1. The spatial domain is now broken into 3D zones, just like you cut your cheese cake. It has layers and pieces;
2. Water flows through the 3D domain and its speed depends on gradient and conductivity.

A zoomed view of the 3D setup is illustrated here:
Figure 1. The spatial discretization of the study domain.

If you look at the above figure, different cell/zone have different shape/size and hydrologic properties.

We have to know where permafrost is located and how deep they are. This is defined using the permafrost map:
Figure 2. The spatial distribution of permafrost and thickness.

Note that we also defined the stream network similar to my earlier study. In fact, it is a much complicated process than it appears to be.

We have to consider how groundwater interacts with stream in permafrost regions.

We first need to ask, is there permafrost under stream bed?
And we also have to ask whether there are permafrost next to stream.
In the end, we have to design the model structure to be very realistic and computationally friendly. For example, should the stream in the first layer or the second layer where permafrost rests? Can there be two-way interactions depending on stream stage?
Overall, the design is illustrated in Figure 3.
Figure 3. The interactions between groundwater and stream water in permafrost regions.

We ran the simulation for 36 years driven by the surface infiltration and stream discharge. Some results are listed here:
Figure 4. The vertical groundwater flow between layer 1 and 2.

This result demonstrates that most vertical flow occurs in permafrost-free zones, which is not surprising. It also implies that in the warming climate where there is less permafrost, the spatial distribution will definitely change.
Figure 5. Time series of groundwater and stream water interactions.

This result first confirms the base flow throughout the year fed by groundwater. It also shows the interactions in different time/season vary with stream conditions.

This study has demonstrated the permafrost plays an important role in GW-SW interactions. It also implies this relationship will change in the warming climate.

During this study, a IDL-based MODFLOW system was developed. Later on, this system is converted to Python-based, so you may try out MODFLOW simulation in any region without too much effort.

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.…