├── .gitignore ├── README.md ├── data ├── mask.txt ├── sst.txt └── wind.txt ├── embm.py └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | bin/ 12 | build/ 13 | develop-eggs/ 14 | dist/ 15 | eggs/ 16 | lib/ 17 | lib64/ 18 | parts/ 19 | sdist/ 20 | var/ 21 | *.egg-info/ 22 | .installed.cfg 23 | *.egg 24 | 25 | # Installer logs 26 | pip-log.txt 27 | pip-delete-this-directory.txt 28 | 29 | # Unit test / coverage reports 30 | htmlcov/ 31 | .tox/ 32 | .coverage 33 | .cache 34 | nosetests.xml 35 | coverage.xml 36 | 37 | # Translations 38 | *.mo 39 | 40 | # Mr Developer 41 | .mr.developer.cfg 42 | .project 43 | .pydevproject 44 | 45 | # Rope 46 | .ropeproject 47 | 48 | # Django stuff: 49 | *.log 50 | *.pot 51 | 52 | # Sphinx documentation 53 | docs/_build/ 54 | 55 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | embm 2 | =========== 3 | 4 | A trivial global atmosphere energy-moisture balance model (EMBM) written in Python 3. Loosely based on [Fanning and Weaver 1996](http://dx.doi.org/10.1029/96JD01017). This is a class project. 5 | 6 | # Requirements 7 | 8 | * [Python 3](https://www.python.org/) 9 | * [Numpy](http://www.numpy.org/) (embm was written with version 1.8.1) 10 | 11 | # How do I run this? 12 | 13 | For a complete example, see the [project's wiki page](https://github.com/brews/embm/wiki). A very simple example is below. 14 | 15 | First, [download a copy](https://github.com/brews/embm/archive/master.zip) of the embm code. Unpackage the code and open a Python shell in the same directory as `embm.py`. In the Python shell, type: 16 | 17 | ``` 18 | import embm 19 | 20 | m = embm.Model() 21 | m.step(10000) 22 | ``` 23 | You can plot or just quickly checkout the fruits of your model's labor: 24 | ``` 25 | m.t[1] 26 | m.q[1] 27 | ``` 28 | 29 | This sets up a model, which we assign to `m`. The model then runs through 10,000 time-steps, roughly 208 days in "model time" with the default settings. This is more than enough time for the model to spin up. This takes under a minute to run on my old laptop. 30 | 31 | You can change settings and parameters or analyze variables within the model by interacting with the model instance, in this case, `m`. 32 | 33 | For more information see the documentation within the code or [the project's humble wiki](https://github.com/brews/embm/wiki). 34 | 35 | # What's the purpose of this? 36 | 37 | The model, as originally described by [Fanning and Weaver 1996](http://dx.doi.org/10.1029/96JD01017), was designed as a simple atmosphere component attached to a larger ocean circulation model. It now can be used to test theoretical claims or as a simple exercise. 38 | 39 | The model treats the atmosphere as a single-layered slab gridded into 4° x 5° cells. It accounts for simple energy (e.g. from the ocean or incoming solar radiation) and moisture exchange (e.g. crude evaporation, precipitation, and humidity) across the grid. 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4.6 5.0 5.2 5.3 5.5 5.9 5.7 5.5 2.3 0.7 0.6 0.7 0.8 0.9 3.0 3.5 3.6 4.0 4.2 4.5 4.8 5.4 6.1 6.5 7.2 1.9 0.9 1.2 1.6 2.2 3.2 0.9 4.2 5.4 5.7 6.5 7.0 7.2 7.1 7.1 7.1 7.0 6.8 6.5 6.2 2.7 1.0 2.4 2.5 2.9 2.4 1.6 3.6 4.8 4.5 4.3 4.5 4.7 19 | 4.0 4.3 4.3 4.3 4.2 3.7 3.5 3.9 4.4 4.7 4.9 5.2 5.6 5.9 6.3 6.5 6.6 6.7 6.7 6.7 6.6 5.1 1.7 1.8 0.7 0.3 0.7 1.3 2.5 4.7 5.4 5.8 6.1 6.2 6.4 6.6 6.6 6.7 7.0 0.8 1.1 1.5 1.7 1.6 2.1 0.3 4.2 5.6 6.6 7.3 7.8 7.9 8.0 8.1 8.1 7.9 7.5 6.8 5.4 3.1 1.6 0.4 1.4 1.3 0.5 2.7 5.8 5.3 5.1 5.1 4.8 3.8 20 | 3.7 3.8 4.0 4.6 4.5 4.1 4.2 4.5 5.2 5.6 5.9 6.4 6.8 7.0 7.1 7.3 7.4 7.3 7.2 7.0 7.1 0.6 1.5 0.4 0.3 0.3 0.7 1.7 1.8 5.6 6.5 7.0 7.3 7.3 7.2 6.9 6.4 6.2 5.4 0.4 0.8 1.3 1.8 1.4 1.3 0.8 4.7 6.0 6.7 6.7 6.8 7.0 7.1 7.3 7.3 7.1 6.8 5.9 4.5 3.0 1.6 0.7 0.3 1.3 2.3 5.0 4.5 4.5 4.3 4.0 3.8 3.5 21 | 2.8 3.2 3.7 4.0 4.2 4.5 4.7 4.7 5.0 5.8 6.4 6.7 7.0 7.2 7.3 7.4 7.4 7.4 7.3 6.8 4.6 1.2 0.3 0.3 0.2 0.3 0.5 1.5 3.2 4.9 7.0 7.3 7.5 7.5 7.3 6.8 6.1 5.5 4.6 1.2 0.4 0.7 1.5 2.3 1.9 4.0 5.6 4.8 4.7 4.7 4.7 4.6 4.7 5.0 5.1 5.0 4.7 3.9 2.7 2.3 1.5 1.3 0.9 2.8 3.1 3.7 2.7 3.0 2.5 2.5 2.7 2.8 22 | 2.4 2.9 3.3 3.6 4.0 4.5 4.9 5.1 5.4 5.7 6.0 6.2 6.3 6.3 6.5 6.5 6.4 6.3 5.9 5.7 1.9 0.2 0.3 0.3 0.3 0.3 0.4 0.6 2.5 4.7 6.3 6.4 6.5 6.6 6.6 6.2 5.8 5.0 3.8 1.2 0.1 0.2 1.4 2.2 3.3 4.4 4.0 2.8 2.5 2.4 2.0 1.6 1.9 2.4 2.9 3.0 2.3 1.0 1.6 1.3 1.4 1.4 2.0 2.1 0.4 0.6 2.5 1.6 1.0 1.3 1.5 1.9 23 | 2.7 3.3 3.8 4.1 4.5 4.8 5.0 5.3 5.4 5.4 5.3 5.2 5.1 4.9 4.7 4.6 4.4 4.2 4.1 3.8 1.7 0.4 0.4 0.4 0.4 0.7 0.6 2.3 5.6 5.4 4.7 4.7 4.6 4.7 5.0 5.2 5.0 4.7 1.8 1.0 0.3 0.1 0.6 1.5 2.8 3.5 2.4 1.9 1.3 0.9 0.6 0.8 1.4 1.5 1.6 1.0 0.3 0.2 1.1 0.3 0.3 1.4 1.2 0.5 0.3 0.7 1.5 0.9 0.8 1.0 1.5 2.1 24 | 3.6 4.0 4.4 4.6 4.8 5.1 5.3 5.2 5.1 5.0 4.8 4.6 4.3 3.9 3.6 3.2 3.3 3.6 3.6 3.3 2.5 0.6 0.2 0.3 1.0 0.9 3.6 5.9 5.2 4.3 3.6 2.7 2.5 3.1 3.7 4.3 4.3 4.2 1.9 0.7 0.6 0.3 0.5 1.4 2.7 2.7 1.5 1.1 0.5 0.5 0.7 1.2 2.0 2.5 2.1 1.7 0.2 0.3 0.3 0.1 0.3 0.6 0.5 0.3 0.4 1.0 0.8 0.6 1.0 1.9 2.5 3.1 25 | 5.1 5.3 5.5 5.8 6.0 6.1 6.0 5.6 5.2 4.8 4.2 3.6 3.0 2.2 1.8 1.5 1.4 2.0 2.8 2.7 2.8 0.2 0.4 0.8 1.4 3.3 5.7 6.1 5.8 4.7 3.7 2.3 0.9 2.3 2.2 2.0 2.6 2.0 1.2 1.0 1.1 0.8 0.6 0.9 1.9 2.5 2.2 1.0 0.5 0.9 1.5 2.5 2.1 2.8 2.2 1.2 0.2 1.2 0.8 0.7 1.0 0.4 0.6 0.8 1.3 1.8 1.9 2.1 2.7 3.4 3.9 4.6 26 | 6.4 6.4 6.6 7.0 7.5 7.3 7.0 6.7 6.3 5.8 5.1 4.1 3.1 2.3 1.6 0.9 1.1 1.2 1.1 1.6 3.1 1.5 1.3 3.4 5.4 6.7 7.0 7.0 6.5 6.0 5.0 4.1 3.2 2.5 0.9 1.2 1.2 1.3 1.1 0.7 0.8 0.2 0.6 0.7 1.0 1.2 1.5 2.2 1.3 1.8 2.4 3.2 1.0 1.9 2.1 1.5 0.9 0.3 1.4 1.1 2.0 1.6 1.9 2.3 3.0 3.3 3.8 4.9 5.5 5.6 6.1 6.4 27 | 6.9 6.9 6.8 7.3 7.8 7.9 7.5 7.3 7.3 7.0 6.6 6.0 5.0 4.0 2.8 1.7 1.9 2.0 1.6 1.5 7.0 8.6 7.9 7.2 6.8 6.9 7.2 7.2 7.3 6.9 6.6 6.0 5.4 1.4 0.5 0.4 0.2 0.4 0.5 1.0 0.9 1.0 0.7 0.5 1.1 1.7 2.4 2.4 1.3 2.2 3.0 1.7 0.9 2.0 1.8 2.0 0.5 0.1 1.4 1.6 1.7 2.3 3.1 3.7 4.2 4.6 5.1 5.8 6.4 6.6 6.9 6.9 28 | 6.4 6.4 6.4 6.2 5.2 5.5 6.6 7.2 7.3 7.3 6.9 6.4 5.7 4.3 3.0 1.2 0.3 1.3 1.3 4.9 5.2 5.0 5.8 5.9 6.3 6.4 6.5 6.8 6.7 6.9 6.8 6.7 6.9 2.6 1.5 1.6 0.9 0.8 1.8 1.9 3.3 3.4 2.2 1.2 1.4 0.1 0.7 2.8 2.0 1.8 3.2 1.0 0.8 2.4 2.3 1.2 0.6 0.6 2.7 3.6 3.2 3.3 3.8 4.2 4.6 4.7 5.1 5.5 5.9 6.2 6.3 6.4 29 | 5.0 5.0 5.1 5.1 5.0 5.3 5.7 6.2 6.4 6.3 6.0 5.4 4.8 4.4 3.1 1.2 1.4 3.5 4.4 4.7 5.0 5.1 5.2 5.0 5.0 4.9 5.0 5.1 5.5 5.5 6.0 6.1 7.0 3.9 3.1 2.5 1.8 0.9 1.7 2.4 2.6 3.0 2.7 2.4 1.9 1.2 1.4 0.7 2.0 3.3 2.3 0.7 0.7 0.5 1.0 0.6 0.7 0.8 0.9 3.0 4.0 3.3 3.4 3.4 3.6 3.7 3.8 4.0 4.4 4.7 4.9 4.9 30 | 3.0 3.1 3.4 3.6 4.2 4.7 4.5 4.6 4.8 4.7 4.7 4.3 4.5 4.9 2.0 0.7 2.0 2.9 3.0 2.6 1.7 2.8 2.9 2.6 2.6 2.6 2.7 3.0 3.1 3.7 4.0 4.7 5.3 5.7 2.4 1.7 2.1 1.4 1.4 1.9 1.5 1.8 2.4 2.7 0.9 0.5 1.5 2.3 1.9 2.3 1.4 1.0 0.6 0.8 0.8 0.9 1.9 1.5 1.1 0.7 2.9 3.3 2.1 1.5 1.5 1.6 1.9 2.1 2.3 2.6 2.8 2.9 31 | 0.8 1.0 1.0 1.2 1.6 2.1 2.5 2.7 2.6 2.9 3.3 4.5 5.2 3.1 0.7 0.6 1.6 1.2 0.8 1.0 0.5 0.4 0.6 0.5 0.8 0.7 0.8 0.9 1.2 1.3 2.1 2.8 3.1 4.4 3.2 0.3 1.0 1.3 0.8 1.2 1.4 1.4 2.2 2.5 0.8 0.5 1.6 1.1 1.4 1.8 0.9 1.4 1.0 3.2 3.6 3.7 3.0 2.5 1.3 0.8 0.8 2.8 1.9 1.0 1.1 1.1 0.9 0.8 0.9 0.9 0.9 0.8 32 | 2.0 1.8 1.7 1.3 1.1 1.0 1.0 0.8 0.6 1.4 2.9 5.4 3.1 0.9 0.5 1.2 1.4 0.9 0.3 0.4 0.5 1.0 1.7 2.3 2.4 2.3 2.1 1.7 1.2 0.7 0.5 1.4 2.1 2.8 3.3 0.7 0.7 0.5 1.0 0.8 1.7 3.0 3.5 2.2 1.5 0.5 0.7 0.8 1.9 1.2 1.4 1.4 3.5 2.7 3.0 2.3 2.1 1.5 0.8 0.4 0.6 2.0 1.5 1.1 1.3 1.2 1.5 1.8 2.1 2.1 2.1 2.1 33 | 3.3 3.3 3.1 2.8 2.7 2.6 2.4 2.3 2.0 1.9 3.2 4.2 0.5 0.8 1.1 1.7 0.7 0.9 0.7 1.0 1.0 1.2 2.4 2.6 2.9 3.1 3.0 2.9 2.6 2.1 1.6 1.3 1.5 2.3 2.8 0.5 0.7 1.4 1.8 1.5 0.8 1.7 1.0 0.4 0.5 0.9 1.7 1.3 1.2 0.8 0.9 2.1 1.1 1.0 0.9 1.1 1.2 0.5 0.9 0.5 0.4 1.1 2.0 2.2 1.4 1.8 1.7 1.9 2.3 2.6 2.9 3.2 34 | 3.7 3.7 3.9 3.8 3.7 3.7 3.6 3.5 3.2 3.0 2.8 1.6 0.8 0.7 1.5 1.9 0.3 0.5 0.8 1.1 1.5 1.4 2.0 2.2 2.4 2.2 2.2 3.1 3.4 3.2 2.7 2.3 1.9 2.1 1.4 0.7 0.9 1.7 0.9 0.4 0.2 0.6 1.2 1.2 0.6 1.0 2.0 1.5 1.6 1.7 0.9 1.0 0.6 0.9 0.9 1.6 2.3 2.2 1.7 2.2 1.3 1.3 2.0 2.7 2.0 2.0 2.0 2.3 2.6 2.9 3.2 3.3 35 | 3.4 3.5 3.7 4.0 4.1 4.2 4.1 4.0 3.8 3.5 3.2 1.5 0.8 1.1 2.0 1.4 0.7 0.5 1.0 0.9 0.9 1.2 1.4 1.7 2.6 2.4 2.9 3.5 3.8 3.8 3.8 3.3 2.9 2.4 1.8 1.7 0.9 0.6 0.4 0.4 0.3 0.6 0.6 0.7 1.0 0.8 1.0 0.6 0.6 0.9 1.1 0.9 0.4 0.4 0.7 1.6 2.3 1.1 1.2 1.8 1.9 1.0 1.5 1.1 2.0 1.4 2.3 2.7 3.1 3.3 3.3 3.5 36 | 2.2 2.3 2.6 2.9 3.3 3.8 4.0 4.0 3.6 3.4 2.3 1.1 0.8 2.0 2.0 1.0 0.8 0.5 0.6 0.7 0.8 0.8 1.0 1.1 1.3 2.0 3.3 4.1 4.0 3.8 4.1 4.1 3.8 3.5 2.5 2.0 1.3 1.1 1.2 1.1 0.6 0.5 0.3 0.3 0.5 0.4 0.4 0.4 0.4 0.5 1.0 1.0 0.8 1.2 1.2 0.8 1.1 1.0 1.2 2.1 1.1 1.1 0.5 0.5 1.3 1.6 2.0 2.2 2.2 2.1 2.2 2.2 37 | 0.3 0.7 0.9 1.3 1.6 2.1 2.9 3.3 3.2 2.5 1.8 1.0 1.8 1.8 0.7 0.4 0.3 0.3 0.6 1.1 1.3 1.0 1.0 1.0 1.3 2.4 2.8 3.0 3.2 3.5 3.8 3.9 3.8 3.6 2.8 2.3 2.1 2.1 1.3 1.4 0.8 0.7 0.6 0.7 0.9 0.9 0.8 1.1 1.1 1.1 1.3 1.0 1.1 1.6 1.5 1.3 1.8 0.8 0.7 1.3 1.0 1.2 1.0 1.1 2.1 1.8 1.7 0.6 1.0 1.5 0.5 0.4 38 | 1.9 1.5 1.4 0.8 0.5 0.4 0.6 2.5 2.8 1.8 1.4 1.4 1.2 0.6 0.4 0.3 0.4 0.9 1.5 1.9 1.5 0.9 1.1 1.3 2.9 3.1 1.9 1.8 2.4 3.0 3.0 3.1 3.1 3.0 3.1 2.5 2.2 1.4 0.6 0.9 1.8 1.0 0.9 0.9 0.8 0.8 0.9 0.9 1.0 0.9 0.9 0.9 1.2 1.1 1.2 1.1 0.9 1.1 1.5 1.3 1.1 0.8 0.9 1.5 1.9 2.1 2.3 1.7 0.6 1.8 2.6 2.5 39 | 3.2 2.8 1.9 1.1 0.7 0.9 1.2 1.7 1.3 0.9 1.5 1.2 0.3 0.2 0.2 0.2 1.1 1.4 1.6 1.4 0.3 0.7 1.2 1.2 2.9 1.6 2.2 2.6 3.2 0.8 1.1 1.3 1.4 1.2 1.4 1.8 2.2 2.6 1.4 0.7 1.0 0.7 0.6 0.6 0.7 0.7 0.7 0.8 0.7 0.6 0.7 0.8 0.7 0.9 1.1 1.1 1.1 1.0 0.6 1.0 0.9 0.6 0.6 0.4 0.8 1.3 1.5 1.6 1.7 1.6 1.3 2.3 40 | 2.1 2.4 2.5 1.8 1.2 1.0 1.0 0.7 0.4 0.5 0.7 0.4 0.3 0.2 0.6 1.1 1.0 0.8 1.2 2.0 1.7 0.7 0.7 1.0 3.3 1.1 3.8 2.3 3.7 5.9 5.3 3.8 2.0 0.7 0.3 0.4 1.2 1.9 2.1 1.5 0.7 0.2 0.4 0.8 1.0 0.8 0.7 0.6 0.6 0.7 0.6 0.4 0.7 0.9 1.1 0.8 0.8 0.6 0.6 0.8 0.1 0.8 0.4 0.4 0.6 1.0 1.0 0.3 0.2 0.7 1.1 1.6 41 | 0.9 1.8 2.4 2.5 1.7 1.2 1.1 0.6 0.2 0.5 0.6 0.7 0.6 0.8 1.0 1.0 1.1 1.3 1.4 0.8 0.8 0.8 1.0 1.9 1.8 1.4 4.1 4.2 1.1 3.2 4.9 4.6 3.8 2.8 1.8 1.1 0.8 0.5 0.6 1.3 1.4 1.2 1.2 1.4 1.3 1.1 1.2 0.9 0.8 0.6 0.4 0.3 0.4 1.0 1.7 1.6 1.3 0.8 0.5 0.5 0.4 0.8 0.7 0.6 0.4 0.3 0.5 0.8 0.6 0.5 0.5 0.3 42 | 0.9 1.1 1.3 1.3 1.4 1.6 1.5 1.1 0.8 0.7 0.4 0.3 0.5 1.1 1.6 1.6 1.2 0.8 0.5 0.6 1.4 2.3 1.9 1.3 3.7 4.9 4.5 3.4 2.7 3.3 4.6 5.1 4.6 3.8 2.9 2.3 1.9 1.4 1.4 1.7 1.6 1.4 1.3 1.1 0.8 0.9 1.0 0.7 0.4 0.2 0.2 0.3 0.5 0.6 0.6 0.5 0.4 0.4 0.1 0.2 0.1 0.6 0.8 0.7 0.7 0.7 0.7 0.7 0.9 1.1 1.1 0.9 43 | 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.8 0.6 0.4 0.4 0.8 1.4 1.9 1.8 1.2 0.8 1.0 1.3 1.5 1.9 2.0 2.4 3.6 5.1 5.3 4.6 3.9 3.9 4.4 5.0 5.2 4.7 3.8 2.6 1.9 1.5 1.3 1.3 1.3 1.2 1.0 1.1 1.1 0.9 0.7 0.7 0.6 0.4 0.3 0.3 0.6 0.9 1.0 1.0 0.9 0.8 0.5 0.4 0.3 0.3 0.8 1.1 1.2 1.0 0.8 0.8 0.8 0.9 0.8 0.6 0.3 44 | 1.3 1.2 1.1 1.0 0.9 0.9 0.8 0.9 1.1 1.5 1.7 1.9 1.7 1.2 0.3 0.7 1.4 1.7 1.6 1.3 1.1 1.1 1.2 1.6 2.2 2.8 3.3 3.6 3.7 3.6 3.5 3.5 3.3 2.9 2.3 1.7 1.0 0.6 0.2 0.1 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.8 0.9 0.8 0.8 0.7 0.7 0.6 0.5 0.5 0.6 0.7 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.2 1.3 45 | 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.2 1.1 1.1 1.0 0.9 0.7 0.5 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.1 1.1 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.1 1.1 1.1 1.1 1.0 1.0 0.9 0.9 0.9 1.0 46 | 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.2 1.1 1.1 1.0 0.9 0.7 0.5 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.1 1.1 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.1 1.1 1.1 1.1 1.0 1.0 0.9 0.9 0.9 1.0 47 | -------------------------------------------------------------------------------- /embm.py: -------------------------------------------------------------------------------- 1 | # 2014-04-11 2 | # Copyright 2014 S. Brewster Malevich 3 | # 4 | # embm is free software: you can redistribute it and/or modify 5 | # it under the terms of the GNU General Public License as published by 6 | # the Free Software Foundation, either version 3 of the License, or 7 | # (at your option) any later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | # 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see 16 | 17 | 18 | """ 19 | Energy-moisture balance climate model based on [1]_. 20 | 21 | Notes 22 | ----- 23 | Special thanks to Prof. Jianjun Yin at the University of 24 | Arizona, Dept. Geosciences for input and education. 25 | 26 | References 27 | ---------- 28 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 29 | energy-moisture balance model: Climatology, interpentadal 30 | climate change, and coupling to an ocean general 31 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 32 | doi:10.1029/96JD01017. 33 | """ 34 | 35 | 36 | import numpy as np 37 | 38 | 39 | __all__ = ["vapor_pressure", "specific_humidity", "embm"] 40 | 41 | 42 | SECONDS_PER_YEAR = 3.15569e7 43 | 44 | 45 | def vapor_pressure(temp): 46 | """Return saturated vapor pressure (mb) for a given temp (K). 47 | 48 | Notes 49 | ----- 50 | Equations for saturated vapor pressure at a given air temp are not 51 | give in [1]_. We're using the below definition. 52 | 53 | References 54 | ---------- 55 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 56 | energy-moisture balance model: Climatology, interpentadal 57 | climate change, and coupling to an ocean general 58 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 59 | doi:10.1029/96JD01017. 60 | """ 61 | temp_c = temp - 273.15 62 | return 6.112 * np.exp((17.67*temp_c) / (temp_c+243.5)) 63 | 64 | 65 | def specific_humidity(temp): 66 | """Return saturated specific humidity (kg/kg) for a given temp (K). 67 | 68 | Notes 69 | ----- 70 | Equations for saturated specific humidity at a given air temp are 71 | not give in [1]_. We're using the below definition. 72 | 73 | References 74 | ---------- 75 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 76 | energy-moisture balance model: Climatology, interpentadal 77 | climate change, and coupling to an ocean general 78 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 79 | doi:10.1029/96JD01017. 80 | """ 81 | vapor_p = vapor_pressure(temp) 82 | return 0.622 * (vapor_p / (1013.26 - 0.378*vapor_p)) 83 | 84 | 85 | class Model(object): 86 | """Create an EMBM. 87 | 88 | Energy-moisture balance model (EMBM) based on [1]_. 89 | 90 | Attributes 91 | ---------- 92 | annual_shortwave : (J) array 93 | Annual shortwave insolation distribution by latitude. 94 | c_rhoa : float 95 | Heat capacity of dry air (10^3 * J/(kg K)). 96 | coalbedo : (J) array 97 | Also known as (1 - α). 98 | dalton : (J, I) array 99 | The Dalton number. 100 | e : (J, I) array 101 | Global evaporation (m/yr). 102 | earth_radius : float 103 | The radius of the model's planet (m). 104 | emissivity_atmosphere : (J) array 105 | Atmospheric emissivity. 106 | emissivity_ocean : float 107 | Oceanic emissivity. 108 | emissivity_planet : (J) array 109 | Planetary emissivity. 110 | epsilon_land : float 111 | Solar scattering coefficient over land. 112 | epsilon_sea : float 113 | Solar scattering coefficient over the ocean. 114 | h_atmosphere : int or float 115 | Atmospheric scale depth (m). 116 | h_humid : int or float 117 | Specific humidity scale depth (m). 118 | lat_range : (J) array 119 | Gives the latitude for each of the model's grid cells. 120 | latent_heat_evap : float 121 | Latent heat of evaporation (2.5e6 * J/kg). 122 | lon_range : (I) array 123 | Gives the latitude for each of the model's grid cells. 124 | m_t : (J, I) array 125 | Eddy-diffusive horizontal moisture transport parameterization. 126 | nlat : int 127 | Number of latitudinal cells in the model, J. 128 | nlon : int 129 | Number of longitudinal cells in the model, I. 130 | nu_heat : (J) array 131 | Eddy diffusivity for heat. 132 | nu_moisture : (J) array 133 | Eddy diffusivity for moisture. 134 | ocean_mask : (J, I) array 135 | Binary array indicating which of the model's cells are over 136 | oceans (`1`) or land (`0`). 137 | p : (J, I) array 138 | Precipitation for each of the model's cells (m/yr). 139 | pcip_flag : (J, I) array 140 | Binary array indicating whether precipitation is to occur (1) 141 | in a given model cell. 142 | q : (3, J, I) array 143 | Specific humidity (kg/kg) for a given model cell for three 144 | time steps n-1 (0, J, I), n (1, J, I), and n+1 (2, J, I). 145 | q_lh : (J, I) array 146 | Latent heat flux into the atmosphere. 147 | q_lw : (J, I) array 148 | Infrared emission flux. 149 | q_rr : (J, I) array 150 | Radiative flux into the atmosphere. 151 | q_sh : (J, I) array 152 | Sensible heat flux from the ocean. 153 | q_ssw : (J, I) array 154 | Shortwave radiation absorption flux. 155 | q_t : (J, I) array 156 | Eddy-diffusive horizontal heat transport parameterization. 157 | rho_air : int or float 158 | Surface air density (kg/m^3). 159 | rho_sea : int or float 160 | Sea surface density (kg/m^3). 161 | solar_constant : int or float 162 | The solar constant (W/m^3). 163 | sst : (J, I) array 164 | Sea-surface temperatures. 165 | stanton : (J, I) array 166 | The Stanton number. 167 | stefanboltz : float 168 | The Stefan-Boltzmann constant (W/(m^2 * K^4)). 169 | steps_run : int 170 | The number of steps the model has run through. 171 | t : (3, J, I) array 172 | Air temperature (K) for a given model cell for three 173 | time steps n-1 (0, J, I), n (1, J, I), and n+1 (2, J, I). 174 | time_step : float 175 | The number of seconds that pass with a single model step. 176 | wind : (J, I) array 177 | Wind speed climatology (m/s). 178 | x_step : (J) array 179 | The distance (m) covered with each cell in the longitudinal 180 | direction. 181 | y_step : float 182 | The distance (m) covered with each cell in the latitudinal 183 | direction. 184 | 185 | Methods 186 | ------- 187 | evaluate_evap() 188 | Evaluate model forcing terms at time n. 189 | evaluate_forcing() 190 | Evaluate model forcing terms at time n. 191 | evaluate_pcip() 192 | Evaluate the model precipitation variable at time n+1. 193 | evaluate_q_diffusion() 194 | Evaluate the model moisture diffusion at time n+1. 195 | evaluate_t_diffusion() 196 | Evaluate the model heat diffusion at time n+1. 197 | global_mean(x) 198 | Get the grid-area averaged mean for a model variable. 199 | reset() 200 | Reset the model's variables to initial state. 201 | step(nstep=1, trace=False, euler_steps=10) 202 | Run the model for a period of number of steps. 203 | step_q_diffusion() 204 | Update specific humidity at time n+1 from diffusion terms. 205 | step_t_diffusion() 206 | Update air temperature at time n+1 from diffusion terms. 207 | step_t_forcing(euler=False) 208 | Update air temperature at time n+1 from forcing terms. 209 | 210 | References 211 | ---------- 212 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 213 | energy-moisture balance model: Climatology, interpentadal 214 | climate change, and coupling to an ocean general circulation 215 | model, J. Geophys. Res., 101(D10), 15111–15128, 216 | doi:10.1029/96JD01017. 217 | 218 | Examples 219 | -------- 220 | >>> import embm 221 | >>> m = embm.Model() 222 | >>> m.step(5000) 223 | >>> m.t[1] # Air temperature for plotting, etc.. 224 | """ 225 | 226 | def __init__(self): 227 | self._initialize_constants() 228 | self._initialize_variables() 229 | 230 | def _initialize_constants(self): 231 | """ 232 | 233 | Notes 234 | ----- 235 | This model breaks the scattering coefficient (C_0) from [1]_ 236 | into a coefficient for land and for sea. 237 | 238 | References 239 | ---------- 240 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 241 | energy-moisture balance model: Climatology, interpentadal 242 | climate change, and coupling to an ocean general 243 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 244 | doi:10.1029/96JD01017. 245 | """ 246 | self.nlon = 72 247 | self.nlat = 46 248 | self.time_step = 3600 / 2 249 | self.earth_radius = 6371 * 1e3 250 | self.rho_air = 1.25 251 | self.rho_sea = 1024 252 | self.epsilon_sea = 0.65 253 | self.epsilon_land = 0.3 254 | self.c_rhoa = 1e3 255 | self.emissivity_ocean = 0.96 256 | self.h_atmosphere = 8400 257 | self.h_humid = 1800 258 | self.latent_heat_evap = 2.5e6 259 | self.solar_constant = 1360 260 | self.stefanboltz = 5.67e-8 261 | self.lat_range = np.linspace(-90, 90, self.nlat, endpoint = True) 262 | self.lon_range = np.linspace(-180, 180, self.nlon, endpoint = True) 263 | self.x_step = (self.earth_radius * 2 264 | * np.cos(self.lat_range * np.pi/180) * np.pi / self.nlon) 265 | self.x_step[0] = 1; self.x_step[-1] = 1 266 | self.y_step = self.earth_radius * 2 * np.pi / self.nlat 267 | 268 | # TODO: This IO should use a method and be done in main(). 269 | self.ocean_mask = np.loadtxt("./data/mask.txt", dtype = "i") 270 | self.wind = np.loadtxt("./data/wind.txt", dtype = "d") 271 | self.sst = np.loadtxt("./data/sst.txt", dtype = "f") 272 | self.sst[self.sst == -999] = np.nan 273 | self.sst += 273.15 # Convert C to Kelvin. 274 | 275 | def _initialize_variables(self): 276 | self.steps_run = 0 277 | self.t = np.ones((3, self.nlat, self.nlon)) * 273.15 278 | self.q = np.zeros((3, self.nlat, self.nlon)) 279 | self._calc_diffusion_coefs() 280 | self._calc_annual_shortwave() 281 | self._calc_coalbedo() 282 | self._scattering = np.zeros((self.nlat, self.nlon)) 283 | self._scattering[self.ocean_mask == 1] = self.epsilon_sea 284 | self._scattering[self.ocean_mask == 0] = self.epsilon_land 285 | self._calc_emissivity() 286 | self._calc_pcip_flag 287 | self.p = np.zeros(self.wind.shape) 288 | 289 | def _calc_diffusion_coefs(self): 290 | """Set the eddy-diffusive coefficients for model latitudes. 291 | 292 | Notes 293 | ----- 294 | Heat diffusion and moisture diffusion parameterizations 295 | (ν and κ, in [1]_, respectively) are plotted but the equation 296 | is not given. We're using the below definition. 297 | 298 | References 299 | ---------- 300 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 301 | energy-moisture balance model: Climatology, interpentadal 302 | climate change, and coupling to an ocean general 303 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 304 | doi:10.1029/96JD01017. 305 | """ 306 | rad = self.lat_range * np.pi / 180 307 | sin_lat = np.sin(rad) 308 | self.nu_heat = 3e6 * (0.81 - 1.08 * sin_lat**2 309 | + 0.74 * sin_lat**4) 310 | abs_sin = np.abs(sin_lat) 311 | self.nu_moisture = 1.7e6 * (1.9823 312 | - 17.3501 * abs_sin 313 | + 117.2489 * abs_sin**2 314 | - 274.1129 * abs_sin**3 315 | + 258.2244 * abs_sin**4 316 | - 85.7967 * abs_sin**5) 317 | 318 | def _calc_emissivity(self): 319 | """Set emissivities for model latitudes. 320 | 321 | Notes 322 | ----- 323 | Atmospheric and planetary emissivity are plotted in [1]_, but 324 | no equation is given. We're using the below definition. 325 | 326 | References 327 | ---------- 328 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 329 | energy-moisture balance model: Climatology, interpentadal 330 | climate change, and coupling to an ocean general 331 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 332 | doi:10.1029/96JD01017. 333 | """ 334 | rad = self.lat_range * np.pi/180 335 | sin_lat = np.sin(rad) 336 | self.emissivity_atmosphere = (0.8666 337 | + 0.0408 * sin_lat - 0.2553 * sin_lat**2 338 | - 0.466 * sin_lat**3 + 0.9877 * sin_lat**4 339 | + 2.0257 * sin_lat**5 - 2.3374 * sin_lat**6 340 | - 3.199 * sin_lat**7 + 2.8581 * sin_lat**8 341 | + 1.6070 * sin_lat**9 - 1.2685 * sin_lat**10) 342 | self.emissivity_planet = (0.5531 343 | - 0.1296 * sin_lat + 0.6796 * sin_lat**2 344 | + 0.7116 * sin_lat**3 - 2.794 * sin_lat**4 345 | - 1.3592 * sin_lat**5 + 3.8831 * sin_lat**6 346 | + 0.8348 * sin_lat**7 - 1.9536 * sin_lat**8) 347 | 348 | def _calc_annual_shortwave(self): 349 | """Set the annual shortwave radiation for model latitudes. 350 | 351 | Notes 352 | ----- 353 | The annual shortwave distribution is plotted in [1]_, but no 354 | equation is given. We're defining it here as 355 | S(φ) = 1.5*(1 - sin^2(φ)). 356 | 357 | References 358 | ---------- 359 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 360 | energy-moisture balance model: Climatology, interpentadal 361 | climate change, and coupling to an ocean general 362 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 363 | doi:10.1029/96JD01017. 364 | """ 365 | self.annual_shortwave = 1.5*(1 - np.sin(self.lat_range * np.pi/180)**2) 366 | 367 | def _calc_coalbedo(self): 368 | """Set the co-albedo for model latitudes. 369 | 370 | Notes 371 | ----- 372 | The coalbedo (1 - α) is plotted in [1]_, but no 373 | equation is given. Defined here as 374 | (1 - α) = 0.7995 - 0.315*sin^2(φ). 375 | 376 | References 377 | ---------- 378 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 379 | energy-moisture balance model: Climatology, interpentadal 380 | climate change, and coupling to an ocean general 381 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 382 | doi:10.1029/96JD01017. 383 | """ 384 | self.coalbedo = 0.7995 - 0.315 * np.sin(self.lat_range * np.pi/180)**2 385 | 386 | def _calc_diffusion(self, x, coef): 387 | """Calculate weighted diffusion. 388 | 389 | Parameters 390 | ---------- 391 | x : array-like 392 | Either `self.t` or `self.q`. Needs shape 393 | (3, self.lat, self.lon). 394 | coef : int or float 395 | Weight coefficient for the gradient of `x`. 396 | 397 | Returns 398 | ------- 399 | array_like 400 | Weighted-diffusion array shaped as (self.lat, self.lon). 401 | 402 | Notes 403 | ----- 404 | This is basically a lazy and cheaply vectorized approach to: 405 | ∇ • (coef ∇ x) 406 | """ 407 | # 1st derivative. 408 | grad1 = np.gradient(x, self.y_step, self.x_step[:, np.newaxis]) 409 | # x component. 410 | grad1[1] *= coef[:, np.newaxis] 411 | grad1[1][:, 0] = (x[:, 1] - x[:, -1]) / (2*self.x_step)*coef 412 | grad1[1][:, -1] = (x[:, 0] - x[:, -2]) / (2*self.x_step)*coef 413 | 414 | # 2nd derivative. 415 | grad2 = [np.gradient(grad1[0], self.y_step, self.x_step[:, np.newaxis])[0], 416 | np.gradient(grad1[1], self.y_step, self.x_step[:, np.newaxis])[1]] 417 | # y component. 418 | grad2[0] *= coef[:, np.newaxis] 419 | # x component. 420 | grad2[1][:, 0] = (grad1[1][:, 1] - grad1[1][:, -1]) / (2*self.x_step) 421 | grad2[1][:, -1] = (grad1[1][:, 0] - grad1[1][:, -2]) / (2*self.x_step) 422 | return grad2[0] + grad2[1] 423 | 424 | def _calc_pcip_flag(self): 425 | """Set precipitation flags. 426 | 427 | Notes 428 | ----- 429 | This is from eq. 13 and p113 of [1]_. 430 | 431 | References 432 | ---------- 433 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 434 | energy-moisture balance model: Climatology, interpentadal 435 | climate change, and coupling to an ocean general 436 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 437 | doi:10.1029/96JD01017. 438 | """ 439 | rel_humidity = self.q[2] / specific_humidity(self.t[2]) 440 | out = np.zeros(rel_humidity.shape) 441 | out[rel_humidity >= 0.85] = 1 442 | self.pcip_flag = out 443 | 444 | def reset(self): 445 | """Reset the model's variables to initial state. 446 | """ 447 | self._initialize_variables() 448 | 449 | def evaluate_forcing(self): 450 | """Evaluate model forcing terms at time n. 451 | 452 | Notes 453 | ----- 454 | The Dalton number is from eq. 18 of [1]_. 455 | 456 | `q_ssw` is from eq. 4 of [1]_. 457 | 458 | `q_lw` is from eq. 5a of [1]_. 459 | 460 | `q_rr` is from eq. 6 of [1]_. 461 | 462 | `q_sh` is from eq. 7 of [1]_. 463 | 464 | `q_lh` is from eq. 8 of [1]_. 465 | 466 | References 467 | ---------- 468 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 469 | energy-moisture balance model: Climatology, interpentadal 470 | climate change, and coupling to an ocean general 471 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 472 | doi:10.1029/96JD01017. 473 | """ 474 | self.dalton = (1e-3 * (1.0022 - 0.0822 * (self.t[1]-self.sst) 475 | + 0.0266*self.wind)) 476 | self.stanton = 0.94 * self.dalton 477 | self.q_ssw = (self.solar_constant/4 * self.annual_shortwave[:, np.newaxis] 478 | * self.coalbedo[:, np.newaxis] * (1 - self._scattering)) 479 | self.q_lw = (self.emissivity_planet[:, np.newaxis] 480 | * self.stefanboltz * self.t[1]**4) 481 | self.q_rr = (self.emissivity_ocean * self.stefanboltz * self.sst**4 482 | - self.emissivity_atmosphere[:, np.newaxis]*self.stefanboltz*self.t[1]**4) 483 | self.q_rr[self.ocean_mask == 0] = 0 484 | self.q_sh = (self.rho_air * self.stanton * self.c_rhoa * self.wind 485 | * (self.sst - self.t[1])) 486 | self.q_sh[self.ocean_mask == 0] = 0 487 | self.q_lh = ((self.rho_sea/SECONDS_PER_YEAR) 488 | * self.latent_heat_evap * self.p) 489 | 490 | def evaluate_evap(self): 491 | """Evaluate model evaporation variable at time n. 492 | 493 | Notes 494 | ----- 495 | This is from eq. 11 of [1]_. 496 | 497 | References 498 | ---------- 499 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 500 | energy-moisture balance model: Climatology, interpentadal 501 | climate change, and coupling to an ocean general 502 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 503 | doi:10.1029/96JD01017. 504 | """ 505 | self.e = ((self.rho_air * self.dalton * self.wind * SECONDS_PER_YEAR) 506 | /self.rho_sea * (specific_humidity(self.sst) - self.q[1])) 507 | self.e[self.ocean_mask == 0] = 0 508 | 509 | def evaluate_pcip(self): 510 | """Evaluate the model precipitation variable at time n+1. 511 | 512 | Notes 513 | ----- 514 | This is from eq. 12 of [1]_. 515 | 516 | References 517 | ---------- 518 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 519 | energy-moisture balance model: Climatology, interpentadal 520 | climate change, and coupling to an ocean general 521 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 522 | doi:10.1029/96JD01017. 523 | 524 | """ 525 | self._calc_pcip_flag() 526 | self.p = ((self.rho_air * self.h_humid * SECONDS_PER_YEAR) 527 | /(self.rho_sea*self.time_step) * self.pcip_flag 528 | * (self.q[2] - 0.85*specific_humidity(self.t[2]))) 529 | self.q[2][self.pcip_flag == 1] = (0.85 530 | * specific_humidity(self.t[2][self.pcip_flag == 1])) 531 | 532 | def evaluate_t_diffusion(self): 533 | """Evaluate the model heat diffusion at time n+1. 534 | 535 | Notes 536 | ----- 537 | Defined in eq. 3 of [1]_. 538 | 539 | References 540 | ---------- 541 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 542 | energy-moisture balance model: Climatology, interpentadal 543 | climate change, and coupling to an ocean general 544 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 545 | doi:10.1029/96JD01017. 546 | """ 547 | self.q_t = (self.rho_air * self.h_atmosphere * self.c_rhoa 548 | * self._calc_diffusion(self.t[2], self.nu_heat)) 549 | 550 | def evaluate_q_diffusion(self): 551 | """Evaluate the model moisture diffusion at time n+1. 552 | 553 | Notes 554 | ----- 555 | Defined in eq. 10 of [1]_. 556 | 557 | References 558 | ---------- 559 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 560 | energy-moisture balance model: Climatology, interpentadal 561 | climate change, and coupling to an ocean general 562 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 563 | doi:10.1029/96JD01017. 564 | """ 565 | self.m_t = (self.rho_air * self.h_humid 566 | * self._calc_diffusion(self.q[2], self.nu_moisture)) 567 | 568 | def step_t_forcing(self, euler=False): 569 | """Update air temperature at time n+1 from forcing terms. 570 | 571 | Parameters 572 | ---------- 573 | euler : bool 574 | Indicates whether or not to do time differencing with a 575 | Euler forward scheme or a leapfrog scheme. 576 | 577 | Notes 578 | ----- 579 | This uses a leapfrog/Euler-forward scheme. The majority of 580 | work is done by a leapfrog scheme but this should be balanced 581 | out by performing a Euler forward scheme-based step every now 582 | and then (~10 steps with the model's default settings). See 583 | [2]_ for a review of these methods. 584 | 585 | References 586 | ---------- 587 | .. [1] Cushman-Roisin, B., and J. Beckers (2011), Introduction 588 | to Geophysical Fluid Dynamics Physical and Numerical 589 | Aspects, 2nd ed. Academic Press. 590 | """ 591 | if euler: 592 | # Do Euler forward time differencing. 593 | self.t[2] = (self.t[1] + self.time_step 594 | /(self.rho_air * self.h_atmosphere * self.c_rhoa) 595 | * (self.q_ssw - self.q_lw + self.q_rr + self.q_sh + self.q_lh)) 596 | else: 597 | # Do leapfrog time differencing. 598 | self.t[2] = (self.t[0] + 2*self.time_step 599 | /(self.rho_air * self.h_atmosphere * self.c_rhoa) 600 | * (self.q_ssw - self.q_lw + self.q_rr + self.q_sh + self.q_lh)) 601 | 602 | def step_t_diffusion(self): 603 | """Update air temperature at time n+1 from diffusion terms. 604 | 605 | This uses the Matsuno predictor-corrector scheme. It needs to 606 | be run two times. See [1]_ for a review. 607 | 608 | References 609 | ---------- 610 | .. [1] Cushman-Roisin, B., and J. Beckers (2011), Introduction 611 | to Geophysical Fluid Dynamics Physical and Numerical 612 | Aspects, 2nd ed. Academic Press. 613 | """ 614 | self.t[2] += (self.time_step * self.q_t 615 | / (self.rho_air * self.h_atmosphere * self.c_rhoa)) 616 | self.t[2, 0, :] = self.t[2, 1, :].mean() 617 | self.t[2, -1, :] = self.t[2, -2, :].mean() 618 | 619 | def step_q_diffusion(self): 620 | """Update specific humidity at time n+1 from diffusion terms. 621 | 622 | This uses the Matsuno predictor-corrector scheme. It needs to 623 | be run two times. See [1]_ for a review. 624 | 625 | References 626 | ---------- 627 | .. [1] Cushman-Roisin, B., and J. Beckers (2011), Introduction 628 | to Geophysical Fluid Dynamics Physical and Numerical 629 | Aspects, 2nd ed. Academic Press. 630 | """ 631 | self.q[2] += (self.time_step 632 | * (self.m_t + (self.rho_sea * (self.e - self.p))/SECONDS_PER_YEAR) 633 | / (self.rho_air * self.h_humid)) 634 | self.q[2, 0, :] = self.q[2, 1, :].mean() 635 | self.q[2, -1, :] = self.q[2, -2, :].mean() 636 | 637 | def global_mean(self, x): 638 | """Get the grid-area averaged mean for a model variable. 639 | """ 640 | w = np.repeat(self.x_step * self.y_step, self.nlon) 641 | return np.average(x.flat, weights = w) 642 | 643 | def step(self, nstep=1, trace=False, euler_steps=10): 644 | """Run the model for a period of number of steps. 645 | 646 | Parameters 647 | ---------- 648 | nstep : int, optional 649 | The number of time steps to run through. Default is 1. 650 | trace : bool, optional 651 | Indicating whether you would like the global-mean specific 652 | humidity, precipitation, and air temperature averages for 653 | each time step to be stored and returned. Default is 654 | `False`. 655 | euler_steps : int, optional 656 | After how many time steps the temperature forcing 657 | integration should switch from a Leapfrog scheme to a 658 | Euler forward scheme. The default is 10 steps. 659 | 660 | Returns 661 | ------- 662 | t_hist : array-like 663 | Only returned if `trace = True`. Array giving the 664 | evolution of the model's air temperature as the model 665 | steps through time 666 | q_hist : array-like 667 | Only returned if `trace = True`. Array giving the 668 | evolution of the model's specific humidity as the model 669 | steps through time 670 | p_hist : array-like 671 | Only returned if `trace = True`. Array giving the 672 | evolution of the model's precipitation as the model steps 673 | through time. 674 | 675 | 676 | Notes 677 | ----- 678 | We're breaking down the contribution to changes in `t` and `q` 679 | into separate time differencing schemes. This is a different 680 | approach from that used in [1]_. See [2]_ for a review of 681 | these methods. 682 | 683 | References 684 | ---------- 685 | .. [2] Cushman-Roisin, B., and J. Beckers (2011), Introduction 686 | to Geophysical Fluid Dynamics Physical and Numerical 687 | Aspects, 2nd ed. Academic Press. 688 | .. [1] Fanning, A. F., and A. J. Weaver (1996), An atmospheric 689 | energy-moisture balance model: Climatology, interpentadal 690 | climate change, and coupling to an ocean general 691 | circulation model, J. Geophys. Res., 101(D10), 15111–15128, 692 | doi:10.1029/96JD01017. 693 | """ 694 | if trace: 695 | t_hist = np.zeros(nstep) 696 | q_hist = np.zeros(nstep) 697 | p_hist = np.zeros(nstep) 698 | 699 | for i in range(nstep): 700 | # Time step 701 | self.evaluate_forcing() 702 | self.evaluate_evap() 703 | 704 | # Leapfrog/Euler-forward step 705 | if i % euler_steps: 706 | self.step_t_forcing(euler = True) 707 | else: 708 | self.step_t_forcing() 709 | 710 | # Predictor step 711 | self.evaluate_t_diffusion() 712 | self.step_t_diffusion() 713 | self.evaluate_q_diffusion() 714 | self.step_q_diffusion() 715 | 716 | # Corrector step 717 | self.evaluate_t_diffusion() 718 | self.step_t_diffusion() 719 | self.evaluate_q_diffusion() 720 | self.step_q_diffusion() 721 | 722 | self.evaluate_pcip() 723 | 724 | # Shifting one step forward in time. 725 | for v in [self.t, self.q]: 726 | v[0] = np.copy(v[1]) 727 | v[1] = np.copy(v[2]) 728 | # TODO: Check why we can't assign to v[2]. Something is off here? 729 | # v[2] = 730 | if trace: 731 | t_hist[i] = self.global_mean(self.t[1]) 732 | q_hist[i] = self.global_mean(self.q[1]) 733 | p_hist[i] = self.global_mean(self.p) 734 | self.steps_run += 1 735 | if trace: 736 | return t_hist, q_hist, p_hist 737 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . --------------------------------------------------------------------------------