"Cut off all unnecessary actions." - Benjamin Franklin
This article describes how to draw schematics that enable new DART users to develop an intuition about how the various components of DART work.
The purpose of this endeavor is to simplify the schematics and to illustrate how to create a visual language that allows for new concepts to be introduced with greater ease.
Conceptual spaces
Within neuroscience, there is mounting evidence that human capacity for abstract thought is built upon the capacity for spatial navigation. The hippocampus and entorhinal cortex are used when animals navigate physical spaces. These same parts of the brain are also active when humans attempt to understand complex abstract concepts. While this neuroscience discussion is beyond the scope if this article, please see, "New evidence for the strange geometry of thought" if you want to learn more.
The most important aspect to consider when drawing schematics is how the axes are used. In the Manhattan and Lanai DART diagrams, the x and y axes are spent in the service of illustrating the concept of an assimilation cycle. While this is a valid use of the x and y axes, a cycle is one of the easiest data assimilation concepts to describe -- a process occurs, returns to a recognizable starting point, and the process repeats again if necessary.
Thus, spending the x and y axes to illustrate the concept of a cycle relinquishes visual territory that could otherwise be allocated to illustrate other concepts.
The simplified schematic design uses the axes differently:
- the x axis is used as a hybrid axis that depicts process and time
- the y axis is used as a hybrid axis that depicts input and output, as well as variations in state space.
Visual cues
When describing concepts graphically, visual vocabulary is limited. In order,
- axis
- location
- color
- shape
- size
- proximity
are the most effective visual cues that can be used to instruct the reader. These cues must be used wisely.
Building a consistent visual vocabulary
The subsequent figures demonstrate how to use the six visual cues to construct a visual vocabulary. In this analogy the axes serve as syntax – they provide the structure in which the remaining five cues can be used.
Observation converter
Observations are drawn using ellipses and are colored orange. Ellipses and orange are both suggestive of the letter "O" which is the first letter of the word "observation." Source data are depicted higher on the y-axis, an arrangement which indicates that they serve as input. The observation sequence file is depicted to the right along the x-axis, suggesting that it comes after the source data.
Perturb single instance
Model state is drawn using a parallelogram and is colored blue. Parallelograms are suggestive of the projection of a 3-dimensional domain. The sky and ocean, both commonly modeled domains, are blue.
Inflation
The y-axis is used to represent variations in state space. Depicting the concept of inflation becomes obvious in this setting.
Assimilation cycle
Since the observation sequence file is outlined in the same shape as the model state, depicting assimilation is relatively straightforward.
Increments
Differences between stages within the process can be meaningful. Computing increments follows from the concept of the pre-assimilation and analysis stages.
Representativeness Error
Using two colormaps, the yellow-blue colormap for model state and the orange-purple colormap for observations and the real world, allows for drawing essential concepts such as representativeness error.
"In this example, the model simulates a large-scale low-temperature anomaly at the same location it occurs in the real world. But since the model has lower resolution than the real world, it doesn't resolve gradients as sharply. When the model and real world temperatures are compared at a specific point along the edge of the anomaly, the model's estimate of the temperature is biased."
Probability density functions
Perfect model obs
The cues can be used to expand the vocabulary to illustrate nuanced differences between files used in DART such as set_def.out, obs_seq.in and obs_seq.out. In this case, it is obvious that the obs_seq.out created by perfect_model_obs is different from the observation sequence file created by an observation converter.
Colorblind safe palettes
The Manhattan and Lanai diagrams are difficult for readers with protanopia and deuteranopia, the two most common forms of color blindness, to interpret. These simplified diagrams use colors from colormaps that are easy for people with color blindness to distinguish: the yellow-blue colormap is known as viridis and the orange-purple colormap is known as plasma in these colormaps from Matplotlib.