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WEEK:4 CREATING GRAPHS FOR THE DATA

The final week assignment is about providing a visual representation of my data and findings using univariate and bivariate graphs.

Using different kinds of data visualization, I will attempt to answer some of the research questions below:

Is crater diameter associated with crater depth ?

Do craters occur most often near the equator, the southern or northern hemisphere ?

Does crater depth depend on crater location ?

While attempting to answer these questions, it became obvious that the dataset required further cleaning to exclude additional ambiguous records. For example, all craters with zero number of ejecta layers were excluded in order to establish a clear relationship between crater depth and crater diameter. This final working dataset is called 'Fresh Uneroded Mars Craters'.

Creating and Visualizing New Working Dataset

The plot below is a 2D crater location map showing all craters (76,512) in the working dataset created in Week 3. This working dataset includes only craters with diameter greater than 0 and less than or equal to 100km; and depth greater than 0 and less than or equal to 3km.

As previously discussed in Week 3, the crater location plot reveals an overall trend in crater occurrence with some well-defined crater clusters. Overall, there are more craters in the southern hemisphere (0 to -90 degrees latitude) than in the northern hemisphere (0 to 90 degrees latitude). Moreover, crater population density increases in the middle of Mars near the equatorial region (-45 to 45 degrees latitude) but decreases towards the tips of both north and south poles respectively.

The red histogram on top of the plot shows the distribution of Crater Longitude while the blue histogram to the right of the plot shows the distribution of Crater Latitude.

CODE:

Univariate Graph of Crater DEPTH_GROUP:

CODE:

This graph is unimodal with its highest peak at the category of 0 to 0.3 km depth. It is skewed to the right as there are higher frequencies in the lower crater depth groups. This suggests that shallower craters are more abundant than deep craters on Mars.

Univariate Graph of Crater DIAMETER_GROUP:

CODE:

Univariate Graph of Crater LATITUDE_GROUP:

CODE:

This graph is unimodal with its highest peak at the category of -30 to -15 degrees latitude. It seems to be skewed to the right however the skewness is not pronounced. It also appears to have a semi-symmetrical shape. This suggests that there are higher number of craters near the equatorial region in the middle of Mars (-45 to 45 degrees latitude), than at the North Pole (45 to 90 degrees latitude) and South Pole (-45 to -90 degrees latitude) respectively. Notice that peak crater occurrence is not exactly at the equator but rather slightly to the south of the equator (-30 to -15 degrees latitude).

Univariate Graph of Crater Ejecta NUMBER_LAYERS:

CODE:

This graph is unimodal with its highest peak at the category of 0 number of crater ejecta layers. It is skewed to the right as there are higher frequencies in the lower number of crater ejecta layers. This suggests that craters with smaller number of ejecta layers are more abundant on Mars.

Is Crater Diameter Associated with Crater Depth?

CODE:

The graph above plots the depth of craters to the diameter of craters. We can see that the scatter graph appears noisy and does not show a clear relationship or trend between the two variables. However, it seems that there could be a positive weak linear relationship between crater depth and crater diameter. Therefore, I decided to investigate the dataset further, to see if there are other variables which could help reduce the noise and bring out any hidden trend in the scatter graph. The graph below is the result of that investigation.

The graph above plots the depth of craters to the diameter of craters, coloured by number of crater ejecta layers. We can see that a beautiful trend has suddenly emerged. There is a somewhat linear relationship between crater depth and crater diameter for all crater ejecta number of layers except NUMBER_LAYERS = 0. It also appears strange to see that both large craters (crater diameter > 40km) as well as deep craters (crater depth > 1km) have NUMBER_LAYERS as zero. You would expect that such significant craters should have several layers of ejecta. My explanation of this strange phenomenon is that these craters originally had so many ejecta layers, which were later completely eroded away by geological processes occurring on the surface of Mars. I therefore decided to create a new dataset excluding all craters with no ejecta layer, which was called 'Fresh Uneroded Crater Dataset'. The plot below shows crater depth to crater diameter relationship for craters belonging to this new dataset.

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kunalverma2000-blog · 5 years ago

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WEEK 3:Making Data Management Variables As Frequency Distributions Using Python

This assignment involves making data management decisions for the variables chosen to answer my research questions. These data management decisions include removing invalid data, selecting subset working dataset or representative sample, creating secondary variables and binning or grouping continuous variables.

The final working dataset includes only craters with:

Crater depth greater than zero and crater depth less than or equal to 3km

Crater diameter greater than zero and crater diameter less than or equal to 100km

Python Data Analysis Interpretation With Python Code:

Creating and Visualizing New Working Dataset

The plot below shows a 2D map of the entire original Mars crater database. All the 384,343 craters were plotted with Latitude on the Y axis and Longitude on the X axis. The red histogram on top of the plot shows the distribution of Crater Longitude while the blue histogram to the right of the plot shows the distribution of Crater Latitude. Notice that the number of craters is just too large for any meaningful visualization. Defining a new subset working dataset is therefore necessary for optimal data analysis.

Code

This second figure below is a scatterplot of Crater Diameter (size) vs Crater Depth. This plot was used to define a new subset working dataset, with all invalid points and outliers removed. The red rectangular block defines the boundaries of the working dataset, which includes only craters with diameter greater than 0 and less than or equal to 100km; and depth greater than 0 and less than or equal to 3km.

The plot below is another 2D crater location map but this time only displaying the working dataset, which contains 76,512 craters. Notice that the visualization has greatly improved compared to the location map of the entire database shown above. Most importantly, crater latitude and longitude histograms have similar distribution in both the working dataset and the entire Mars database. This suggests that the working dataset is an excellent representative sample of the entire Mars crater population.

The plot reveals an overall trend in crater occurrence with some well-defined crater clusters. Overall, there are more craters in the southern hemisphere (0 to -90 degrees latitude) than in the northern hemisphere (0 to 90 degrees latitude). Moreover, crater population density increases in the middle of Mars near the equatorial region (-45 to 45 degrees latitude) but decreases towards the tips of both north and south poles respectively.

Frequency Distribution of First Variable: DEPTH_GROUP

Code

I created a new variable called DEPTH_GROUP by collapsing crater depth variable (DEPTH_RIMFLOOR_TOPOG) into 10 different groups. Craters in the 0.0 to 0.3 km depth group are the most abundant, with 41,242 craters making up about 53.9% of the working dataset crater population.

Frequency Distribution of Second Variable: DIAMETER_GROUP

Code

A second new variable called DIAMETER_GROUP was also created by collapsing crater diameter variable (DIAM_CIRCLE_IMAGE) into 20 different groups. Craters with diameter between 0 and 5 km are the most abundant, with 32,845 craters making up about 42.93% of the working dataset crater population.

Frequency Distribution of Third Variable: LATITUDE_GROUP

Code

A third and final new variable, LATITUDE_GROUP, was created by collapsing crater latitude variable (LATITUDE_CIRCLE_IMAGE) into 12 different groups or regions. The highest crater occurrence is within the -30 to -15 degrees LATITUDE_GROUP. This group contains 12,886 craters which accounts for about 16.84% of the working dataset crater population. The distribution also shows that craters mostly occur in the middle of Mars (across 6 groups) between -45 to 45 degrees latitude. There are also more craters (47,974 craters) in the southern hemisphere than the northern hemisphere (76,512 - 47,974 = 28,538 craters).

Frequency Distribution of Fourth Variable: NUMBER_LAYERS

Code

Having defined a new working dataset, I therefore generated a new frequency distribution for the NUMBER_LAYERS variable. The most abundant NUMBER_LAYERS is 0. There are 58,447 craters (about 76.39%) which do not have ejecta layers.

Data Loading, Error Handling and Data Conditioning

Code

Putting all Four Analyses Together and Writing Output:

Code

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kunalverma2000-blog · 5 years ago

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Week 2 Data Analysis Interpretation:Using Python

Frequency Distribution of First Variable: NUMBER_LAYERS

CODE

The Mars crater database contains a record of the number of layers each impact crater ejecta has. This record is represented by the NUMBER_LAYERS variable. Of the total 384,343 craters studied, about 94.87% do not have ejecta layers. However, 15,467 craters have 1 ejecta layer, making up 4.02% of the total crater population.

0.89% and 0.19% of craters have 2 to 3 number of ejecta layers respectively. The highest number of ejecta layer is 5; with only 5 Mars craters (0.001 %) making it into this ejecta layer category.

My next step is to analysis and check if there is a relationship between number of ejecta layers and crater depth or diameter.

Frequency Distribution of Second Variable: MORPHOLOGY_EJECTA_3

CODE

The craters were divided into 3 morphology groups based on crater ejecta shape: MORPHOLOGY_EJECTA_1, MORPHOLOGY_EJECTA_2 and MORPHOLOGY_EJECTA_3. Each group was further subdivided into different morphology classes based on different naming conventions. The second variable to be examined is MORPHOLOGY_EJECTA_3 group, which contains 28 individual morphology classifications.

The frequency table above shows that 349 craters belong to the Pin-Cushion morphology class, which is equivalent to 0.09% of the total crater population. This is followed by the Small-Crown and Pseudo-Butterfly morphology categories with 264 (0.07%) and 118 (0.03%) craters respectively. The rest of the morphology categories were only observed in small number of craters.

However, majority of the craters, 383,050 craters making up 99.66% of the total crater population, were not classified and therefore were reported as missing values.

My next step of this analysis will be to find out if the available morphology data is sufficient to answer the already framed research questions.

Frequency Distribution of Third Variable: MORPHOLOGY_EJECTA_2

The third variable to be examined is MORPHOLOGY_EJECTA_2 group, which contains 103 individual morphology classifications.

CODE

The frequency table above shows that there are 103 different morphology categories within the MORPHOLOGY_EJECTA_2 group. However, only a few morphology categories were observed in more than 10 different craters out of the 384,343 Mars craters in the study database.

364, 867 craters (94.93%) out of the total 384, 343 craters were not classified into any morphology category and therefore were reported as missing values. The HuSL and HuBL morphology categories occurred 6,109 and 4,424 times (1.59% and 1.15%) respectively. This is followed by SmSL, HuAm, Hu, SmBL, SmAm, Sm and HuSL/SmSL morphology categories, which were identified in different number of craters, ranging between 2,713 and 204. The rest of the morphology categories have less than 80 crater occurrences each.

Data Loading, Error Handling and Data Conditioning

CODE

Putting all Three Analyses Together

CODE

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kunalverma2000-blog · 5 years ago

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Week 2 Data Analysis Interpretation:Using Python

Frequency Distribution of First Variable: NUMBER_LAYERS

CODE

0.89% and 0.19% of craters have 2 to 3 number of ejecta layers respectively. The highest number of ejecta layer is 5; with only 5 Mars craters (0.001 %) making it into this ejecta layer category.

My next step is to analysis and check if there is a relationship between number of ejecta layers and crater depth or diameter.

Frequency Distribution of Second Variable: MORPHOLOGY_EJECTA_3

CODE

However, majority of the craters, 383,050 craters making up 99.66% of the total crater population, were not classified and therefore were reported as missing values.

My next step of this analysis will be to find out if the available morphology data is sufficient to answer the already framed research questions.

Frequency Distribution of Third Variable: MORPHOLOGY_EJECTA_2

The third variable to be examined is MORPHOLOGY_EJECTA_2 group, which contains 103 individual morphology classifications.

CODE

Data Loading, Error Handling and Data Conditioning

CODE

Putting all Three Analyses Together

CODE

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kunalverma2000-blog · 5 years ago

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MARS CRATERS STUDY

After reviewing the materials . I have decided that I am interested in physical characteristics of the craters, specifically the diameter (DIAM_CIRCLE_IMAGE) and depth (DEPTH_RIMFLOOR_TOPOG). While the morphology category data (MORPHOLOGY_EJECTA_1 through 3) is interesting too. This data is not available for most craters listed in the data set. Additionally, the available data on morphology may prove difficult to interpret based on my existing knowledge. I have decided to restrict my personal codebook to the following variables taken from the list in the Mars Crater Codebook –

SPECIFIC TOPIC OF INTEREST

- Is there an association between the width of the crater and the depth of the rim of the crater?

CODE BOOK

1. CRATER_ID :Crater ID for internal use, in light of the rigion of the planet (1/16ths), the "pass" under which the crater was recognized, and the request where in it was distinguished.

2. LATITUDE_CIRCLE_IMAGE: Latitude from the derived center of a non-linear least-squares circle fit to the vertices selected to manually identify the crater rim (units are decimal degrees North).

3. LONGITUDE_CIRCLE_IMAGE: Longitude from the derived center of a non-linear least-squares circle fit to the vertices selected to manually identify the crater rim (units are decimal degrees East).

4. DIAM_CIRCLE_IMAGE: Diameter from a non-linear least-squares circle fit to the vertices selected to manually identify the crater rim (units are km).

5. DEPTH_RIMFLOOR_TOPOG: Average elevation of each of the manually determined N points along (or inside) the crater rim (units are km).

o Depth Rim –‐ Points are selected as relative topographic highs under the assumption they are the least eroded so most original points along the rim.

o Depth Floor – Points were chosen as the lowest elevation that did not include visible embedded craters.

MORPHOLOGY_EJECTA_1: ejecta morphology classified.

MORPHOLOGY_EJECTA_2: the morphology of the layer(s) itself/themselves.

MORPHOLOGY_EJECTA_3: overall texture and/pr shape of some of the layer(s)/ejecta that are generally unique and deserve separate morphological classification.

SECOND TOPIC TO EXPLOREASSOCIATION WITH ORIGINAL TOPIC

Is there an association between the width of the crater and the depth of the floor of the crater? In other words, is the depth of the floor of the crater dependent upon the diameter of the crater?

SOME BASIC QUESTION ASSOCIATION WITH SECOND TOPIC

Additional questions to be investigated in this study include the following:

- Is there an association/relation between the area of craters (based on its latitude & longitude) and the number of craters?Is there grouping of craters or there is the distribution of craters normally distributed?

- Is there an association/relation between the width of the crater and the number of ejecta layers?

I will concentrate on whether there is a relationship between crater diameter and depth in kilometers. As a stretch objective, I will determine if there is a secondary association between the noted characterstics and the crater location. The last may not be conceivable in the accessible time. While there are a few Python libraries that handle area information — models incorporate GeographicLib, GeoPandas, and ArcPy — these libraries may require some acclimation to deal with the coordinate system specific to mars to Mars.

Based on the literature review (below) my hypothesis is:

As rim slope is somewhat related to crater depth so I can hypothesize that crater diameter and depth do have a direct correlation to each other. The degree to which they are related remains unknown at this point until I begin analysis.

H1: It is theorized that there is a correlation between the diameter of a crater and the depth of a crater.

H0: Given a random sample set of craters, the depth of a crater on Mars is not dependent upon the diameter width of the crater when assessed at the 95% confidence level.

LITRECTURE REVIEW(REFRENCES)

Data source: Google Scholar

Data Queries: cratering on mars, Mars Cratering depth, Mars Cratering size

Synopsis and literature review findings: There are many papers referencing cratering on Mars as well as a comparison of Mars cratering to Lunar cratering. Barlow, Hartmann, and Ivanov seem to be primary sources. Topics referenced focus on surface properties of craters such as diameter, location, and morphology.

Robbins, S. J. (2011), Planetary Surface Properties, Cratering Physics, and the Volcanic History of Mars from a New Global Martian Crater Database., Site: Stuart Robbins, Astro/Geophysicist on the Web, 1–239, address: http://about.sjrdesign.net/files/thesis/RobbinsThesis_LargeMB.pdf, codebook: https://d396qusza40orc.cloudfront.net/phoenixassets/data-management-visualization/Mars%20Crater%20Codebook.pdf, data set: https://d18ky98rnyall9.cloudfront.net/_b190b54e08fd8a7020b9f120015c2dab_marscrater_pds.csv?Expires=1505865600&Signature=hlpupZ1s7N3Wxc8zZTdoN5U7M6WZK~ogycatsSlGxj45JJg2eDW6xlGUl-DTSFWzjPBZOn3QSFHnZHsQnSrjKowRM7OZgctqX1iY4iTJV7pYKqXRhnBeDFJHwaLywKHLzlbK8bi5CKE5jX~xHxXfE~sGIzuOE4l1fnWliaoXAXA_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A

Barlow, N. G. (1988). Crater size-frequency distributions and a revised Martian relative chronology. Icarus, 75(2), 285-305.

Barlow, N. G., & Bradley, T. L. (1990). Martian impact craters: Correlations of ejecta and interior morphologies with diameter, latitude, and terrain. Icarus, 87(1), 156-179.

Barlow, N. G., Boyce, J. M., Costard, F. M., Craddock, R. A., Garvin, J. B., Sakimoto, S. E., … & Soderblom, L. A. (2000). Standardizing the nomenclature of Martian impact crater ejecta morphologies. Journal of Geophysical Research, 105(E11), 26-733.

Chapman, C. R. (1974). Cratering on Mars I. Cratering and obliteration history. Icarus, 22(3), 272-291.

Hartmann, W. K. (1966). Martian cratering. Icarus, 5(1), 565-576.

Hartmann, W. K., & Neukum, G. (2001). Cratering chronology and the evolution of Mars. In Chronology and evolution of Mars (pp. 165-194). Springer Netherlands.

Ivanov, B. A. (2001). Mars/Moon cratering rate ratio estimates. In Chronology and evolution of Mars (p

McEwen, A. S. (2003, July). Secondary cratering on Mars: Implications for age dating and surface properties. In Sixth International Conference on Mars (Vol. 1, p. 3268).

Nimmo, F., & Gilmore, M. S. (2001). Constraints on the depth of magnetized crust on Mars from impact craters. Journal of Geophysical Research: Planets, 106(E6), 12315-12323.

Werner, S. C., Ivanov, B. A., & Neukum, G. (2009). Theoretical analysis of secondary cratering on Mars and an image-based study on the Cerberus Plains. Icarus, 200(2), 406-417.

Aharonson, O., M. T. Zuber, and D. H. Rothman (2001), Statistics of Mars’ topography from the Mars Orbiter Laser Altimeter: Slopes, correlations, and physical Models, J. Geophys. Res., 106(E10), 23723–23735, doi:10.1029/2000JE001403.

The Martian impact cratering record, Strom, Robert G.; Croft, Steven K.; Barlow, Nadine G.

Martian cratering II: Asteroid impact history, William K. Hartmann

Cratering Chronology and the Evolution of Mars, William K. Hartmann; Gerhard Neukum

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