Rod

This project tries to find a correlation between the Diameter of a Crater and its depth. For more information please read my previous publications: Homework 3: Managing Data, Homework 2: Running my first Python Program about Mars Craters and Homework 1: Getting your Research Project Started. In this homework even though since the beginning of the Project I chose 3 points (Coordinates) with the only purpose of showing results, I am going to show only one of the three locations mentioned before. I put the Homework 4 in 3 publications because the Nature of this assignment.

PYTHON PROGRAM:

# -*- coding: utf-8 -*-

“”“ Created on Sun Apr 10 20:43:27 2016 @author: Rodolfo Lerma C

”“”

#FIRST PART OF THE CODE

import pandas import numpy mars = pandas.read_csv(‘marscrater_pds.csv’, low_memory=False) #upper-case all DataFrame column names - place afer code for loading data aboave mars.columns = map(str.upper, mars.columns) # bug fix for display formats to avoid run time errors - put after code for loading data above pandas.set_option('display.float_format’, lambda x:’%f’%x) #print(len(mars)) #number of observations (rows) #print(len(mars.columns)) # number of variables (columns) #setting variables you will be working with to numeric mars['DIAM_CIRCLE_IMAGE’] = mars['DIAM_CIRCLE_IMAGE’].convert_objects(convert_numeric=True) mars['DEPTH_RIMFLOOR_TOPOG’] = mars['DEPTH_RIMFLOOR_TOPOG’].convert_objects(convert_numeric=True) mars['LATITUDE_CIRCLE_IMAGE’] = mars['LATITUDE_CIRCLE_IMAGE’].convert_objects(convert_numeric=True) mars['LONGITUDE_CIRCLE_IMAGE’] = mars['LONGITUDE_CIRCLE_IMAGE’].convert_objects(convert_numeric=True)

print(’&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&’)

#1 SUBSET OF DATA print ('Latitude between -70 and -75 Degrees and Longitude between 20 and 15’) #Random Sample print (’———-Subset 1———’) sub1=mars[(mars['LATITUDE_CIRCLE_IMAGE’]<=-70) & (mars['LATITUDE_CIRCLE_IMAGE’]>=-75) & (mars['LONGITUDE_CIRCLE_IMAGE’]<=20) & (mars['LONGITUDE_CIRCLE_IMAGE’]>=15) & (mars['DEPTH_RIMFLOOR_TOPOG’] > 0)] #make a copy of my new subsetted data sub2 = sub1.copy() sub2['Diam_Subgroups’]=pandas.cut(sub2.DIAM_CIRCLE_IMAGE, [0, 5, 10, 16], labels=[“0-5 km”,“5-10 km”,“10-15 km”]) c4 = sub2['Diam_Subgroups’].value_counts(sort=False) p4 = sub2['Diam_Subgroups’].value_counts(sort=False, normalize=True) print(c4) print(p4) print (pandas.crosstab(sub2['Diam_Subgroups’], sub2['DIAM_CIRCLE_IMAGE’])) print (pandas.crosstab(sub2['Diam_Subgroups’], sub2['DEPTH_RIMFLOOR_TOPOG’]))

desc1 = sub2['DIAM_CIRCLE_IMAGE'].describe()

print (desc1)

desc2 = sub2['DEPTH_RIMFLOOR_TOPOG'].describe()

print (desc2)

bar1=seaborn.boxplot (x="DIAM_CIRCLE_IMAGE", data=sub2)

plt.xlabel('Diameter of the Creater')

plt.title('Diameter in Lat -70,-75 Long 20,15')

bar2=seaborn.boxplot(x="DEPTH_RIMFLOOR_TOPOG", data=sub2)

plt.xlabel('Depth of the Creater')

plt.title('Depth in Lat -70,-75 Long 20,15')

scat3 = seaborn.regplot(x=sub2["DIAM_CIRCLE_IMAGE"], y=sub2["DEPTH_RIMFLOOR_TOPOG"],data=mars)

plt.xlabel('Diameter of the Creater')

plt.ylabel('Depth of the Crater')

plt.title('Scatterplot for Diameter Vs Depth in Lat -70,-75 Long 20,15')

print(’&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&’)

#2 SUBSET OF DATA print ('Latitude between 35 and 30 Degrees and Longitude between 20 and 15’) #Random Sample print (’———-Subset 2———’) sub3=mars[(mars['LATITUDE_CIRCLE_IMAGE’]<=35) & (mars['LATITUDE_CIRCLE_IMAGE’]>=30) & (mars['LONGITUDE_CIRCLE_IMAGE’]<=20) & (mars['LONGITUDE_CIRCLE_IMAGE’]>=15) & (mars['DEPTH_RIMFLOOR_TOPOG’] > 0)] sub4 = sub3.copy() sub4['Diam_Subgroups_2’]=pandas.cut(sub4.DIAM_CIRCLE_IMAGE, [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 90], labels=[“0-5 km”,“5-10 km”,“10-15 km”,“15-20 km”,“20-25km”,“25-30 km”,“30-35 km”,“35-40 km”,“40-45 km”,“45-50 km”,“50-55 km”,“55-60 km”,“60-65 km”,“65-70 km”,“70-75 km”,“75-80 km”]) c6 = sub4['Diam_Subgroups_2’].value_counts(sort=False) p6 = sub4['Diam_Subgroups_2’].value_counts(sort=False, normalize=True) print(c6) print(p6)

print (pandas.crosstab(sub4['Diam_Subgroups_2’], sub4['DIAM_CIRCLE_IMAGE’])) print (pandas.crosstab(sub4['Diam_Subgroups_2’], sub4['DEPTH_RIMFLOOR_TOPOG’]))

print(’&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&’)

#3 SUBSET OF DATA print ('Latitude between 60 and 55 Degrees and Longitude between 20 and 15’) #Random Sample print (’———-Subset 3———’) sub5=mars[(mars['LATITUDE_CIRCLE_IMAGE’]<=60) & (mars['LATITUDE_CIRCLE_IMAGE’]>=55) & (mars['LONGITUDE_CIRCLE_IMAGE’]<=20) & (mars['LONGITUDE_CIRCLE_IMAGE’]>=15) & (mars['DEPTH_RIMFLOOR_TOPOG’] > 0)] sub6 = sub5.copy() sub6['Diam_Subgroups_3’]=pandas.cut(sub6.DIAM_CIRCLE_IMAGE, [0, 5, 10, 15, 20, 30], labels=[“0-5 km”,“5-10 km”,“10-15 km”,“15-20 km”,“20-25km”]) c8 = sub6['Diam_Subgroups_3’].value_counts(sort=False) p8 = sub6['Diam_Subgroups_3’].value_counts(sort=False, normalize=True) print(c8) print(p8)

print (pandas.crosstab(sub6['Diam_Subgroups_3’], sub6['DIAM_CIRCLE_IMAGE’])) print (pandas.crosstab(sub6['Diam_Subgroups_3’], sub6['DEPTH_RIMFLOOR_TOPOG’]))

Homework 4: Creating graphs for my Project data (Project about Mars Craters - Part 2)

Latitude between -70 and -75 Degrees and Longitude between 20 and 15

----------Subset 1---------

count   13.000000

mean     6.691538

std      4.138037

min      3.030000

25%      3.480000

50%      4.960000

75%      8.850000

max     15.170000

Name: DIAM_CIRCLE_IMAGE, dtype: float64

 count   13.000000

mean     0.280000

std      0.217141

min      0.070000

25%      0.140000

50%      0.220000

75%      0.310000

max      0.740000

CONCLUSION AND NOTES:

There are some things that need to be clarified here. First of all in order to only focus this research in the Diameter-Depth correlation at this point I just picked up 3 different locations in mars in the assumption that this will reduce bias for “Type of Terrain”. As here in Earth at different locations the soil behave different, therefore an specific place (longitude and latitude) must be chosen in order to minimize the bias for soil hardness and just focus the research on Diameter-Depth correlation. Secondly in this set of data in particular talking about the Depth information, it seems that maybe the instrumentation has not enough range to manage depths under 0.01 Km. Then this information since is the majority could mislead to a conclusion (correlation or not correlation). Then considering this possibility, I took the decision to not include these points in my analysis. Since the result were too large to put it here I summarized the information in the next following paragraph

In the first group:

Craters Latitude (-70,-75) Longitude (20,15) For this combination it is possible to see 3 groups, and if you see the information you can notice that as the diameter is increase so the depth.

In the first graph it is possible to see even though the mean is around 5, most of the information is on the right side of the mean, and also it is possible to see that the variation of the diameter is from 3 Km to 15 Km. On the second graph, now talking about Depth the mean is about 0.2 Km with a distribution of the information from 0.08 Km to 0.45 Km, with two possible Outliers.

On the 3rd graph is visually possible to see the correlation I was assuming from this investigation. My independent variable is the Diameter and my Dependent variable is the Depth. In this investigation I assumed that the diameter is directly related with the size of the Crater, directly. But the Depth is a dependent variable, since the Depth is going to vary according to the size of the crater and the location in Mars.

I did the same for my other 2 groups, for in which I see the same pattern. As I increment the Diameter I see an increment in the Depth of the crater.

Conclusion:

This project tries to find a correlation between the Diameter of a Crater and its depth. For more information please read my previous publications: Homework 2: Running my first Python Program about Mars Craters and Homework 1: Getting your Research Project Started. This HW was submitted in different publications because the nature of each part of this assignment.

This HW was submitted in different publications because the nature of each part of this assignment.

PYTHON PROGRAM:

# -*- coding: utf-8 -*-

""" Created on Sun Apr 10 20:43:27 2016 @author: Rodolfo Lerma C

"""

#FIRST PART OF THE CODE

import pandas import numpy mars = pandas.read_csv('marscrater_pds.csv', low_memory=False) #upper-case all DataFrame column names - place afer code for loading data aboave mars.columns = map(str.upper, mars.columns) # bug fix for display formats to avoid run time errors - put after code for loading data above pandas.set_option('display.float_format', lambda x:'%f'%x) #print(len(mars)) #number of observations (rows) #print(len(mars.columns)) # number of variables (columns) #setting variables you will be working with to numeric mars['DIAM_CIRCLE_IMAGE'] = mars['DIAM_CIRCLE_IMAGE'].convert_objects(convert_numeric=True) mars['DEPTH_RIMFLOOR_TOPOG'] = mars['DEPTH_RIMFLOOR_TOPOG'].convert_objects(convert_numeric=True) mars['LATITUDE_CIRCLE_IMAGE'] = mars['LATITUDE_CIRCLE_IMAGE'].convert_objects(convert_numeric=True) mars['LONGITUDE_CIRCLE_IMAGE'] = mars['LONGITUDE_CIRCLE_IMAGE'].convert_objects(convert_numeric=True)

print('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&')

#1 SUBSET OF DATA print ('Latitude between -70 and -75 Degrees and Longitude between 20 and 15') #Random Sample print ('----------Subset 1---------') sub1=mars[(mars['LATITUDE_CIRCLE_IMAGE']<=-70) & (mars['LATITUDE_CIRCLE_IMAGE']>=-75) & (mars['LONGITUDE_CIRCLE_IMAGE']<=20) & (mars['LONGITUDE_CIRCLE_IMAGE']>=15) & (mars['DEPTH_RIMFLOOR_TOPOG'] > 0)] #make a copy of my new subsetted data sub2 = sub1.copy() sub2['Diam_Subgroups']=pandas.cut(sub2.DIAM_CIRCLE_IMAGE, [0, 5, 10, 16], labels=["0-5 km","5-10 km","10-15 km"]) c4 = sub2['Diam_Subgroups'].value_counts(sort=False) p4 = sub2['Diam_Subgroups'].value_counts(sort=False, normalize=True) print(c4) print(p4) print (pandas.crosstab(sub2['Diam_Subgroups'], sub2['DIAM_CIRCLE_IMAGE'])) print (pandas.crosstab(sub2['Diam_Subgroups'], sub2['DEPTH_RIMFLOOR_TOPOG']))

print('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&')

#2 SUBSET OF DATA print ('Latitude between 35 and 30 Degrees and Longitude between 20 and 15') #Random Sample print ('----------Subset 2---------') sub3=mars[(mars['LATITUDE_CIRCLE_IMAGE']<=35) & (mars['LATITUDE_CIRCLE_IMAGE']>=30) & (mars['LONGITUDE_CIRCLE_IMAGE']<=20) & (mars['LONGITUDE_CIRCLE_IMAGE']>=15) & (mars['DEPTH_RIMFLOOR_TOPOG'] > 0)] sub4 = sub3.copy() sub4['Diam_Subgroups_2']=pandas.cut(sub4.DIAM_CIRCLE_IMAGE, [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 90], labels=["0-5 km","5-10 km","10-15 km","15-20 km","20-25km","25-30 km","30-35 km","35-40 km","40-45 km","45-50 km","50-55 km","55-60 km","60-65 km","65-70 km","70-75 km","75-80 km"]) c6 = sub4['Diam_Subgroups_2'].value_counts(sort=False) p6 = sub4['Diam_Subgroups_2'].value_counts(sort=False, normalize=True) print(c6) print(p6)

print (pandas.crosstab(sub4['Diam_Subgroups_2'], sub4['DIAM_CIRCLE_IMAGE'])) print (pandas.crosstab(sub4['Diam_Subgroups_2'], sub4['DEPTH_RIMFLOOR_TOPOG']))

print('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&')

#3 SUBSET OF DATA print ('Latitude between 60 and 55 Degrees and Longitude between 20 and 15') #Random Sample print ('----------Subset 3---------') sub5=mars[(mars['LATITUDE_CIRCLE_IMAGE']<=60) & (mars['LATITUDE_CIRCLE_IMAGE']>=55) & (mars['LONGITUDE_CIRCLE_IMAGE']<=20) & (mars['LONGITUDE_CIRCLE_IMAGE']>=15) & (mars['DEPTH_RIMFLOOR_TOPOG'] > 0)] sub6 = sub5.copy() sub6['Diam_Subgroups_3']=pandas.cut(sub6.DIAM_CIRCLE_IMAGE, [0, 5, 10, 15, 20, 30], labels=["0-5 km","5-10 km","10-15 km","15-20 km","20-25km"]) c8 = sub6['Diam_Subgroups_3'].value_counts(sort=False) p8 = sub6['Diam_Subgroups_3'].value_counts(sort=False, normalize=True) print(c8) print(p8)

print (pandas.crosstab(sub6['Diam_Subgroups_3'], sub6['DIAM_CIRCLE_IMAGE'])) print (pandas.crosstab(sub6['Diam_Subgroups_3'], sub6['DEPTH_RIMFLOOR_TOPOG']))

print('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&')

RESULTS:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Latitude between -70 and -75 Degrees and Longitude between 20 and 15 ----------Subset 1---------

                COUNT 0-5 km         7 5-10 km       3 10-15 km     3                   PERCENT 0-5 km        0.538462 5-10 km      0.230769 10-15 km    0.230769 DIAM_CIRCLE_IMAGE  3.030000   3.160000   3.450000   3.480000   3.660000   \ Diam_Subgroups                                                             0-5 km                     1          1          1          1          1   5-10 km                   0          0          0          0          0   10-15 km                 0          0          0          0          0  

DIAM_CIRCLE_IMAGE  4.270000   4.960000   5.560000   6.810000   8.850000   \ Diam_Subgroups                                                             0-5 km                     1          1          0          0          0   5-10 km                   0          0          1          1          1   10-15 km                 0          0          0          0          0  

DIAM_CIRCLE_IMAGE  12.080000  12.510000  15.170000   Diam_Subgroups                                       0-5 km                     0          0          0   5-10 km                   0          0          0   10-15 km                 1          1          1   DEPTH_RIMFLOOR_TOPOG  0.070000  0.080000  0.090000  0.140000  0.150000  \ Diam_Subgroups                                                           0-5 km                       1         1         1         1         1   5-10 km                     0         0         0         0         0   10-15 km                   0         0         0         0         0  

DEPTH_RIMFLOOR_TOPOG  0.180000  0.220000  0.240000  0.300000  0.310000  \ Diam_Subgroups                                                           0-5 km                       1         1         0         0         0   5-10 km                     0         0         1         1         1   10-15 km                   0         0         0         0         0  

DEPTH_RIMFLOOR_TOPOG  0.450000  0.670000  0.740000   Diam_Subgroups                                       0-5 km                       0         0         0   5-10 km                     0         0         0   10-15 km                   1         1         1  &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

CONCLUSION AND NOTES:

There are some things that need to be clarified here. First of all in order to only focus this research in the Diameter-Depth correlation at this point I just picked up 3 different locations in mars in the assumption that this will reduce bias for “Type of Terrain”. As here in Earth at different locations the soil behave different, therefore an specific place (longitude and latitude) must be chosen in order to minimize the bias for soil hardness and just focus the research on Diameter-Depth correlation. Secondly in this set of data in particular talking about the Depth information, it seems that maybe the instrumentation has not enough range to manage depths under 0.01 Km. Then this information since is the majority could mislead to a conclusion (correlation or not correlation). Then considering this possibility, I took the decision to not include these points in my analysis. Since the result were to large to put it here I summarized the information in the next following paragraph

In the first group:

Craters Latitude (-70,-75) Longitude (20,15) For this combination it is possible to see 3 groups, and if you see the information you can notice that as the diameter is increase so the depth. But an statistic analysis must be done in order to prove this evidence not only in a visual form.

In the second group:

Craters Latitude (35,30) Longitude (20,15) In this group we have around 14 groups and in general they show this correlation, but still would be better to analyze the information by an analytic form.

In the third group:

Craters Latitude (60,55) Longitude (20,15) 5 Groups are shown in this group. And they seems to behave in the same way, but further analysis needs to be done.

Conclusion:

In this part of the project I run my first Python program.

This project tries to find a correlation between the Diameter of a Crater and its depth. For more information please read my previous publication: Homework 1: Getting your Research Project Started. This homework was submitted in different publications because the nature of each part of this assignment. PYTHON PROGRAM:

# -*- coding: utf-8 -*-

""" Created on Sun Apr 10 20:43:27 2016 @author: Rodolfo Lerma C

""" import pandas import numpy mars = pandas.read_csv('marscrater_pds.csv', low_memory=False) #upper-case all DataFrame column names - place afer code for loading data aboave mars.columns = map(str.upper, mars.columns) # bug fix for display formats to avoid run time errors - put after code for loading data above pandas.set_option('display.float_format', lambda x:'%f'%x) print(len(mars)) #number of observations (rows) print(len(mars.columns)) # number of variables (columns) #setting variables you will be working with to numeric mars['DIAM_CIRCLE_IMAGE'] = mars['DIAM_CIRCLE_IMAGE'].convert_objects(convert_numeric=True) mars['DEPTH_RIMFLOOR_TOPOG'] = mars['DEPTH_RIMFLOOR_TOPOG'].convert_objects(convert_numeric=True) mars['LATITUDE_CIRCLE_IMAGE'] = mars['LATITUDE_CIRCLE_IMAGE'].convert_objects(convert_numeric=True) mars['LONGITUDE_CIRCLE_IMAGE'] = mars['LONGITUDE_CIRCLE_IMAGE'].convert_objects(convert_numeric=True)

Homework 2:  Running my first Python Program about Mars Craters (continuation)

There are some things that need to be clarify here. First of all in order to only focus this research in the Diameter-Depth correlation at this point I just picked up 3 different locations in mars in the assumption that this will reduce bias for “Type of Terrain”. As here in Earth at different locations the soil behave different, therefore an specific place (longitude and latitude) must be chosen in order to minimize the bias for soil hardness and just focus the research on Diameter-Depth correlation. In the first group: Craters Latitude (-70,-75) Longitude (20,15)

It is possible to see that most of the information was founded in Craters between 0-5 km of diameter. This gave to the research analysis a possible target group, since around 95 of our data is in this range, then might be reasonable to filter even more the information and just focus this project on Craters in specific locations with diameters between 0-5 km

In the second group: Craters Latitude (35,30) Longitude (20,15)

This group supports what the previous group has told us about narrowing the data using only craters between 0-5 km of diameter. In this case 87% of all data was in this specific range. In this specific zone of Mars we have greater dispersion of data, since we can see craters from 1 Km to even 80 Km. But the largest concentration of data still in the same range as the first group (as I said before)

In the third group: Craters Latitude (60,55) Longitude (20,15)

This last groups validates what the 2 previous points told us. Here 86.5% of all data was between the well known range (0-5 km).

Codebook: MARS Crater Codebook

After looking through the MARS Crater Codebook, I have decided that I am particularly interested in the relationship between the depths and diameters of Mars’s craters. The specific variables that I will be using in this study include (depth, in km)  DEPTH_RIMFLOOR_TOPOG and  DIAM_CIRCLE_IMAGE (diameter, in km).

For my literature, I have chosen to use Stuart Robbin’s “ Planetary Surface Properties, Cratering Physics, and the Volcanic History of Mars from a New Global Martian Crater Database” (pgs. 84-89). (LINK: http://about.sjrdesign.net/files/thesis/RobbinsThesis_LargeMB.pdf)

Summary:

"As is readily apparent from Fig. 26, except for craters D"30 km there is no uniform, global depth/Diameter ratio even for a small diameter range that can be quoted for the planet because of a significant shallowing near the poles. (p.89)...Across the surface of a planetary body, one might expect the ratio of a crater's depth to diameter to be constant since it is a gravity-dominated feature (Melosh, 1989). But, while gravity dominates, terrain properties control this final ratio, as illustrated in this section. This affects any "global" depth/Diameter ratio (d/D) one may quote, as has been done throughout the literature for decades (e.g., Pike, 1980; Garvin et al., 2000, 2003; Boyce and Garbeil, 2007; Stepinski et al., 2009) (p. 84).”