R programming and other questions related to Modeling

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Wilfrid Laurier University Department of Geography and Environmental Studies
GG101 – Introduction to Physical Geography
Lab 4: Humidity and Stability
Tasks and Questions
Part 1 Saturation Vapour Pressure and Air Temperature Relation In the lab 4 background reading document the relation between the Saturation Vapour Pressure and Air Temperature is described (see Figure 1 in the handout), the same relation is also described in the text (Figure 7.10) and is covered in lecture 9. We also defined how we calculate relative humidity (Equation 1) and how that can be done using vapour pressure as the humidity measure (Equation 2). The Saturation Vapour Pressure vs Air Temperature relation, and its connection to Relative Humidity through Equation 2, is central to understanding humidity conditions. For a parcel of air there are five variables that are associated with these relations, they are: (i) air temperature, (ii) saturation vapour pressure, (iii) dew point temperature, (iv) actual vapour pressure, and (v) relative humidity. In the table below, we see the five variables listed as columns. In the first two rows all of the data are present. In rows 3 and 4, there are only two of the five data points given for each entry.
Task 1 Working with the lab demonstrator, confirm that the answers (cell entries) in the first two rows (air samples 1 and 2) are correct.
Task 2 Working with the lab demonstrator, identify the cell entries for air samples 3 and 4 that are blank and devise the method to compute the value of the blank entries. Calculate the values of the missing entries and confirm with the lab demonstrator that you have the correct answers.
Task 3 The lab demonstrator will provide you with data entries for two of the variables for air samples 5 and 6, record those values.
Question 1 (6 marks) For air samples 5 and 6, what are the correct values for the missing cell entries? Show all your work.
Air
Sample
Air
Temperature
(oC)
Saturation
Vapour
Pressure
(es in mb)
Dew Point
Temperature
(Td in oC)
Actual
Vapour
Pressure (ea)
Relative
Humidity
(%)
1 20 23.5 14 16 68
2 5 9 -6 4 44
3 6 2
4 25 80
5 6
Part 2 Relative Humidity Calculations from Psychrometer Readings The use of a psychrometer will be reviewed by the lab demonstrator. When using a psychrometer we record the dry bulb temperature (air temperature) and the wet bulb temperature. From these two values the difference between the dry and wet bulb temperatures is determined (dry bulb temperature – wet bulb temperature), this quantity is often referred to as the wet-bulb depression. A psychrometric table or graph is then used to estimate the relative humidity from these data. The table below has a series of locations with dry and wet bulb temperature columns, and columns for the temperature difference and relative humidity.
Location
Dry Bulb
Temperature
(Ta in oC)
Wet Bulb
Temperature
(Tw in oC)
Temperature
Difference
(Ta – Tw)
Relative
Humidity
(%)
A B C D
Task 4 Your lab demonstrator will provide you with dry bulb and wet bulb temperatures for Locations A, B, C and D. Very carefully record that information.
Question 2 (4 marks) For each location, calculate the temperature difference and determine the relative humidity and enter those values into the table that you submit.
Question 3 (2 marks) One of the Locations (A, B, C or D) is an indoor environment in a structure in the midlatitudes of a building during the month of January. For this location you know the following: (i) the data were recorded inside the building, (ii) the building does not have a humidified air system, (iii) the heating in the building is a forced air system with a natural gas furnace, (iv) the combustion air for the furnace is drawn from the outside air, and (v) the outside air temperature at the time of the data collection was -5oC. What Location (A, B, C or D) is the indoor sampling environment described above? Briefly explain why this is the case.
Question 4 (2 marks) One of the Locations (A, B, C or D) is an outdoor environment on a floodplain adjacent to a river in the mid-latitudes in the month of June. The air was sampled in the early morning hours at sunrise. What Location (A, B, C or D) is the outdoor sampling environment described above? Briefly explain why this is the case.
Part 3 Hourly Variations in Temperature and Relative Humidity In this section we will examine hourly variations in temperature and relative humidity for one day from a climate station in southern Ontario. Go to the following URL: https://weather.gc.ca/ Then select the link ‘Past Weather’, this will take you to the page: https://climate.weather.gc.ca/ On this page select the link ‘Historical Data’ which is: https://climate.weather.gc.ca/historical_data/search_historic_data_e.html. In the Search by Station Name, type in London A and click Search. You will select Hourly data and set the date to October 5, 2020, as shown below and press the GO button. This search will bring up a data table that shows hourly data from the lobation on October 5, 2020. The data appears as below. Review the data for that day.
Task 5 (4 marks) The hourly data from the London A (London A) October 5, 2020 have been downloaded and are in the Excel spreadsheet: London_Oct_5_2020.xlsx, which is in the Lab 4 folder. Download that file and open the spreadsheet. Working with the lab demonstrator produce a graph that is a time series of changes in temperature and relative humidity through the course of that day. On the x-axis will be time (in hours), and there will be two y-axes, one will have temperature, and the second will have relative humidity. For Task 5, produce a fully labelled graph, and copy that graph into your answer document.
Question 5 (2 marks) Describe the relation between air temperature and relative humidity over the course of that day.
Question 6 (2 marks) The hourly data show that fog was present between 2 am and 4 am and then the conditions gradually cleared. Describe the conditions that contributed to the development of that fog that morning, why did it form?
Part 4 Stability and Lapse Rates Review the section on stability in the background document and the materials in lecture 9.
Scenario A meteorological balloon (radiosonde) is sent aloft and air temperatures are recorded at 400 m intervals from the surface to 4800 metres altitude. The data are presented in the table below. The air temperature data represent the environmental lapse rate (i.e. the temperature of the surrounding air).
Task 6
(a) Graph the temperature data on the accompanying sheet of paper. Use a landscape orientation for your graph. Plot temperature on the horizontal axis (1 cm = 2oC) and height on the vertical axis (1 cm = 400 m). Label your graph fully. (3 marks)
Height above
Surface (m) Air Temperature (oC) Parcel Temperature (oC)
0 17 17
400 14
800 10
1200 3
1600 0
2000 -2
2400 -5
2800 -7
3200 -11
3600 -16
4000 -19
4400 -22
4800 -24
Task 6
(b) A parcel of air is forced to rise from the surface. The parcel temperature is 17oC at the surface. The lifting condensation level (elevation at which the dew point temperature is reached) for this parcel is 1.2 km (1200 m). For this parcel assume an MAR (moist adiabatic lapse rate) of 0.5oC/100 m and a DALR (dry adiabatic lapse rate) of 1.0oC/100 m. (4 marks) (i) Calculate the temperature of the rising air parcel from the surface to 4800 metres and enter those data in the table above. (ii) Plot the air parcel temperatures by drawing a second line on the temperature height graph. (iii) Add a labelled horizontal line to your graph at the altitude of the Lifting Condensation Level (LCL).
(c) On your graph, identify the layer(s) in the profile at which the air parcel is stable and the layer(s) at which the air parcel is unstable. You may use vertical double-headed arrows to show the altitude range of the unstable layer(s) and the stable layer(s) (ù). Label the layers as stable and unstable. (1 marks)
BONUS (2 marks) What type of clouds would develop based on the stability conditions of the air parcel?

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