tThismks
The third image has problem 11 from the textbook. The plots need to be done in Matlab. I need help with this asap
MAE578, Spring 2023 Homework \#4 (16 points) A statement of collaboration is required. Computer codes (if any are used) should be included in your submission. Problem 1 ( 5 points) In the afternoon of a hot summer day, the surface generally warms up faster than the air aloft. This produces a near-surface layer with an enhanced lapse rate of temperature. Consider an environmental temperature profile, shown as the solid line in Fig. 1, with a constant lapse rate of \( 8^{\circ} \mathrm{C} / \mathrm{km} \) above \( 250 \mathrm{~m} \) and an enhanced (also constant) lapse rate of \( 11^{\circ} \mathrm{C} / \mathrm{km} \) from the surface to \( 250 \mathrm{~m} \) height. The surface temperature and pressure are given as \( 300^{\circ} \mathrm{K} \) and \( 1000 \mathrm{mb} \). The air is completely dry. If an air parcel initially located at the surface is pushed up with an initial upward velocity of \( 0.01 \mathrm{~m} / \mathrm{s} \) (i.e., \( w(0)=0.01 \mathrm{~m} / \mathrm{s} \) and \( \mathrm{z}(0)=0 \), where \( w(t) \) and \( \mathrm{z}(t) \) are the vertical velocity and height of the parcel as a function of time), find the maximum height, \( H \), that the parcel will reach. This is the height where the parcel first comes to a stop. In addition, plot the vertical velocity of the parcel as a function of height over the range of \( 0 \leq \mathrm{z} \leq H \). [In this problem, we assume that the parcel undergoes an adiabatic process as it ascends. It does not mix with the environment or exchange heat with the environment.] Problem 2 ( 3 points) An air parcel has an initial temperature of \( 300^{\circ} \mathrm{K} \) and initial specific humidity of \( 16 \mathrm{~g} / \mathrm{kg} \). It is initially located at the \( 1000 \mathrm{mb} \) pressure level (marked as "Level 1" in Fig. 2). (a) What are the relative humidity and partial pressure of water vapor for this air parcel? (b) If the parcel is adiabatically lifted upward, at what pressure level (marked as "Level 2" in Fig. 2) will condensation begin to occur in the parcel? What is the temperature of the parcel at this level? (c) What is the distance (in meters) between Level 1 and Level 2 ?
Problem 3 (6 points) Solve Problem 11, Part (a) and (b), in the problem set for Chapter 4 in textbook. In Part (a), in addition to determining the specific humidity at \( \mathrm{z}=3 \mathrm{~km} \), also make a plot of specific humidity as a function of height. \( q(\mathrm{z}) \), over the entire cloud column from \( 1 \mathrm{~km} \) to \( 9 \mathrm{~km} \). (Note: Depending on your approach, the given information of " \( p_{T}=330 \mathrm{mb} \) " might be redundant. It suffices to know \( p_{B}=880 \mathrm{mb} \).) Problem 4 ( 2 points) An air parcel is carried by the ambient flow over a mountain, following the path guided by the green arrows in Fig. 3. At position \( \mathbf{A} \), the parcel has an elevation of \( 1 \mathrm{~km} \) and is saturated, with specific humidity \( q=15 \mathrm{~g} / \mathrm{kg} \). The parcel ascends through a cloud layer (shaded region in Fig. 3) by a moist adiabatic process. Within the cloud, the environment is saturated and is in equilibrium. All liquid water that is condensed in the parcel falls out as precipitation. The parcel exits the cloud just as it reaches position \( \mathbf{B} \) at the top of the mountain, with an elevation of \( 3 \mathrm{~km} \). At this point, the specific humidity of the parcel is known to be \( q=9 \mathrm{~g} / \mathrm{kg} \). Afterward, the parcel descends to position \( \mathbf{C} \) following an unsaturated dry adiabatic process. The elevation of \( \mathbf{C} \) is \( 1 \mathrm{~km} \). The temperatures of the parcel at \( \mathbf{A}, \mathbf{B} \), and \( \mathbf{C} \) are denoted as \( T_{\mathrm{A}}, T_{\mathrm{B}} \), and \( T_{\mathrm{C}} \). (a) Estimate \( T_{\mathrm{B}}-T_{\mathrm{A}} \), i.e., the difference in the temperature of the parcel between \( \mathbf{B} \) and \( \mathbf{A} \). (b) Estimate \( T_{\mathrm{C}}-T_{\mathrm{A}} \), i.e., the difference in the temperature of the parcel between \( \mathbf{C} \) and \( \mathbf{A} \).