[ K] McAlpine, hmwk #5, ATMS 611. J.D. McAlpine ATMS 611 HMWK #5

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1 McAline, hmwk 5, ATMS 6 J.D. McAline ATMS 6 HMWK Rainro evaorating (is 2 C) : 8 C, calculate mixing ratio of - sat. mixing ratio at 2 C is 8.7 g/kg (assume wet-bulb temerature) - L e = 2.25*0 6 J/kg - c w =952 J/kg/ K - c = 004 J/kg/ K - We can assume that the immeiately at the surface of the rainro is coole to saturation an therefore the here is also 2 C an mixing ratio is 8.7 g/kg. In other wors, we are assuming that 2 C is the wet-bulb tem. Therefore, our task is to fin how many g/kg of water must have been evaorate to cool the 6 C. We can subtract this amount from the 8.7 g/kg saturation mixing ratio to fin the actual mixing ratio in the ambient. [ K] & J 6024$ % kg & J *004$ % kg 6 * & = 6024$ K % 2.25*0 J kg & kg H 2O & kg $ = $ % J % kg H 2O 8.7 g/kg 2.7 g/kg = 6.0 g/kg This roblem emonstrates Norman s rule: water evaorate into the will cool until the immeiately at the surface of the water (which is also coole because it is the same temerature as the water) reaches its saturation mixing ratio. This metho can be use with a sling sychrometer to etermine the ambient mixing ratio. The roblem is also solve using a Skew-T chart (attache) an Norman s rule mb, 25 C, saturate aiabatic lase rate - how much tem change at 250 mb with C surface tem increase Refer to attache Skew-T lot follow saturate aiabatic lase rates in both cases lot reveals initial 250 mb tem of ~ -35 C lot reveals altere tem of ~ +3 C with surface increase of + C

2 McAline, hmwk 5, ATMS arcel: 000 mb, 5 C, 4 C T : use the skew T lot: (refer to attache skew T lot) a) - mixing ratio: 5 g/kg - relative humiity: 5(g/kg) / 0.5 (g/kg)= 48% - wet-bulb tem: 9 C - otential tem: 288 K - wet-bulb otential tem: 282 K b) same arameters as for a: but now if arcel rises to 900 mb - temerature: about 7 K - mixing ratio: 5 g/kg - relative humiity: 5(g/kg)/ 6.5 (g/kg)= 77% - wet-bulb tem: 4.5 C - otential tem: 288 K - wet-bulb otential tem: 282 K c) same arameters as for a: but now if arcel rises to 800 mb - temerature: about - C - mixing ratio: 4.2 g/kg - relative humiity: 4.2 g/kg / 4.2 g/kg = 00% - wet-bulb tem: 272 K (saturate mass) - otential tem: 293 K - wet-bulb otential tem: 282 K ) lifting conensation level: about 840 mb 3.53 ==> refer to attache chart a) AB: unstable: lifte arcels will be warmer than environment BC: neutral: lifte arcels will be same tem. as environment CD: neutral: lifte arcels (saturate) will be same tem. as environment DE: stable: lifte arcels will be cooler than environment EF: stable: lifte arcels will be cooler than environment FG: slightly stable: lifte arcels will be slightly cooler than environment b) convectively unstable? AB: yes BC: yes CD: no, neutral DE: yes, but a lot of energy is require to ush arcels u to the LFC since this layer contains a strong inversion EF: yes, but a ecent amount of energy is require to saturate the layer FG: yes 2

3 McAline, hmwk 5, ATMS Show that the conitions for the formation of a mirage (the increase of ensity with height) are realize if the ecrease in atmosheric temerature with height excees 3.5*Γ (ignore the suggestion about the D equation, since the roblem can seemingly be solve by just using the ieal gas equation) = ( R T ln P = ln ( + ln R z ( = + ( z T ( = ' ( z T ( = ' ( z T ( = ' ( z T T z T z T z + ( ' & T = $ + ( z T % z + lnt T z ( g ' g ' R T g R z (from hyrostatic equation) (from ieal gas equation) conitions for mirage: ρ/z > 0 : ensity increases with height assuming Γ =g/c, therefore: ) ( T = z T & + ) ' z ( T g % & + z R < 0 ' $ T g < z R T z T 004 < z 287 T > 3.5 z c < R g R % > 0 $ therefore, it is shown that for mirage conitions to occur (ρ/z >0), the lase rate T/z must excee 3.5 times the ry aiabatic lase rate (temerature nees to fall off greater than 34.3 K/km) 3

4 McAline, hmwk 5, ATMS 6 UNR-DRI Lase rate roblem: The height ifference of two groun base weather stations (UNR an DRI) in Reno is 43 meters. Obtain ata from these two sites (from the historical ata link: Passwor is wrcc4) for the month of Setember 200. refer to sreasheet: ressure an temerature ownloae for both stations a) Calculate an lot the lase rate an the otential temerature at these two sites as a function of time. use Poisson eqn to etermine otential tem (brought own to 000 mb): ' = R & c o T $ % 4

5 McAline, hmwk 5, ATMS 6 b) What fraction of time is there a temerature inversion? roughly 43% of the time (refer to sreasheet) inversion conitions occur almost every night from sunown to sunrise c) Are there times when the lase rate is greater than the aiabatic lase rate? yes, it is a common occurrence, lase rate rising >9.8 K/km almost every ay uring afternoon hours. ) Interret finings: First of all, taking a look at the otential temerature comarison lot a number of atterns are aarent. First of all, both lotlines reveal the iurnal attern of warming an cooling corresoning to erios of incoming an outgoing raiation. The DRI station has a smaller average range of minimum-maximum otential temerature srea comare to the UNR station. Both atasets are fly close in value uring warming an cooling erios. However, uring the eak temerature hours, the UNR temerature tens to eak above the temerature of the DRI station. During nighttime hours, the UNR otential temerature cools to a much greater egree than the DRI temerature. Thus, a strong inversion occurs almost nightly. This attern is inicative of the ecouling of valley from the hillto uring night. At night the cool ools into the valley bowl, forming a strong inversion 5

6 McAline, hmwk 5, ATMS 6 which revents mixing with the above it. Once the aily solar raiation begins, the valley quickly warms an begins mixing with the uer level, resulting in a mixe layer with a near constant otential temerature. This ecouling is not evient in ays 8-0, likely ue to the influence of a synotic isturbance. The lack of heating uring the ay (base on the low maximum otential tems.) suggests that clous, win, an ossibly reciitation occurre uring this erio. These conitions romote a well-mixe neutral atmoshere an as a result, the otential temeratures are equivalent at both stations. The Lase Rate lot reveals the strength of the inversion that occurs at night. Maximum inversion magnitues reach nearly -70 K/km: very strong inversions ue to the high loss of heat ue to the high an ry esert an the ooling of coole in the valley. The Lase Rate lot also reveals that the lase rate becomes suer-aiabatic nearly every ay uring maximum heating hours. As a result, we might exect that thermal lumes occur over the city nearly every ay uring this erio. We can assume that scattere cumulus clous occurre aroun the valley uring this erio, if sufficient moisture was resent. The UNR site is also locate within an urban area an the extra heating ue to lower albeo (comare to the hills) an mechanical activity coul be resulting in a localize suer-aiabatic region. 6

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