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AN INDEX FOR MEASURING TIlE BREAKDOWN OF SURFACE-BASEDINVERSIONS IN TIlE INTERMOUNTAIN WESf

Leslie R. ColinNational Weather Service

Boise, ID, USA

1. INTRODUCTION

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Winter weather in the Intermountain West isoften characterized by long periods of surface­based inversion conditions causing fog, stratus,haze, and smoke in the valleys. Theseinversions most often form when radiationalcooling occurs during extended periods of highpressure aloft. The breakdown of an inversionis often a sudden event, resulting in rapidwarming and improvements in ceiling, visibility,and air quality. Forecasting inversion breakdownis therefore important, but difficult underoperational conditions. Time constraIntspreclude elaborate investigations of boundarylayer stability, winds, and mixing potential.What is needed is a. simple index for gauginginversion strength, and thresholds of that indexcorresponding to inversion breakdown. Thepurpose of this paper is to develop such anindex, while trying to keep it as simple and easyto use as possible.

The U.S. National Weather Service (NWS)National Meteorological Center (NMC) routinelypublishes model forecast output values in tabularform (NWS, 1985) as shown in Fi~re 1.

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. Fe::tJ.D'2 k&.a:: C!S12eeQJrPUT FRO"I H::I1 JZZ tI£C 2'Ii 94lTPTTAIR'2R3 WVll P'SDDF"J.' HHlTlTS TTPTTRIR2R3 VV'lA..I P5DDF"F" Won1T3TSSE/V/948661 lI»e7 _130 __ CEc/_lSl B731J5 172818 _10_e601~ -1"f804 85J2Z26 047e&e3elt tl683:J9otWSl e8687 1521~ 04S8Jae96126259SW8" &4'J1i!e e~~ 1~ esJel5 1J2Z2e~18017'Sl6'9581 el3B3 V'2R04~ lsel~ IS4&4 lRll2'22'S <48B583982"169995S1 BI2V3 872617 _0060l!!l5 2<lBZJSJ7978J 81002 102321 ..-e=3e0eS9683i!1 -e79J ~ll 3'J0oIf(lI8'g2 ~.e 1'5300 lV'2'21S ""'0S629'7~7906 -e9ai! 142815 ~790 36016899'2'3781683 52918 35JI&'I~

~3613 -eGW 2eJ0t .. c7ee9?'92 ~sees 8t1es 152816 i!'9Oe9?ge4llleoee783635 -1616 ~t1 ~l "'S0OC9'C.JSl" el3e'9 2J281 .. Z"719589PmV/ge986'J .311ie9 1~1C'8 51eBeJee tFR.......7683·t9 fJlGI12 ~32'e16 S2'&4e300e&e2295SJ761 e0685 1"'2226 seMQJee ~$ e8S1e Z22'el1 S2'e56Cee

.J202~ e5803 11222'9 S0leo4100 J2ee19-478AG fJi0geS 1921~1 S2e102'991~"969J87 810462 102.32'5· 04'iIOOo4W 11J008!iII686Y9 ~J 17a19 SIeG&4992402629868 fI59i30 esri!'61g 0449B03'99 24811969978 f6J01 1042'824 04907'8398~ ee;"N .I1:::Je12 J6OS0<n1 3':'e~9105 essoe IJC!TI6 43Cl6OO95:w;ee~ ~l 16291" cge"S1890 36elC944)1)~ 17381$ ~9989~39S4&16 -eeee 223ele 290191'92 "~3?5 -1589 2'23"18 >40196'91"aeee91:s:JSJ ~lS ~nee7 1C"eP279:J <4SCCJe9"i1D11 ""'".4 i!GOCe9 310e9~

IlOI ..../S8?l6'5 -1509 2'51609~ Pll-4.·/S8S1J9 ~7 2-te3e8 4S009B92eEi0007<4B66J -17'85 CSC213 <47809')95 ~12 eeJMI 2281e ",70895J90412'00074816:&1 e21e6 192"'IS 5.,......('1097 I~TC76 el80B 2Z2JIC S002999SIB007'939172 81504 21231&~ Jaooe1J'!;11073 ~1e6 222313 Sl02'999S2040eeB8B<48e -oc'02 19i!317 ~19-4 ~l'e804 el0e6 19iC'51" 201ee9S:J0eI8Iie8"8967 elgel 1211&~ ~ et'7eS ~16 <t901ee92X003949739 tk.~ 102121~ ~1 else) 132117 Sl""'0e9J<42012?Sl'916 eJlee lZ31JS~1 ~ eJI8e IJ2Z21~"B0e381S216 ~..e6 223317 3198'118'7 4BeC9977-4C5 IIr2'8el IC'.29H "~J

Figure 1. NMC tabulated model forecast output.

These bulletins are issued twice daily to allNWS field forecast offices, for the OOZ and 12Zforecast cycles, for both the Eta and the NGMmodels. Among the categories are 1000 to 500mb thickness (dam) in the HH column, andmean sea level pressure (mb) in the PS column.This paper will show how to use only these twoquantities to derive meaningful informationabout the strength and breakdown of surface­based inversions.

2. METIIOD

Figure 2 shows a typical example of asurface inversion. It differs from a lapsesounding by having relatively large 1000 to 500mb thickness (HH) indicating warm air aloft,and also relatively large mean sea level pressure(PS) indicating cold air at the surface. Thiscombination immediately suggests using the sumHH+PS as a measure of inversion strength. Thelarger the sum, the more likely the soundingshould look like Figure 2.

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Figure 2. Pseudoadiabatic sounding illustratinga strong surface-based radiational inversion.

• 5'" AES/CMOS WorkshoE on OflCrational Meteorology.w.

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Figure 3.

Figure 3 shows that this is indeed the caseduring winter at the representative stationsSpokane, WA (GEG), and Boise, ill (BOI).The abscissa in Figure 3 does not represent truesurface-based conditions, but rather analyzedtemperature difference from the lowest 35 mblayer (f1 in Figure 1) to near the 900 robsurface (T3) (NWS, 1981). The strength of aninversion, as measured by how much colder T1is than T3 (at OOZ times only, Le., afternoon),is shown to be correlated with large values ofHH+PS. A major advantage in using HH andPS (unlike T1 and T3), is that both are alsoroutinely available in graphical form and inhistorical records. When HH + PS is less thanabout 60, T1 is warm enough compared to T3 topromote mixing, so that the value 60 may be

.taken as the threshold corresponding tobreakdown of the inversion.

Therefore to use this method, one merelyneeds to scan the HH and PS columns, notingwhen their sum drops below 60 (inversionsgenerally occur with sums well above 60), andforecasting inversion breakdown at that time.

...-------------_._--lUI and l'S vs Surface IllVl'rsioll

(HOI and GI'X;) (:m7 willIe)' cases)

0", -r-,-t-, ''','-rl'' "., ,_.I _<4 -.\ ') I 0 1 7·' ~ I

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Figure 4.

75

Figure 4 shows values of HH and PSseparately as they contribute to the sum. Notethat HH and PS both increase as inversionstrength (T1-T3) increases.

Figure 5 illustrates average low levelmoisture during surface inversions. Rlrepresents model analyzed relative humidity inthe lowest 35 mb, while R2 represents meanhumidity in the layer above it up to 500 mb.Note that R1 is usually larger than R2 duringsurface inversions, and that RI-R2 tends toincrease as the inversions strengthen. But sincethe HH+ PS trace is similar to the R1-R2 trace,it is not necessary to us~' the latter. .

I1H+PS awl WI dif v::; Surfac(' IIlV('l"sioll

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Figure 5.

Figure 6 contains information about truesurface conditions, since observed maximumtemperatures are included in the ordinate. Hereit can be seen that observed maxima are aboutthe same as Tl during inversions, but when Tlbecomes about 4 degs C warmer than T3,observed maxima also become much warmerthan Tl, indicating complete mixirtg~.-----_._._-------_..--------

Observed Max l.el1lp-T1 Vl-i 1'1-'1'3

(HOI <lIlt! GE(;) (:m7 winl.e!" enl-i(~)

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II 1.I1...,.q

Figure 6.

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Figure 7 shows how average boundary layerwind speed varies with inversion strength. Ingeneral inversion strength is insensitive toboundary layer wind speed, although there is aslight tendency for lighter winds to occur withstronger inversions.

Doundary Layer Wind V~ src IIIVCl~iol1

(DOl awl (;1';(;) (:m7 wil1lC'I- cases)

--'------- -------------------,1I11+1.2:1J(i['S \'$ Surfacc' Illve'rsiol1

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411" 1 r"1 "r "roT· r"·"··r I"-Y-,.·,., \ I I , !.l 1

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Figure 8.

2.1 Modifications in the Method

Figure 7.

o .., ~-, -1 -r- "~I- I'· ,- , . I I

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(1101. GE{;. ·l/:J/!J:~-l/I\/!H)

~~-lj~" -------------

Since HH is large in summer, large valuesof HH+PS can also occur in summer. Figure 9shows that HH +PS has maxima in both summer(when T1-T3 is large) and in winter. Duringsummer, afternoon surface-based inversionsnever occur, i.e., there is always a lapsecondition. Therefore, increases in HH must be ,felt all the way to the surface, resulting in a'­positive correlation between HH and surfacetemperature.

It is assumed that changes in PSaffecttemperatures only near the surface, whilechanges in HH affect temperatures uniformlythroughout the entire 1000 mb to 500 mb layer.This assumption is justified indirectly as follows:

f)' ,--,-,•• , • I-I"-T"'--' 9 r- 1 . 1 I 1-

., • .l 1 I .1 " 1-4 7 (I ;' .. Ii Il

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Figure 9.

(1)T = gx HHR In ( PS )

500

In an index as simple as HH+PS, one mustbe aware of several assumptions and simplif­ications. For one thing, HH and PS havedifferent units. From the hypsometric equation,e.g., Holton (1979),

where T is mean virtual temperature from sealevel to 500 mb, g is gravity, R the gasconstant, HH thickness from sea level to 500 mb(Le., 500 mb height), and PS sea level pressure,it is seen that a change in HH of 1 damcorresponds to a change of about 1.2416 rob inPS when typical values of 560 dam are used forHH, and 1000 mb for PS. After normalizing,the index becomes HH+1.2416PS. Figure 8shows the modified relationship to T1-TIinversion strength. Note that little additionalbenefit is gained using the modified index.•

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4. REFERENCES

Holton, J.R., 1979. An Introduction toDynamic Meteorology. Academic Press, NewYork. 391 p.

I· ,.-=-~~ 5th AES/CMOS Workshop on Operational Meteorology::e;;:fti

But note from Figure 9 that it is thedifferenceHH-PS which correlates very stronglywith T1-TI lapse rate during summer. For thisto happen, PS must be playing only a minorrole.

77

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In winter, on the other hand, changes in HHoften do not affect conditions near the surface.In other words, surface temperature seems to becontrolled by PS in the winter and by HH in thesummer. This explains why it is possible forHH +PS to have maxima in both summer andwinter.

We now have the results that the sumHH + PS correlates well with TI-T3 duringwinter, while the difference HH-PS correlateswell with Tl-TI during summer.

The two results can be combined bymultiplying PS by a parameter which rangesfrom -1 in summer to + 1 in winter, and thenadding to HH.

3. SUMMARY

The simple combination of HH+PS, takenfrom routine NMC-published numerical forecastoutput, provides a means of evaluating thestrength of surface inversions in theintermountain region of the western U.S., inwhich inversion strength itself is measured bythe magnitude of T1-TI. Surface inversionsusually occur when HH+PS is larger than 60,but tend to break when HH+PS falls below 60.Large values ofHH+PS during summer are dueto large values of HH alone, and are notassociated with surface inversions. Normalizingunits of HH and PS provides 'little if anyadditional benefit over using HH+PS directly.

National Weather Service, 1985. FOUSMessages from the RAFS. NWS Tech.Procedures Bull. No. 351, National Oceanic andAtmospheric Administration, U. S. Departmentof Commerce, 7 p.

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2 .

SURFACE BASED INVERSION INDEX (HH + PS)

On the FOUS tables FRH72 or FRTH72, find the sum HH + PS.

Refer to Figure 1. High numbers of HH + PS (greater thanabout 68) correspond to surface-based inversions, indicatinga combination of cold air at the surface (high PS) and warmair above (high HH) .

The left half of Figure 1 indicate surface-based inversions(when Tl is colder than T3), Tl being temperature 35 mbabove the model surface, and T3 the temperature near 900 mb.

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3. Figure 2 shows how HH and PS contribute to the sum HH + PS.During winter inversions, PS dominates. During summer, HHdominates .