;======================================================================== ; SKEWT.PRO (IDL CODE) ; ; Draw a Skew-T, Log(P) diagram given a temperature range for your data. ; ; Originator: Andrew F. Loughe (afl@cdc.noaa.gov) ; CIRES/NOAA ; Boulder, CO USA ; This code carries no warranty or claim ; as to its usefulness or accuracy! ; ; A Number of the functions found in this file were converted from ; FORTRAN code that was received from NCAR in Boulder, CO USA. ; The original source of the equations is thought to be: ; "Algorithms for Generating a Skew-T, Log P Diagram ; and Computing Selected Meteorological Quantities" ; by G.S. Stipanuk, White Sands Missle Range, Report ECOM-5515. ; ;======================================================================== ; FUNCTION TO COMPUTE SATURATION VAPOR PRESSURE GIVEN TEMP IN KELVIN. ; ESAT(MILLIBARS), T(KELVIN) FUNCTION ESAT, T TC = T - 273.16 ESAT = 6.1078 * EXP( (17.2693882 * TC) / (TC + 237.3) ) RETURN, ESAT END ;======================================================================== ; FUNCTION TO COMPUTE MIXING RATIO GIVEN TEMP. AND PRESS. ; W(GRAMS WATER VAPOR/KILOGRAM DRY AIR), P(MILLIBAR) FUNCTION W, T, P IF (T GE 999.) THEN GOTO, JUMP10 X = ESAT(T) W = 621.97 * X / (P - X) RETURN, W JUMP10: W = 0.0 RETURN, W END ;======================================================================== ; FUNCTION TO COMPUTE SATURATION ADIABATIC TEMP AT 1000 MB GIVEN T & P. ; OS AND T (KELVIN), P (MILLIBARS ) FUNCTION OS, T, P IF (T LT 100.) THEN T1 = T + 273.16 IF (T GE 100.) THEN T1 = T OS = T1 * ((1000./P)^.286) / (EXP( -2.6518986*W(T1,P) / T1) ) RETURN, OS END ;======================================================================== ; FUNCTION TO COMPUTE THE TEMPERATURE (KELVIN) OF AIR AT A GIVEN ; PRESSURE AND WITH A GIVEN MIXING RATIO. ; TMR(KELVIN), W(GRAMS WATER VAPOR/KILOGRAM DRY AIR), P(MILLIBAR) FUNCTION TMR, W, P X = ALOG10 ( W * P / (622.+ W) ) TMR = 10. ^ ( .0498646455 * X + 2.4082965 ) - 7.07475 + \$ 38.9114 * ( (10.^( .0915 * X ) - 1.2035 )^2 ) RETURN, TMR END ;======================================================================== ; FUNCTION TO COMPUTE TEMPERATUE (KELVIN) OF A MOIST ADIABAT GIVEN ; OS(KELVIN), P(MILLIBARS) ; SIGN(A,B) REPLACES THE ALGEBRAIC SIGN OF A WITH THE SIGN OF B FUNCTION TSA, OS, P A = OS TQ = 253.16 D = 120 FOR I = 1, 12 DO BEGIN D = D/2. ; IF THE TEMPERATURE DIFFERENCE, X, IS SMALL, EXIT THIS LOOP. X = A * EXP (-2.6518986*W(TQ,P)/TQ)-TQ*((1000./P)^.286) IF ( ABS(X) LT 0.01 ) THEN GOTO, JUMP2 ; TQ = TQ + SIGN(D,X) IF (X LT 0) THEN D = -ABS(D) IF (X GT 0) THEN D = ABS(D) TQ = TQ + D ENDFOR JUMP2: TSA=TQ RETURN, TSA END ;======================================================================== ; Function to determine position (temp, press) when the isotherms ; in the diagram are rotated (skewed) 45 degrees to the right. ; Used for finding the points needed to connect the dots when ; drawing ALL of the lines (except pressure). ; Originator: Andrew F. Loughe Function Tnew, T, P COMMON RANGES, trange, prange P0 = prange(0) xy1 = convert_coord( [T, P0], /data, /to_device) xy2 = convert_coord( [T, P], /data, /to_device) dy = xy2(1) - xy1(1) dx = dy ; dx = dy for this 45-45-90 triangle xy = convert_coord( [xy2(0)+dx, xy2(1)], /device, /to_data) Tnew = xy(0) return, Tnew end ;======================================================================== ; Function to determine position (temp, press) in the unskewed ; coordinate system (Opposite of Tnew). ; Used only when placing the labels on various lines. ; Originator: Andrew F. Loughe Function Told, T, METHOD COMMON RANGES, trange, prange P0 = prange(0) P1 = prange(1) T0 = trange(0) T1 = trange(1) if (method eq 1) then begin xy1 = convert_coord( [T, P0], /data, /to_device ) xy2 = convert_coord( [T0, P0], /data, /to_device ) dx = xy2(0) - xy1(0) xy = convert_coord( [xy2(0), xy2(1)+dx], /device, /to_data ) xy1 = convert_coord( [xy(0), xy(1)], /data, /to_device ) xy2 = convert_coord( [xy(0), P1], /data, /to_device ) dy = xy2(1) - xy1(1) xy = convert_coord([xy1(0)+(dy/2.), xy1(1)+(dy/2.)],\$ /device, /to_data) endif if (method eq 2) then begin xy1 = convert_coord( [T, P0], /data, /to_device ) xy2 = convert_coord( [T1, P0], /data, /to_device ) dx = xy2(0) - xy1(0) xy = convert_coord( [xy1(0)+dx/2. , xy1(1)+dx/2.], \$ /device, /to_data) endif return, xy end ;======================================================================== ; Function to determine the necessary trange for plotting the sounding. Function T_RANGE, p_range, t, td, p COMMON RANGES, trange, prange trange = [-40, 40] ; Default which can be changed if (p_range eq 0) then \$ prange = [1050, 100] ; Default which can be changed ; Find number of data levels szd = size(t) nlevels = szd(1) ; Ensure that temperatures are in Celsius. if ( (total(t)/nlevels) gt 100. ) then t = t - 273.16 if ( (total(td)/nlevels) gt 100. ) then td = td - 273.16 ; Set up dummy plot space. if (!d.name eq 'PS') then device, /inch, xsize=7, ysize=7 daspect = FLOAT(!D.Y_SIZE)/FLOAT(!D.X_SIZE) * \$ (trange(1)-trange(0))/80. margin = 0.1 aspect = 1.0 ; A square x0 = 0.50 - (0.5 - margin)*(daspect/aspect) y0 = margin x1 = 0.50 + (0.5 - margin)*(daspect/aspect) y1 = 1.0 - margin !P.position=[x0,y0,x1,y1] plot_io, trange, prange, yrange=prange, /nodata, /xs, /ys, \$ color=!p.background, /noerase !p.multi(0) = !p.multi(0) + 1 ; Determine necessary temperature range for the diagram. xx0 = fltarr(nlevels) & yy0=xx0 & xx1=xx0 & yy1=yy0 for i = 0, nlevels-1 do begin xx0(i) = tnew( t(i), p(i) ) yy0(i) = p(i) xx1(i) = tnew( td(i), p(i) ) yy1(i) = p(i) endfor xbegin = fix( (min(xx1)-10.) / 10. ) * 10. xend = fix( (max(xx0)+10.) / 10. ) * 10. return, [xbegin, xend] end ;======================================================================== ; ; PROCEDURE TO DRAW A SKEW-T, Log(P) DIAGRAM GIVEN A DESIRED ; TEMPERATURE RANGE FOR THE DATA. ; ; Originator: Andrew F. Loughe ; PRO SKEWT, t_range, everyT=everyT, everyDA=everyDA, \$ everySA=everySA, everyW=everyW, title=title, notitle=notitle on_error, 2 COMMON RANGES, trange, prange if (n_elements(everyT) le 0) then everyT = 10 ; T = Temperature if (n_elements(everyDA) le 0) then everyDA = 10 ; DA = Dry adiabat if (n_elements(everySA) le 0) then everySA = 1 ; SA = Saturated adiabat if (n_elements(everyW) le 0) then everyW = 1 ; W = Mixing ratio if (not keyword_set(title)) then title='Skew-T, Log(P) Diagram' if (keyword_set(notitle)) then title=' ' if (n_elements(prange)) eq 0 then prange = [1050., 100] if (N_params() eq 0) then \$ message,\$ 'EXAMPLE: skewt, [-20, 20], everyT=10, everyDA=10, everySA=2, everyW=2' if (n_elements(t_range)) eq 1 then t_range=[-40., 40.] ; Set some defaults trange = t_range charsize = .8 ; Set default character size !p.multi = [0,1,1] !P.background=7 ; Set default color positions colors, black, magenta, cyan, yellow, green, red, blue, white, navy, \$ gold, pink, aquamarine, orchid, gray, sky, beige ; Make plot square for arbitrarily chosen trange of 80 degrees. ; Code from Ken Bowman if (!d.name eq 'PS') then device, /inch, xsize=7, ysize=7 daspect = FLOAT(!D.Y_SIZE)/FLOAT(!D.X_SIZE) * (trange(1)-trange(0))/80. margin = 0.1 aspect = 1.0 ; A square x0 = 0.50 - (0.5 - margin)*(daspect/aspect) y0 = margin x1 = 0.50 + (0.75 - margin)*(daspect/aspect) y1 = 1.0 - margin !P.POSITION = [x0, y0, x1, y1] ; Set value of sytem variable. ; Determine character height and width. Apply charsize. char_ht = convert_coord([0, !d.y_ch_size], /device, /to_norm) char_ht = char_ht(1) * 1.0 if (!d.name ne 'X' and charsize gt 1.) then \$ char_ht = char_ht * charsize char_wd = convert_coord([0, !d.x_ch_size], /device, /to_norm) char_wd = char_wd(1) ; Create the plot space. plot_io, trange, prange, yrange=prange, /nodata, /xs, /ys, \$ xticklen=.01, ytickname=replicate(' ',30), charsize=charsize, \$ title=title,color=0 ; Print PRESSURE title along the y-axis. lnt=alog(prange(1)) & lnb=alog(prange(0)) & avg=exp(.5*(lnt+lnb)) xy = convert_coord([trange(0), avg],/data,/to_norm) xyouts, xy(0)-(5.*char_wd), xy(1), 'PRESSURE (hPa)', orient=90, \$ /norm, align=.5,color=0 ; Print TEMPERATURE title along the x-axis. xy = convert_coord([.5*(trange(0)+trange(1)), prange(0)], /data, /to_norm) xyouts, xy(0), xy(1)-(3.*char_ht), 'TEMPERATURE (!uo!nC)', align=.5, /norm,color=0 ; Draw Pressure labels next to tick marks along the y-axis. pressures = [1050,1000,900,800,700,600,500,400,300,200,100] for i = 0, 10 do begin ytick = pressures(i) if (ytick ge prange(1)) then begin xy = convert_coord( [trange(0), ytick], /data, /to_norm ) xyouts, xy(0)-(.2*char_wd), xy(1)-(.25*char_ht), \$ strcompress(string(ytick),/remove_all), align=1, \$ charsize=charsize, /norm,color=0 plots, [trange(0), trange(1)], [ytick, ytick], color=0 ; Horizontal line. endif endfor clip=[trange(0),prange(0),trange(1),prange(1)] ; Define clipping space. ;======================================================================== ; Draw skewed isotherms every "everyT (10C)" (Lines are straight). for temp = trange(0)-100, trange(1)+5, everyT do begin x0 = temp y0 = prange(0) x1 = temp y1 = prange(1) ; Draw the line. newx0 = tnew(x0, y0) ; Find rotated temperature position newx1 = tnew(x1, y1) ; Find rotated temperature position plots, [newx0, newx1], [y0, y1], color=BLUE, clip=clip, noclip=0 ; Draw line labels ; Use method #1 in xy function to determine a place for the label. drew_label = 'no' xy = Told(temp, 1) if ( xy(0) gt trange(0) and xy(0) lt trange(1) and \$ xy(1) gt prange(1) and xy(1) lt prange(0) ) then begin drew_label = 'yes' xyouts, xy(0), xy(1), strcompress(string(fix(temp)), /rem),\$ color=BLUE, orient=45, align=.5, charsize=charsize endif ; Use method #2 in xy function to determine a place for the label. if (drew_label eq 'no') then xy = Told(temp, 2) if ( xy(0) gt trange(0) and xy(0) lt trange(1) and \$ xy(1) gt prange(1) and xy(1) lt prange(0) and \$ drew_label eq 'no') then begin xyouts, xy(0), xy(1), strcompress(string(fix(temp)), /rem),\$ color=BLUE, orient=45, align=.5, charsize=charsize endif endfor ;======================================================================== ; Draw dry adiabats every "everyDA (10C)" (Lines are curved). for temp = trange(0), trange(0)+220, everyDA do begin x1 = float(temp) y1 = 1050. inc = -2. ; Lines will be curved, so use a small press. increment. drew_label='no' icount = 0 ; Dry adiabats from 1050mb up to prange(1). ; For a given temperature and pressure, compute theta and plot a line. for press = y1, prange(1), inc do begin icount = icount + 1 x0 = float(x1) ; Orig Temp y0 = float(press + inc) ; Orig Press y1 = float(y0 + inc) ; New Press x1 = (temp+273.16) * ( y1 / 1000. ) ^ (287./1004.) ; New Temp x1 = x1 - 273.16 newx0 = tnew(x0, y0) ; Find rotated temperature position newx1 = tnew(x1, y1) ; Find rotated temperature position ; Draw the labels. if (fix(x1) eq fix(trange(0)) and drew_label eq 'no') then begin drew_label='yes' if ( newx1 gt trange(0) and newx1 lt trange(1) and \$ y1 gt prange(1) and y1 lt prange(0) ) then \$ xyouts,newx1,y1,strcompress(string(fix(temp)),/remove),\$ align=.5, color=RED, charsize=charsize, orientation=-45 endif ; Draw the line. if (icount gt 1) then \$ plots, [newx0, newx1], [y0, y1], color=RED, clip=clip, noclip=0 if (newx1 lt trange(0)) then goto, jump2 endfor jump2: dummy=0 endfor ;======================================================================== ; Draw saturated adiabats. Begin at 40C and step backwards by 4C. ; These lines are curved. TS = 40. FOR TS = 40, -64, -everySA*4 DO BEGIN P = 1060. TK = TS + 273.16 AOS = OS(TK, 1000.) ATSA = TSA(AOS, P) - 273.16 FOR J = 0, 85 DO BEGIN P0 = P T0 = ATSA P = P - 10. ATSA = TSA(AOS, P) - 273.16 if (j gt 0) then begin newx0=tnew(T0,P0) ; Find rotated temperature position newx1=tnew(ATSA,P) ; Find rotated temperature position ; Leave a space for the labels and draw them. if (P gt 730 or P lt 700) then \$ plots, [newx0, newx1], [P0, P], \$ color=GREEN, clip=clip, noclip=0 if ( P eq 730 ) then begin if (newx1 gt trange(0) and newx1 lt trange(1)) then \$ xyouts,newx1,P,strcompress(string(fix(TS)),/remove),align=.5,\$ color=GREEN, charsize=charsize endif endif ENDFOR ENDFOR ;======================================================================== ; Draw mixing ratio lines (Lines are straight). ; Find temperature for a given Ws (g/kg) and Press (mb). Ws=[ .1,.2,.4,.6,.8,1.,1.5,2.,2.5,4,5,6,7,8,9,10,12, \$ 14,16,18,20,24,28,32,36,40,44,48,52,56,60,68,76,84 ] for i = 0, N_elements(Ws)-1, everyW do begin press1 = prange(0) tmr1 = tmr(Ws(i), press1) - 273.16 press2 = 200. tmr2 = tmr(Ws(i), press2) - 273.16 newx0=tnew(tmr1,press1) ; Find rotated temperature position newx1=tnew(tmr2,press2) ; Find rotated temperature position ; Draw the line. plots, [newx0, newx1], [press1, press2], color=14, linestyle=2, \$ clip=clip, noclip=0 ; Draw the line label. drew_label='no' if (newx0 gt trange(0) and newx0 lt trange(1)) then begin drew_label='yes' if (Ws(i) ge 1.0) then \$ xyouts, newx0, press1-50, strcompress(string(fix(Ws(i))),/remove),\$ align=.5,color=14, charsize=.6 if (Ws(i) lt 1.0) then \$ xyouts, newx0, press1-50, string(Ws(i),format='(f3.1)'), align=.5,\$ color=14, charsize=.6 endif if (newx1 gt trange(0) and newx1 lt trange(1)) then begin if (Ws(i) ge 1.0) then \$ xyouts, newx1, press2-2, strcompress(string(fix(Ws(i))),/remove),\$ align=.5, color=14, charsize=.6 if (Ws(i) lt 1.0) then \$ xyouts, newx1, press2-2, string(Ws(i),format='(f3.1)'), align=.5,\$ color=14, charsize=.6 endif endfor ;======================================================================== ; Redraw the plot boundary. plots, [trange(0),trange(1),trange(1),trange(0),trange(0)], \$ [prange(0),prange(0),prange(1),prange(1),prange(0)], thick=2, color=0 !p.position = [.05, .05, .95, .95] ; Reset position parameter END ;======================================================================== ; Routine to plot the temperature and dew point temperature sounding ; on top of a skew-T, Log(P) diagram. pro plot_skewt, t, td, p COMMON RANGES, trange, prange ; Find number of data levels szd = size(t) nlevels = szd(1) ; Define clipping space. clip=[trange(0),prange(0),trange(1),prange(1)] ; Ensure that temperatures are in Celsius. if ( (total(t)/nlevels) gt 100. ) then t = t - 273.16 if ( (total(td)/nlevels) gt 100. ) then td = td - 273.16 ; Overplot the data onto the digram. for i = 0, nlevels-2 do begin ; Plot temperature sounding data. x0 = tnew( t(i), p(i) ) y0 = p(i) x1 = tnew( t(i+1), p(i+1) ) y1 = p(i+1) plots, [x0, x1], [y0, y1], clip=clip, noclip=0, thick=2 ; Plot dew point temperature sounding data. x0 = tnew( td(i), p(i) ) y0 = p(i) x1 = tnew( td(i+1), p(i+1) ) y1 = p(i+1) plots, [x0, x1], [y0, y1], clip=clip, noclip=0, thick=2 endfor ; Close Postscript device, rename output file. if ( !d.name eq 'PS') then begin device, /close spawn, 'mv idl.ps skewt.ps' set_plot, 'X' endif end