Пример #1
0
def findLCL0(wv, press0, temp0):
    """
    
    findLCL0(wv, press0, temp0)
   
    Finds the temperature and pressure at the lifting condensation
    level (LCL) of an air parcel (using a rootfinder).

    Parameters
    - - - - - -
    wv : float
         Mixing ratio (K).
    temp0 : float
           Temperature (K).
    press0: float
            pressure (Pa)

    Returns
    - - - - -
    plcl : float
        Pressure at the LCL (Pa).
    Tlcl : float
        Temperature at the LCL (K).
    
    Raises
    - - - -
    NameError
        If the air is saturated at a given wv, temp0 and press0 (i.e. Tdew(wv, press0) >= temp0)
        
    Tests
    - - - - -
    >>> Td = Tdfind(5., 9.e4)
    >>> Td > 280.
    True
    >>> findLCL0(5., 9.e4, 280.)
    Traceback (most recent call last):
        ...
    NameError: parcel is saturated at this pressure
    >>> p1, T1 =  findLCL0(0.001, 9.e4, 280.)
    >>> print T1, p1
    250.226034799 60692.0428535
    
    """
    
    
    Td = Tdfind(wv, press0)
    
    if (Td >= temp0):
        raise NameError('parcel is saturated at this pressure')
    
    theta0 = theta(temp0, press0, wv)
   
    #evalzero = lambda pguess: lclzero(pguess, wv, theta0)
    
    #will return plcl, Tlcl when Tchange returns approx. 0 
    #(i.e. when the parcel temperature = Td)
    plcl = fzero(Tchange, [1000*100, 200*100], (wv, theta0))
    Tlcl = invtheta(theta0, plcl, wv)
    
    return plcl, Tlcl
Пример #2
0
def findLCL0(wv, press0, temp0):
    """
    
    findLCL0(wv, press0, temp0)
   
    Finds the temperature and pressure at the lifting condensation
    level (LCL) of an air parcel (using a rootfinder).

    Parameters
    - - - - - -
    wv : float
         Mixing ratio (K).
    temp0 : float
           Temperature (K).
    press0: float
            pressure (Pa)

    Returns
    - - - - -
    plcl : float
        Pressure at the LCL (Pa).
    Tlcl : float
        Temperature at the LCL (K).
    
    Raises
    - - - -
    NameError
        If the air is saturated at a given wv, temp0 and press0 (i.e. Tdew(wv, press0) >= temp0)
        
    Tests
    - - - - -
    >>> Td = Tdfind(5., 9.e4)
    >>> Td > 280.
    True
    >>> findLCL0(5., 9.e4, 280.)
    Traceback (most recent call last):
        ...
    NameError: parcel is saturated at this pressure
    >>> p1, T1 =  findLCL0(0.001, 9.e4, 280.)
    >>> print T1, p1
    250.226034799 60692.0428535
    
    """

    Td = Tdfind(wv, press0)

    if (Td >= temp0):
        #raise NameError('parcel is saturated at this pressure')
        return press0, temp0

    theta0 = theta(temp0, press0, wv)

    #evalzero = lambda pguess: lclzero(pguess, wv, theta0)

    #will return plcl, Tlcl when Tchange returns approx. 0
    #(i.e. when the parcel temperature = Td)
    plcl = fzero(Tchange, [1000 * 100, 200 * 100], (wv, theta0))
    Tlcl = invtheta(theta0, plcl, wv)

    return plcl, Tlcl
Пример #3
0
def convecSkew(figNum):
      """       
      Usage:  convecSkew(figNum)
      Input:  figNum = integer
       Takes any integer, creates figure(figNum), and plots a
       skewT logp thermodiagram.
      Output: skew=30 and the handle for the plot
      """
      fig=plt.figure(figNum)
      fig.clf()
      ax1=fig.add_subplot(111)
      yplot = range(1000,190,-10)
      xplot = range(-300,-139)
      pvals = np.size(yplot)
      tvals = np.size(xplot)
      temp = np.zeros([pvals, tvals])
      theTheta = np.zeros([pvals, tvals])
      ws = np.zeros([pvals, tvals])
      theThetae = np.zeros([pvals, tvals])      
      skew = 30 #skewness factor (deg C)

      # lay down a reference grid that labels xplot,yplot points 
      # in the new (skewT-lnP) coordinate system .
      # Each value of the temp matrix holds the actual (data)
      # temperature label (in deg C)  of the xplot, yplot coordinate.
      # pairs. The transformation is given by W&H 3.56, p. 78.  Note
      # that there is a sign difference, because rather than
      # taking y= -log(P) like W&H, I take y= +log(P) and
      # then reverse the y axis         
      
      for i in yplot:
            for j in xplot:
                  # Note that we don't have to transform the y
                  # coordinate, as it is still pressure.
                  iInd = yplot.index(i)
                  jInd = xplot.index(j)
                  temp[iInd, jInd] = convertSkewToTemp(j, i, skew)
                  Tk = c.Tc + temp[iInd, jInd]
                  pressPa = i * 100.
                  theTheta[iInd, jInd] = theta(Tk, pressPa)
                  ws[iInd, jInd] = wsat(Tk, pressPa)
                  theThetae[iInd, jInd] = thetaes(Tk, pressPa)
                  
      #
      # Contour the temperature matrix.
      #

      # First, make sure that all plotted lines are solid.
      mpl.rcParams['contour.negative_linestyle'] = 'solid'
      tempLabels = range(-40, 50, 10)
      tempLevs = ax1.contour(xplot, yplot, temp, tempLabels, \
                            colors='k')
      
      #
      # Customize the plot
      #
      ax1.set_yscale('log')
      locs = np.array(range(100, 1100, 100))
      labels = locs
      ax1.set_yticks(locs)
      ax1.set_yticklabels(labels) # Conventionally labels semilog graph.
      ax1.set_ybound((200, 1000))
      plt.setp(ax1.get_xticklabels(), weight='bold')
      plt.setp(ax1.get_yticklabels(), weight='bold')
      ax1.yaxis.grid(True)

      
      thetaLabels = range(200, 390, 10)
      thetaLevs = ax1.contour(xplot, yplot, theTheta, thetaLabels, \
                        colors='b')


      wsLabels =[0.1,0.25,0.5,1,2,3] + range(4, 20, 2) + [20,24,28]

      wsLevs = ax1.contour(xplot, yplot, (ws * 1.e3), wsLabels, \
                        colors='g')

      thetaeLabels = np.arange(250, 410, 10)
      thetaeLevs = ax1.contour(xplot, yplot, theThetae, thetaeLabels, \
                        colors='r') 
      
      # Transform the temperature,dewpoint from data coords to
      # plotting coords.
      ax1.set_title('skew T - lnp chart')
      ax1.set_ylabel('pressure (hPa)')
      ax1.set_xlabel('temperature (deg C)')

      #
      # Crop image to a more usable size
      #    
      

      TempTickLabels = range(-15, 40, 5)

      TempTickCoords = TempTickLabels
      skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
      ax1.set_xticks(skewTickCoords)
      ax1.set_xticklabels(TempTickLabels)

      skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)

      ax1.axis([skewLimits[0], skewLimits[1], 300, 1.e3])
      
      #
      # Create line labels
      #
      fntsz = 9 # Handle for 'fontsize' of the line label.
      ovrlp = True # Handle for 'inline'. Any integer other than 0
                # creates a white space around the label.
                
      thetaeLevs.clabel(thetaeLabels, inline=ovrlp, fmt='%5d', fontsize=fntsz,use_clabeltext=True)
      tempLevs.clabel(inline=ovrlp, fmt='%2d', fontsize=fntsz,use_clabeltext=True)
      thetaLevs.clabel(inline=ovrlp, fmt='%5d', fontsize=fntsz,use_clabeltext=True)
      wsLevs.clabel(inline=ovrlp, fmt='%2d', fontsize=fntsz,use_clabeltext=True)
      #print thetaeLabels
      #
      # Flip the y axis
      #
      
      ax1.invert_yaxis()
      ax1.figure.canvas.draw()
      
      return skew, ax1
Пример #4
0
def convecSkew(figNum):
    """    
      Skew-T diagram for the level of free convection. 
      Take any integer, creates figure(figNum), and plots a
      skewT logp thermodiagram.
      """
    fig = plt.figure(figNum)
    fig.clf()
    ax1 = fig.add_subplot(111)
    yplot = range(1000, 190, -10)
    xplot = range(-300, -139)
    pvals = np.size(yplot)
    tvals = np.size(xplot)
    temp = np.zeros([pvals, tvals])
    theTheta = np.zeros([pvals, tvals])
    ws = np.zeros([pvals, tvals])
    theThetae = np.zeros([pvals, tvals])
    skew = 30  #skewness factor (deg C)
    """
      lay down a reference grid that labels xplot,yplot points 
      in the new (skewT-lnP) coordinate system .
      Each value of the temp matrix holds the actual (data)
      temperature label (in deg C)  of the xplot, yplot coordinate.
      pairs. The transformation is given by W&H 3.56, p. 78.  Note
      that there is a sign difference, because rather than
      taking y= -log(P) like W&H, I take y= +log(P) and
      then reverse the y axis         
      """

    for i in yplot:
        for j in xplot:
            # We don't have to transform the y
            # coordinate, as it is still pressure.
            iInd = yplot.index(i)
            jInd = xplot.index(j)
            temp[iInd, jInd] = convertSkewToTemp(j, i, skew)
            Tk = c.Tc + temp[iInd, jInd]
            pressPa = i * 100.
            theTheta[iInd, jInd] = theta(Tk, pressPa)
            ws[iInd, jInd] = wsat(Tk, pressPa)
            theThetae[iInd, jInd] = thetaes(Tk, pressPa)

    # Contour the temperature matrix.

    # First, make sure that all plotted lines are solid.
    mpl.rcParams["contour.negative_linestyle"] = "solid"
    tempLabels = range(-40, 50, 10)
    tempLevs = ax1.contour(xplot, yplot, temp, tempLabels, \
                          colors="k")

    # Customize the plot
    ax1.set_yscale("log")
    locs = np.array(range(100, 1100, 100))
    labels = locs
    ax1.set_yticks(locs)
    ax1.set_yticklabels(labels)  # Conventionally labels semilog graph.
    ax1.set_ybound((200, 1000))
    plt.setp(ax1.get_xticklabels(), weight="bold")
    plt.setp(ax1.get_yticklabels(), weight="bold")
    ax1.yaxis.grid(True)

    thetaLabels = range(200, 390, 10)
    thetaLevs = ax1.contour(xplot, yplot, theTheta, thetaLabels, \
                      colors="b")

    wsLabels = [0.1, 0.25, 0.5, 1, 2, 3] + range(4, 20, 2) + [20, 24, 28]

    wsLevs = ax1.contour(xplot, yplot, (ws * 1.e3), wsLabels, \
                      colors="g")

    thetaeLabels = np.arange(250, 410, 10)
    thetaeLevs = ax1.contour(xplot, yplot, theThetae, thetaeLabels, \
                      colors="r")

    # Transform the temperature,dewpoint from data coords to
    # plotting coords.
    ax1.set_title("skew T - lnp chart")
    ax1.set_ylabel("pressure (hPa)")
    ax1.set_xlabel("temperature (deg C)")

    #
    # Crop image to a more usable size
    #

    TempTickLabels = range(-15, 40, 5)

    TempTickCoords = TempTickLabels
    skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
    ax1.set_xticks(skewTickCoords)
    ax1.set_xticklabels(TempTickLabels)

    skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)

    ax1.axis([skewLimits[0], skewLimits[1], 300, 1.e3])

    #
    # Create line labels
    #
    fntsz = 9  # Handle for fontsize of the line label.
    ovrlp = True  # Handle for inline. Any integer other than 0
    # creates a white space around the label.

    thetaeLevs.clabel(thetaeLabels,
                      inline=ovrlp,
                      fmt="%5d",
                      fontsize=fntsz,
                      use_clabeltext=True)
    tempLevs.clabel(inline=ovrlp,
                    fmt="%2d",
                    fontsize=fntsz,
                    use_clabeltext=True)
    thetaLevs.clabel(inline=ovrlp,
                     fmt="%5d",
                     fontsize=fntsz,
                     use_clabeltext=True)
    wsLevs.clabel(inline=ovrlp, fmt="%2d", fontsize=fntsz, use_clabeltext=True)
    #print thetaeLabels
    #
    # Flip the y axis
    #

    ax1.invert_yaxis()
    ax1.figure.canvas.draw()

    return skew, ax1
Пример #5
0
"""
Carnot heat engine:

0. Isothermal expansion from A to B 
1. Dry adiabatic expansion from B to C
2. Isothermal compression from C to D (heat flow, Qout,  out of the system)
3. Dry adiabatic compression from D to C

note that Qin > Qout so that work done by the system in the carnot cycle = Qin - Qout > 0
"""

pressA = 1.e5
tempA = 15 + c.Tc
pressC = 0.7e5
tempC = 5 + c.Tc
thetaA = theta(tempA, pressA)
thetaC = theta(tempC, pressC)
thetaB = thetaC
tempB = tempA
term1 = (thetaB / tempB)**(c.cpd / c.Rd)
term1 = 1. / term1
pressB = term1 * 1.e5
tempD = tempC
thetaD = thetaA
term1 = (thetaD / tempD)**(c.cpd / c.Rd)
term1 = 1. / term1
pressD = term1 * 1.e5
plt.figure(1)
skew, ax1 = convecSkew(1)

xtempA = convertTempToSkew(tempA - c.Tc, pressA * 0.01, skew)
Пример #6
0

c=constants()

#Carnot heat engine:
#
#dry adiabatic expansion from B to C 
#isothermal compression from C to D (heat flow, Qout,  out of the system)
#dry adiabatic compression from D to C
#note that Qin > Qout so that work done by the system in the carnot cycle = Qin - Qout > 0

pressA=1.e5
tempA=15 + c.Tc
pressC=0.7e5
tempC=5 + c.Tc;
thetaA=theta(tempA,pressA)
thetaC=theta(tempC,pressC)
thetaB=thetaC
tempB=tempA
term1=(thetaB/tempB)**(c.cpd/c.Rd)
term1=1./term1
pressB=term1*1.e5
tempD=tempC
thetaD=thetaA
term1=(thetaD/tempD)**(c.cpd/c.Rd)
term1=1./term1
pressD=term1*1.e5
plt.figure(1)
skew, ax1 =convecSkew(1)

xtempA=convertTempToSkew(tempA - c.Tc,pressA*0.01,skew)