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Computing Buoyancy Differences Between Two Isobars.

Section 2 requires the ability to compute the volume that an APEX must pump in order to move between two isobars: pi and pf. The following expression applies,

 \begin{displaymath}
\delta v = v \left[ \frac{\rho_i}{\rho_f} - 1
- \left(\fr...
...t(\frac{1}{v}\frac{dv}{dT}\right)\left(T_f-T_i\right)
\right]
\end{displaymath} (12)

where ($\rho_i$, Ti) and ($\rho_f$, Tf) are the in situ density and temperature on isobars pi and pf, respectively. The profile below was collected by APEX 231 and is useful for evaluating (12) at the points located in Figure 1.

   $  APEX-Seabird (110598) ARGOS Message Parser & Calibration Applicator [SwiftWare]
   $  $Revision: 1.4 $  $Date: 1999/03/23 00:10:08 $
   $  Cmd Line: /www/japan-sea/bin/ApexSbe110598-parser if=231.001.msg of=231.001.edf fixes=231.001.msg-all h=/www/japan-sea/data/history.edf 
   $
   $ E    lat     lon       date   time  zbot  zmax sh co           stnid      n
   $ H  43.07  135.17 08/09/1999 17.762     *   807  *  *         231.001     48
   $  VoltCount=139  BatteryVoltage=14.8V
   $  VacuumCount=60 Vacuum=6.0"Hg
   $  BottomPistonPosition=37
   $  SurfacePistonPosition=189
   $  SurfacePressure=5 dbar
   $  SalinityCorrection=-0.0013 psu.
   $  ProfileTermination=0x4 (Pressure unchanged for 25 minutes)
   $  NFix=7   //     lon     lat Julian-sec       date   hour quality
   $  Fix(First): 135.166  43.073  934220743 08-09-1999 17.762       3
   $  Fix:        135.150  43.047  934232799 08-09-1999 21.111       2
   $  Fix:        135.150  43.053  934233239 08-09-1999 21.233       2
   $  Fix:        135.132  43.044  934239311 08-09-1999 22.920       2
   $  Fix:        135.130  43.034  934245250 08-10-1999  0.569       3
   $  Fix:        135.105  43.038  934256118 08-10-1999  3.588       1
   $  Fix(Last):  135.109  43.031  934261970 08-10-1999  5.214       2
   $ F %6.1f %6.3f %7.4f %6.3f %7.4f %14.4f %10.4f
   $ T    p       t        s   theta    sigma  s(uncorrected)   sigma-p
        0.0  19.157  33.1417  19.156  23.5631         33.1404   23.5835
        9.7  19.517  33.3801  19.515  23.6534         33.3788   23.6955
       19.5   6.839  33.9388   6.837  26.6052         33.9375   26.6946
       29.4   3.194  34.0423   3.192  27.1031         34.0410   27.2406
       39.6   2.343  34.0529   2.341  27.1858         34.0516   27.3719
       49.6   1.865  34.0657   1.862  27.2337         34.0644   27.4674
       59.1   1.640  34.0693   1.637  27.2533         34.0680   27.5322
       69.6   1.413  34.0699   1.410  27.2700         34.0686   27.5988
       79.5   1.369  34.0772   1.365  27.2790         34.0759   27.6546
       89.5   1.290  34.0762   1.286  27.2837         34.0749   27.7067
       99.0   1.228  34.0755   1.223  27.2873         34.0742   27.7554
      109.3   1.193  34.0782   1.188  27.2919         34.0769   27.8087
      119.3   1.164  34.0813   1.159  27.2963         34.0800   27.8605
      129.3   1.143  34.0853   1.137  27.3010         34.0840   27.9124
      139.1   1.134  34.0869   1.128  27.3029         34.0856   27.9606
      149.6   1.108  34.0872   1.101  27.3049         34.0859   28.0123
      159.3   1.081  34.0872   1.074  27.3067         34.0859   28.0600
      169.6   1.058  34.0868   1.050  27.3079         34.0855   28.1100
      179.4   1.025  34.0858   1.017  27.3093         34.0845   28.1578
      189.4   1.002  34.0860   0.994  27.3109         34.0847   28.2068
      199.3   0.974  34.0854   0.965  27.3123         34.0841   28.2550
      209.3   0.946  34.0847   0.937  27.3135         34.0834   28.3036
      219.5   0.916  34.0844   0.906  27.3152         34.0831   28.3537
      229.4   0.905  34.0836   0.895  27.3153         34.0823   28.4005
      239.2   0.879  34.0827   0.868  27.3162         34.0814   28.4479
      249.0   0.859  34.0819   0.848  27.3169         34.0806   28.4949
      259.4   0.830  34.0817   0.819  27.3186         34.0804   28.5459
      269.3   0.816  34.0817   0.804  27.3194         34.0804   28.5936
      279.6   0.803  34.0811   0.791  27.3198         34.0798   28.6426
      289.5   0.784  34.0810   0.771  27.3209         34.0797   28.6906
      299.6   0.757  34.0808   0.744  27.3224         34.0795   28.7400
      309.4   0.739  34.0802   0.725  27.3231         34.0789   28.7870
      319.4   0.724  34.0801   0.710  27.3239         34.0788   28.8351
      329.5   0.704  34.0797   0.690  27.3248         34.0784   28.8839
      339.3   0.694  34.0794   0.679  27.3252         34.0781   28.9305
      349.1   0.693  34.0795   0.678  27.3254         34.0782   28.9769
      359.2   0.672  34.0793   0.656  27.3265         34.0780   29.0258
      379.3   0.647  34.0779   0.630  27.3269         34.0766   29.1212
      399.5   0.629  34.0772   0.612  27.3275         34.0759   29.2172
      449.4   0.590  34.0768   0.570  27.3296         34.0755   29.4547
      499.5   0.567  34.0766   0.545  27.3309         34.0753   29.6919
      549.6   0.489  34.0736   0.465  27.3332         34.0723   29.9308
      599.3   0.451  34.0726   0.425  27.3347         34.0713   30.1663
      649.3   0.409  34.0713   0.380  27.3361         34.0700   30.4032
      699.5   0.368  34.0710   0.337  27.3383         34.0697   30.6415
      749.3   0.344  34.0702   0.311  27.3391         34.0689   30.8761
      799.2   0.317  34.0695   0.281  27.3402         34.0682   31.1113
      806.9   0.314  34.0693   0.278  27.3402         34.0680   31.1474



Dana Swift, swift@ocean.washington.edu