Lag correction for the NIXIC conductivity cell.

Slow faster flushing conductivity sensor down to match disfusion of heat in/out of temperature probe.

Conductivity delayed using single pole recursive filter:

         C(t)= a . C(t-Dt) + b.Co(t);

  where C(t) = filtered cond. 

        Co(t) = measured conductivity

        Dt = sample interval

        Tau = temperature sensor time constant

        a = weight related to temperature sensor time constant tau = lag;

        b = (1-a)


    if Tau >>  Dt  we can estimate a using;

         a = e^-(Dt/Tau)   (Bendat & Piersol, 1971)


     as for slow sampling rate instruments: (i.e. as Tau approaches or exceeds  Dt a better estimate is provided by;

         C(t)= a . C(t-Dt) + b.(Co(t)+Co(t-Dt));
   

         a = (1 - 2b)

         b = 1/[1 + 2 (Tau/Dt)]   (Mudge & Lueck, 1994)


    The temperature lag Tau has 2 lowering rate = W cm/s induced components

  1:  The temperature sensor is mounted (Dz=4 cm from the center) at the exhaust of the NIXIC cell.

       This introduces a lowering rate dependent lag Tau:

         Tau(Dz) =  Dz/W

          examples:  Tau = .25  s  @ 12 cm/s
                     Tau = .125 s  @ 25 cm/s
                     Tau = .04  s  @ 100 cm/s  1 m/s typical ship lowering rate

  2:  Lowering rate effects the thickness the thermal boundary layer as follows:

        Tau(W) ~ k.Dr/(W^.5)  Dr radius of temp. probe & k = constant

          examples:  Tau = 1.30  s  @ 12 cm/s  Excell (Schmitt, et al JMR 63, 2005.p. 285)
                     Tau = 0.80 s  @  32 cm/s
            

      Total NIXIC lag is the sum:

         Tau = Tau(W) + Tau(Dz)