Re: [ferret_users] dynamic height calculations [CORRECTION]

[William Kessler <william.s.kessler@xxxxxxxx>]

Sorry for confusion. My original discussion of the unit conversion below was wrong. The corrected discussion is here:

The 1E5 in the second command contains the unit conversions:
- multiplying by 1e4 converts depth in m to pressure in Pa via the hydrostatic eqn: P=rho*g*z
   Here rho*g ~ 1025*9.8=10045 is approximated as 10000
- dividing the result by 10 defines the quantity  “dynamic meter” (units J/kg = m2/s2)
- multiplying by 100 converts dyn-m to dyn-cm

BK

> On Dec 16, 2016, at 5:09 AM, William Kessler <william.s.kessler@xxxxxxxx> wrote:
> 
> A few things I notice:
> 
> * The chapter you attach is from a very good book (Tomczak and Godfrey) that has one of the clearest explanations of this stuff. Find this on p23-26, which is essential stuff for an oceanographer to know. 
> 
> Godfrey likes “steric height” in meters, while most others use “dynamic height” in J/kg=m2/s2=dyn-m. The difference is only a factor of g. Unfortunately Godfrey does not explain the units question completely, especially not the meaning of “dynamic meter”.
> 
> His definition eq(2.5) is an integration in pressure, which is not how it is done in practice. In the ferret script:
> let SVanom = 1/rho_UN(dyn_s,dyn_t,dyn_p) - 1/rho_UN(35,0,dyn_p)
> let/title="Dynamic Height(dyn-cm)" DYN_HT  = 1E5 * dyn_mask * SVanom[z=@din]
> 
> The 1E5 in the second command contains the unit conversions:
> - multiplying by 1e4 converts pressure in dbar to the SI unit Pa
> - dividing by 10 (really should be g) makes the result in geopotential units J/kg, which is defined as “dynamic meter"
> - multiplying by 100 converts to dyn-cm
> This seems sloppy but is the way oceanographers have always done it. Note that using 10 instead of g and a hidden 1000 instead of 1025 for density are compensating errors! (9.8*1025=10045, not 10000). Few if any aspects of the ocean are measured to a precision of less than half a percent, and geostrophic calculations are also a large approximation. There would be no point in fixing the sloppiness. Dynamic meter is simply a defined quantity that approximates distance to acceptable accuracy. As long as we all do it the same way, it works. 
> 
> 
> Two mistakes in your calculation:
> 
> * It is incorrect to use potential temperature for the dynamic ht calculation. The point of the differencing is to compare densities of water at the same depth. Use in situ T (See T&G)
> 
> * The main mistake in your calculation is the subtraction of 1000 in defining ro0 and ro. You’re thinking of sigma-theta, but here it is actual density. I think that accounts for most of the difference in the two plots. 
> 
> let ro0=rho_un(35,0,z[g=tt])-1000                   !! potential density at T=0, S=35, P 
> let al0=1/ro0                                                    !! specific volume i.e. alpha0
> 
> let ro=rho_un(sa,pot,z[g=tt])-1000                  !! potential density 
> let al=1/ro                                                        !! specific volume i.e. alpha
> 
> let dif=al-al0                                                    !! alpha - alpha0
> 
> => Try fixing these two things and see if the plots agree better.
> 
> Billy K
> 
>> On Dec 16, 2016, at 12:11 AM, saurabh rathore <rohitsrb2020@xxxxxxxxx> wrote:
>> 
>> 
>> Hi Ferret users,
>> 
>> might be my query is not posted in ferret mail group. hence i am forwarding it again.
>> 
>> regards, saurabh
>> 
>> 
>> 
>> 
>> ---------- Forwarded message ----------
>> From: saurabh rathore <rohitsrb2020@xxxxxxxxx>
>> Date: Fri, Dec 16, 2016 at 12:50 PM
>> Subject: dynamic height calculations
>> To: ferret users <ferret_users@xxxxxxxx>
>> 
>> 
>> hi ferreters,
>> 
>> i am trying to compute dynamic height by using potential temperature (deg. Celsius) and salinity (psu). 
>> 
>> 1) i used the go dynamic_height.jnl. after using this go script i got the plot but i am confused about the units mentioned by the plot. For dynamic height it is showing dyn-cm instead for dyn-m. i checked the script and found that there is no unit conversion. it is straight forward taking the depth mentioned by the data which is specified for depth i.e. Z[G=Temp] (argo temperature data) in meters. please tell me about the units used in this go script. 
>> 
>> 2) Moreover in the go dynamic_hight script it is defined as SVanom = SV - SV(35,0,0) [ in SV(35,0,0) the depth is zero instead of SV(35,0,z[g=temp]), why the depth is mentioned as zero instead fo variable according to the depth in data ?]
>> 
>> you the see the script by the command go/help dynamic_height.jnl
>> 
>> these are the commands i issued in the calculation.
>> 
>> use ptemp_argo.nc                  ! potential temp
>> use "/media/salt_argo.nc"        ! salinity
>> 
>> let dyn_S=salt[d=2]
>> let dyn_T=ptemp[d=1]
>> let dyn_P=z[gz=ptemp[d=1]]
>> 
>> set region/z=0:2000                ! for dynamic height at z=0 and reference depth is 2000 m
>> 
>> go dynamic_height
>> 
>> fill dyn_ht[l=@ave]
>> 
>> go fland
>> 
>> frame/file=1.png
>> 
>> 3) but if i do my own calculation for this computation but using the following steps 
>> 
>> use ptemp_argo.nc
>> use "/media/salt_argo.nc"
>> 
>> let tm=ptemp[d=1]
>> let sa=salt[d=2]
>> 
>> let ro0=rho_un(35,0,z[g=tt])-1000                   !! potential density at T=0, S=35, P 
>> let al0=1/ro0                                                    !! specific volume i.e. alpha0
>> 
>> let ro=rho_un(sa,pot,z[g=tt])-1000                  !! potential density 
>> let al=1/ro                                                        !! specific volume i.e. alpha
>> 
>> let dif=al-al0                                                    !! alpha - alpha0
>> let ro_ref=ro[z=2000]                                      !! reference potential density i.e. density at reference level of no motion 
>> 
>> let h1=dif*ro_ref                                    
>> let h=h1[z=0:2000@din]                                 !! dynamic height at surface z=0 with reference to z=2000 m
>> 
>> fill h[l=@ave]                                                  !! units in m
>> go fland
>> 
>> frame/file=2.png
>> 
>> but the plot is different from the go dynamic_height script. the dynamic height is more from the script as compare to my script.  i am attaching both the plot and the reference document for the computation.  
>> 
>> regards, saurabh
>> 
>> -- 
>> 
>> 
>> REGARDS
>> 
>> Saurabh Rathore
>> Research Scholar (PhD.)
>> Centre For Oceans, Rivers, Atmosphere & Land Science Technology
>> Indian Institute Of Technology, Kharagpur
>> contact :- 91- 8345984434
>> 
>> 
>> 
>> -- 
>> 
>> 
>> REGARDS
>> 
>> Saurabh Rathore
>> Research Scholar (PhD.)
>> Centre For Oceans, Rivers, Atmosphere & Land Science Technology
>> Indian Institute Of Technology, Kharagpur
>> contact :- 91- 8345984434
>> <1.png><2.png><02P-Basics.pdf>
>