An intermediate time step for currents is produced using a simplified momentum equation.
The currents at these steps are used in the computation of advection and eddy viscosity (and nonlinear friction?).
The simplification consists of

1. starting with CIU, CVI the average of the currents of the previous two steps (tc', tc")
   
2. propagating them ahead using the average of the elevations at the previous two steps (te', te") steps and the currents of the latest step t'
3. without the terms for advection and eddy (but with nonlinear friction)
   
4. Coriolis is also taken from CU, CV at t', which is the central time of the propagation step.
   
5. This gives CIU and CVI at ti' , which are stored in the third segments of the arrays CU(i,j,3), CV(i,j,3).
6. The interlacing computations are called into effect with  CALL TTEQ_Interlace (.true.)

Purpose is to avoid instability of the equation system when the ordinary procedure involves nonlinear terms.
If the consequences of averaging and omission are too strong (frictionless case leaks mass, free oscillations die out fast, ...), a small change to the code can be made to mix the CIU,CIV currents CU,CV:
CU(i,j,3) = ( wi1*CU(i,j,IN3) + wi2*CU(i,j,IQ) ) / (wi1+wi2)

There was a failed attempt to simplify the interstitial propagation using virtual nodes for elevation, trying to get shorter code free from boundary conditions. The keyword was VPEL. Ignore the eventual remnants here.
There was an engineering version otes12h.f; ignore (update this page) if there are references/links to the abandoned production line.

Contents:

• | Physics | Call list parameters |  Prerequisits | Output | Log file messages
  
• | Init | Solve | Parameter setting, application |
• | Parameter setting, rules and arguments | Called subroutines and packages |
• | User interaction | Graphic trace | Graphic display prompter |
• | Examples |

Comments to the program code concerning the physics:

Notations:
{a,b} denotes a vector with components a and b
Int denotes integral, Laplace the so named second  derivative partial differential operator

Advection:

{ADU,ADV} = ({CU,CV}/HV * grad) {CU,CV}

where HV is depth and {CU,CV} vertically integrated current vector.
   If terms like  (CU/HV * d/dx CU/HV) would be integrated, we would formally get terms  d/dx 1/HV. This would imply depth-dependent current variations being advected.
This is certainly the case. However, discretization amplifies small-scale signals, making the system unstable. Instead I have decided to use

       D/Dt Q = d/dt Q + ({u,v}*grad) Q

and Q equals  Integral {u,v} dz  in our case, and  {u,v} = {CU,CV}/HV
The gradients are computed using centred differences. One could argue that down-wind gradients should be used. However, with the typical velocities of metres per second, the grid constant on the order of kilometres, and time steps on the order of 100 seconds or below, the down-wind formulation doesn't make a significant difference.  

Eddy viscosity:

       Delta_CU = ... + eddy_v Laplace (CU) Delta_t

eddy_v = const.

At present we use computationally costly formualation

        Delta_CU = ... + eddy_v * Integral {Laplace (CU/HV)} dz

However, bottom topography might be too rough to expect stable results.

Advection, friction and eddy dissipation may create difficult terms in some regions of the model. Procedures in OTEU12.f may be used to regionally modify the model parameters.
  Advection may be turned off in one region: Call Area_No_Advection(...).
  Model parameters may be redefined in one region: Call Spec_Area(...).
  The actual code of TTEQ (array PARSPA) determines the meaning of the 10 parameters.

Excitation:

TEP: Tide-effective potential composed of astronomical and solid earth tide spectrum, optionally loading tides added.

ETD_SLOPE: Adding regional excitation signals to the potential, explicitly time-dependent. In progress since 2017-08-14.

SAL: Internal self-attraction and -loading optionally by parametrisation;
          or by iteratively adding harmonic solutions to TEP (tedious!)

APR: Sea-level air pressure fields

AB:  Active Boundary tides
AB_Step: A planned step at an Active Boundary (not implemented yet: selection of AB by name; AB-names exist already)

Prerequisits:

• /CAREA/  - area outline, grid resolution. Use GETAR.
• /CABOUN/ - location of driving boundaries.  " GETAB.

• A file hosting common area data for model excitation (/CTPOT/ /CTOPOT/ /CTABOU/ /CEPOCH/ /CTC/ ). Fixed name ETDX.DMP. Found using PATH-parameter and read by TTEQ/ETDREP; produced in preparation step Prep.3 (otem16.f) after Prep.2.
  
• Bathymetry and flag arrays (Prep.1 phase, CREAM.f), supplied through the call list.

• A "dump" file, read from file unit 3, produced by an earlier run of TTEQ with the dump option set.
• /CTABOC/ /CTCC/ - additional tidal currents at active boundaries - Development in progress. Subroutine ETDABM - otes173.f

Output:

• A dump file (unit 2).

• Tide gauge data for a number of sites, hourly samples.
• Tide generating potential data for the same sites.
• Buoy tracing, hourly samples.
A joint sampling interval is used for these effects. Redefine
using a call to SI_TIDE_GAUGE(samp_int).

• Loading effects, time series for a number of sites, hourly samples.
Three files, one for each component RADial, EASt, NORth.
Sampling interval can be redefined. Call SI_EVLOAD(samp_int).
• One harmonically analyzed partial tide map, CMPX data;
• its upper harmonic.

More on ZSUM and Harmonic Solutions

    ntides=(index(CTIDE,'  ')+1)/3
    CALL Count_Packed (FLZ,M,N,MPA)
    CALL CNVCDS (ZSUM,ZSS,IWDIM,ntides+1)
    NPA=1
    CALL SETVER (Nsver)
    FNorm=NRSUM/2.
    do ih=1,ntides
       j=ih*3-2
       k=(ih-1)*IWDIM+1
       kk=k+IWDIM
       tidex=CTIDE(j:j+1)
       CALL OUTZMN (41,ZSS(k),FN,MSUM,1,TYPE,TIDEX)
    enddo

    CALL OUTZMN (iun,ZSS(NTIDES*IWDIM+1),FNorm,MPA,NPA,'Z','M4')

(Obsolete since the advent of solplot:) However, several procedures do not scan row number N-1 in 'Z'-arrays (e.g. ISOSCN), so either the array type should be 'M' or array dimensions   MPA2=MPA+1; NPA2=2 must be used.

CTIDE   - char*2  - Tides for harmonic analysis. Specify e.g. 'M2 O1  '. 
IUSAP   - integer - Log.unit for retrieving tide potential information
                    (OPEN done by routine).
PATH    - char*32 - Path and file name for tide potential.
NVU     - integer - Number of partial tides actually applied.

ZBUFF(NBUFF) - complex - Buffer for tide potential reading,
                    NBUFF = IWDIM >= number of 'S' & 'A'-cells.

H(M,N)     - real - Bathymetry array.
FLZ(M,N),FLM(M,N) - integer - Flag arrays for 'Z' and 'M' grid.

ZSUM(*) - complex - Packed CMPX array: harmonic results for the tides specified
                    in CTIDE and, in addition, the first  harmonic of the
                    first tide in CTIDE. More about ZSUM below.
                    Size equal to (ntides +1)*(number of Land + act.bound. nodes))
                    = (ntides +1)*IWDIM = (ntides +1)*NBUFF
                    where ntides = the number of tides given in CTIDE.

NRSUM   - integer - returned:
                    SOLVE-phase: Number of time steps used for ZSUM.
                          ZSUM must be divided by NRSUM/2. to yield ampli-
                          tudes in [m].
                    INIT-phases: Number of time steps to cover an integer
                          cycle of the basic tide (declared via Call INILTE).

ITEND   - integer - SOLVE-phase: (Adjusted) time step at end of integration.
                    INIT-D-phase: ... at time of dump.
                    INIT-0-phase: 0
                    In both cases:
                          Next time: suggested continuation at  ITEnd + 1.
                          Call LTETIM (ITEnd+1, ITEnd+K*NCYC), where
                          NCYC <- NRSUM from the INIT-phase.

TGP(M,N,2) - real - Work array for tide potential, stepped in time by
                    this routine.

EL(M,N,2),CU(),CV() - real - Work arrays for Finite Difference Scheme:
                    Elevations, SE-, NE-currents.
ADUA(M,N), ADVA()   - real - Work arrays to store advection at interlace times.

EVWORK(4,IWDIM) - real -  Work array for computation of loading effects.
                    IWDIM >= Number of 'S'-cells.

SHOW(M,N)  - real - 'M'-array, selectable grasol-show array

AUST(*)    - real - Packed real work array for Austausch coefficient.
                    Can be equivalenced with ZBUFF. Size >= IWDIM = NBUFF
 

TTEQ contains code for its own initialisation.

Before TTEQ can be called, preparatory calls are required (code in otes01.f) in order to set model parameters etc. TTEQ has two operating modes:
INIT (parameter preparation) and  SOLVE.

INIT has two submodes:
INIT from scratch (INIT-0);
INIT from a dump (INIT-D).
 

INIT-0:

  During INIT-0 - and only there - the time step length is determined.

INIT-D:

INIT-D and INIT-0 return the tide cycle length and the previous closing time step number (ITEnd) through the TTEQ call list (variables NRSUM and IT).
SOLVE should continue at  ITBeg := IT+1  and close at  ITEnd = IT+KCYC*NRSUM after INIT-D.
SOLVE should start at  ITBeg = 0  and close at KCYC*NRSUM after INIT-0.

 Code is in  otes12i.f

The SOLVE-call:

Time step and integration interval (cycle length):

(alt 1)  specify a measure for the subcriticality, a factor on the critical time step. A subcritical step is shorter. The closer the time step to criticality the more exact is the solution (theoretically; this statement is only valid in the deepest part of the model);
         CALL INILTE (0, Subcriticality_Factor, Basic_Tide_Symbol) ! for instance...
         CALL INILTE (0, 0.99, 'S2')

(alt 2) specify the number of time steps in one cycle of the basic tide:
         CALL INILTE (N_steps, 0.0, Basic_Tide_Symbol)

(alt 3) a rounded alt. a fixed step length. In case studies where complete harmonic cycles aren't an issue, the time step can be rounded to integer seconds; or a fixed value can be specified:
         CALL TTEQ_ROUND_DT (QRound_Dt, Fixed_Dt)
Qround_Dt .true. will take precedence, else  Fixed_Dt is accepted if > 0. 

TTEQ differs from LTEQ on the part of the designation of  ITBegin and  ITEnd. It is advantageous to use the S2 tide as the basic tide, which determines the step length of the finite difference scheme. The program can be made synchronous with a UT-clock, thus generating output series for tide gauges and CrustalDynamic Sites at exact hours.
    Recipe: Run a first test (which you will abort) with
         DOUBLE PRECISION DT1, DT_LTE
         ...
         CALL INILTE (0, 0.999, 'S2')
         CALL TTEQ (...
         DT1=DT_LTE ()
to obtain a near-critical time step,  DT1. Abort the program, and choose next time
         CALL INILTE (n, 0.0, 'S2')
where
         n >~ IDINT(((12*3600)/DT1 + 1)/12)*12,

This gives a near critical time step which divides one hour integer. 

   However, the tide subjected to harmonic analysis does not have to be the S2 tide. In that case, ITEnd = IT+KCYC*NRSUM  does not provide an integration interval that covers complete tidal cycles, and the harmonic analysis result would become perturbed. Therefore, use
         CALL TTEQ_ADJT (.TRUE.)
to obtain a complete last cycle of the tide first stated in the CTIDE string, so that its harmonic solution is as accurate as possible.

The number of time steps needed to cover (approximately) an integer number of cycles of the tide CTIDE is automatically adjusted. Thus, the parameters given in Call LTETIM are only the user's suggestion. TTEQ will prolongate the interval as required.

Parameter setting

The loading part requires a separate initiation (INIEVL_ETD).
The other packages engaged by TTEQ (like the tide generating potential) allow/require parameter setting from the calling (the main) program.

 <TTEQ-->>> Trace  0: Fric_r
 <TTEQ-->>> Trace  1: Cori_x       2: Cori_y      3: TGP_x       4: TGP_y
 <TTEQ-->>> Trace  5: Adv_x        6: Adv_y       7: Eddy_x      8: Eddy_y
 <TTEQ-->>> Trace  9:  M_x        10:  M_y       11:   U        12:   V  
 <TTEQ-->>> Trace 13: Fric_x      14: Fric_y     15:  DM_x      16:  DM_y
 <TTEQ-->>> Trace 17: HrmAmp      18: HrmPha     19:  n.u.      20: Depth
 <TTEQ-->>> Trace 21:  TGP        22:  n.u.      23: M_x@.5     24: M_y@.5

Subroutines called from TTEQ:

   tide forcing                                (otes17*.f)
   tide gauge and crustal loading              (oteu16*.f)
   air pressure forcing                        (otes15*.f)
   special areas (modified model parameters)   (oteu12.f)
   user interaction                            (oteu18.f)
   graphic display                             (otes18.f)
   buoys                                       (otes19.f)

Several of these allow/require parameter-setting calls.

Execution options: Reset ZSUM,  Graphics,  Write state arrays

To be called before the iteration is started:

      CALL LTEOPT (OPTION)

LTEOPT - options:                                                 
OPTION        - char*3 = 'rgw' where

r             - 'Y' - reset ZSUM before LTEQ-time stepping,
                'N' - don't ...  '.' - unchanged. Default = 'N'.

g             - 'A' 'E' 'a' or 'e' - graphic display of tide elevation on-line.
                                     Capital letters for prompting mode enable.
                'A' 'P' 'a' or 'p' - graphic display of tide generating potential.
                                     Capital letters for prompting mode enable.

                'N' - don't ...  '.' - unchanged. Default = 'N'.

w             - 'Y' - save state arrays on file, log.unit 2, for later
                      resuming of iteration.
              - 'O' - rewind the file before save.
              - 'N' - don't save.
              - '.' - unchanged. Default = 'N'.

DESCRIPTION OF PHYSICAL PARAMETERS FOR TTEQ:

Some parameters are stored in the dump; their values can only be changed after the INIT-D calls and before the SOLVE call to TTEQ.
(Mark = >D< )

Parameters which must be given before the SOLVE-call :
(Mark = >S<)

The friction parameters are not stored; thus CALL LTEFRI must appear before SOLVE calls. Subsets of parameters can be set by alternative calls.

      CALL SETLTE (T_beg, T_end, FRIC, NF_cons, TF_relax, NF_end, NRAMP,
                   I_mon, J_mon, OPTION)
 

LTETIM - parameters:                                                  >S<
T_beg, T_end  - integer - Model start and end time; preferably
                T_end - T_beg. + 1 = K * (tide.period)/dt. C.f. above
                "Start from an initial solution" how to obtain the
                the integer value: (tide.period)/dt
           CALL LTETIM (T_beg, T_end)

LTEFRI - parameters: Friction / damping and control:                  >S<

                Run-in phase = damping. Uses parameters
                FRIC(1), NF.cons, TF.relax, NF.end.

                Physical friction model: FRIC(2..4);
                dt = used time step [s], check protocol.

FRIC(1..4)    - real, dimension=4. Values must be >= 0 to be accepted.
                Zero value switch the mechanism off.

FRIC(1)       - Friction coeff. for damping during start-up
                dM/dt = p M abs(M)/Hmax.  FRIC(1)= p dt = O(0.1)
 
FRIC(2)       - Linear bottom friction parameter.
                dM/dt = - r M, [r] = 1/s. Here FRIC(2) = r dt, hence
                FRIC(2) should be O(0.1)
 
FRIC(3)       - Quadratic bottom friction parameter.
                dM/dt = - q M abs(M)/H.   FRIC(3)= q dt, e.g. = 0.3
 
FRIC(4)       - Eddy viscosity parameter. Check the code in OTES12i.f
                how eddy visc. is formulated (depth-dependent ?).
                Reasonable values are between 1.e4 and 5.e5 m**2/s
                dM/dt = + v Laplace M, FRIC(4) = v  (!)
                Feature is switched off if FRIC(4) < 1.e-4
 
NF_cons       - integer - Time step until which run-in damping is
                kept constant.
 
TF_relax      - real - Relaxation time (model units of time) for
                exponential decrease of FRIC(1).
 
NF_end        - integer - Time step after which FRIC(1) is 0.
           CALL LTEFRI (FRIC, NF_cons, TF_relax, NF_end)

LTERMP - parameter:                                                   >S<
NRAMP         - integer - Duration of raised-cosine ramp. The driving
                forces are turned on during the start-up phase using
                a raised-cosine ramp. NRAMP is specified in model
                dt-units. No default.
           CALL LTERMP (NRAMP)

LTEMON - parameters:                                                  >D<
I_mon, J_mon  - integer - The position X and Y of a mesh point at
                which characteristic values will be printed during
                time stepping. No defaults.
           CALL LTEMON (I_mon, J_mon)

PARLTE  - parameters (p1,p2,p3,p4,Nonlin):                            >D<
p1            - real - Hmin, the minimum depth for bathymetry. The
                array H(i,j) will be adjusted. Default = 5.0 (meter).
p2            - real - WDT_fric, the time offset inside dt at which the
                friction terms are defined; counted from t+1 backward.
                WDT_fric=0.0 <=> t+1,
                WDT_fric=1.0 <=> t.     Default = 1.0
                which is also the "classical" definition.
p3            - real - G_fac, a factor multiplying gravity. It was
                found that an increase of g -> 1.1 * g improves the
                fit of the discrete dispersion relation w.r.t. the
                continuous case. It's doubtful though. Default = 1.0
p4            - real - SLP = self loading parameter. Applied as
                EL_eff = EL * (1-SLP). Default = 0.0

If a default value for p* is to be used, specify p* <= -1.0

Nonlin        - integer - NONLIN-earities.
                < -1 - default: shallow water
                  -1 - don't change
                   0 - linear
                   1 - shallow water (=default)
                   2 - advection
                   3 - 1 & 2
           CALL PARLTE (Hmin, WDT_fric, G_fac, SLP, NONLIN)

There is a character version for Nonlin:
           CALL PARLTE_NONLIN (string)
string        - character*8 -
                KEEP - don't change the current setting
                +S   - shallow water
                +AM  - Advection (M grad M)/H
                +AU  - Advection (M grad U) (unavailable in this version)

N_steps       - integer - Number of time steps per tidal cycle.
                Default = 0, i.e. P.subcrit is used to determine the
                time interval.
P_subcrit     - dt = P * dt.crit is used; dt will be further adjusted
                downward such that the tidal cycle is divided into an
                integer number of steps.
                Default = 0.75
TIDE          - char*2 - The tide that determines the fine-adjustment of
                the time step.
           CALL INILTE (N_steps, P_subcrit, TIDE)
N.B.: INILTE resets the PARLTE - parameters.

General Parameters (special extensions):
           CALL SETLTE_QGP (i,qq)
           CALL SETLTE_RGP (i,rr)
           CALL SETLTE_IGP (i,kk) unused in this version
where i has type integer, qq logical, rr real, and kk integer.

Using the communication script OC %Z, a prompt will appear where
these parameters can be altered.

Some SETLTE_*GP settings are ready to use:

______________________________________________________________
   i     Meaning of _QGP(i), qq logical values
--------------------------------------------------------------
   1     Use a depth-dependent austausch coefficient
         (qddaus in otes12h.f) Feature is presently
         disabled (commented out with 'ccc' ).

   2     Accumulate harmonic from elevation field

   3     Accumulate harmonic from current fields

   4     Accumulate DC-level in harmonic analysis

   5     Accumulate upper harmonic of basic tide

Under time interlacing:

   6     Include advection at interstitial times
   7     Include advection at passive boundaries
   8     Include austausch at passive boundaries  

______________________________________________________________
   i     Meaning of _RGP(i), floating-point real values
--------------------------------------------------------------
   1     phase cut (usually 0., could be 180.) for the harmonic
         trace graphics showing the phase field

   2     factor on the advection terms (should be 1.0)

   3     effective Coriolis, default = 1.0

______________________________________________________________
   i     Meaning of _IGP(i), integer values
--------------------------------------------------------------
unused

RTRLTE - parameters:
N_save        - integer - Resume with the N'th saved solution from file
                on log.unit 3. If the file contains L sets, L < N,
                the L'th will be taken.
N_cont        - integer - Number of time steps to continue. C.f. above
                "RESUMING A PREVIOUS SOLUTION" for advice how to obtain
                LTETIM parameters if an appropriate value is not known.
           CALL RTRLTE (N_save, N_cont)

TTETEP - parameter:                                                      >?<
N_steps       - integer - Update interval (number of time steps) for the
                tide effective potential. Linear interpolation between.
                Default = 20
           CALL TTETEP (N_steps)

LTETDS - parameters:                                                     >?<
N_steps       - integer - Interval between on-line display of elevation.
                Default = 42
range         - real    - The data range [m].
                Default = 1.0
 
Inquiry:
 = DT_LTE()   - Real*8 entry DT_LTE() returns the time step length [s]

INTERACTION WITH THE OTHER ROUTINES INVOLVED:

Consider these calls from the MAIN program

CALL EXTCTP                    to extend common block space tide potential
CALL EXTCTO                    to extend common block space global load pot.
CALL EXTCTA                    to extend common block space active boundaries.
CALL ETDSEL                    to select partial tides for forcing
CALL ETD_NO_BODY_TIDE
CALL ETD_NO_LOAD_TIDE
CALL ETD_ABZ_TIDE              (de-)select active boundary forcing
CALL ETD_ABZ_Factor            to amplify active boundary tide

Tide forcing, parameter setting  (OTES161.f)
-------------------------------

CALL ENABLE_PLAY_WITH_ETD      to enable code in subr. PLAY_WITH_ETD

Simulated air pressure forcing: (OTES15*.F)
-------------------------------

CALL Pressure_Param            to define size and velocity of a model pressure system
CALL Pressure_Stop             to stop simulation
CALL EXTABP                    to extend the buffer for act.boundary data. 

                               To force with actual met fields, use otemw1.f
 

Regional excitation: (OTES17.F)
--------------------

CALL ETD_TGP_SLOPE (string)    'E:<four parameters>'              for east-west geometry
                               'N:<four parameters>'              for north-south   "
                               'T:<three parameters> [options]'   for timing, event ahead
                               'T!<two parameters>   [options]'   for timing, launch event now!
                               '.?'                               inquire status
                               'RESET'                            switch off
                               See details on parameters here.
                               The update interval for the TGP should be set at a small value;
                               without tides and loading, the computational burden is negligible.
                               The namelist parameter in otemt1.f is IDTTEP , setting the number
                               of diff-eq. time steps to lapse between calls to ETDCMP.

More on active boundaries: (OTES13.f)
--------------------------

CALL FREEAB                    to free the inner row of elevation boundary
CALL ETD_ABZ_Step              to force model with unit step
CALL ETD_ABZ_EAPR              to maintain inverse barometer at act.boundary.
 

Tide gauges  (OTEU16.f)
-----------

CALL IUN_TIDE_GAUGE
CALL ADD_TIDE_GAUGE
CALL SAFE_TGG

CALL IUN_TGP_SENSOR            to output time series of tide generating potential
CALL ADD_TGP_SENSOR
 

Crustal Dynamics Sites (Loading effects)  (OTEU16.f)
----------------------------------------
Calls in that order:
CALL ADD_EVL_SITE             add sites
CALL IUN_EVLOAD               define output file unit
CALL ISOFOR                   define what boxes to be included in load scan
CALL INIEVL_ETD               initialize load routines.

Buoys (OTES19.f)
-----

CALL SET_BUOY                 add buoys
CALL IUN_BUOY                 define output file
CALL SAFE_BUOY
CALL DO_BUOY                  activate time-stepping
 

Special_Areas  (OTEU12.f; user interaction: OTEU18.f)
-------------

CALL AREA_NO_ADVECTION        to avoid advection term in a limited area

CALL SPEC_AREA                to define an area with alternate parameters
CALL SPEC_AREA_PARAM          to set parameters

Use of Spec_Area parameters is flexible. Currently: Parameter(1) factors
the bottom friction terms, P(2) the eddy term, P(3) is a minimum depth.
 

Graphic display
---------------

CALL GRASOL_DS                to display double size color pixels
CALL GRASOL_SS                to display single size
 

The operator may interact with TTEQ. Notice: may. A good, stable solution will rather be one that thrived without the intervening hand of a person. However, some features have been included which allow changing of parameters as the program steps along.

There are two routes of intervention, from a console window (this chapter), and the Graphic Display Prompter at the graphic screen.

The graphic screens, especially the Trace feature, allows mainly logistic interaction. For example, an Active-Boundary step experiment can be initiated from the graphics window.   

When numeric values are expected and you prefer a default value, hit the Escape-key. The Return key will keep you in a loop. (The functions used are  int_prompt_s18  and  real_prompt_s18 .)

Console actions

On the PC, the program scans the keyboard directly. On the UNIX platform, however, the program reads a little communication file. The user writes characters into this file using the OC command.

Use OC from another terminal window or run TTEQ-SOLVE in the background; redirect output for convenience. 

Example OC ^M   : do spell out the two characters, "Caret M" instead of the composed key press CTRL+M on the PC.
Since xterm under Cygwin on a reduced keyboard (laptop) frequently loses the delayed-compose key `^´, a  `%´ or a `\´ (backslash) can be used instead.  Unfortunately, the OC parameter must be put inside quotation marks, e.g.  OC '\E' 

Code
 ^@       The date and time of the next step are written to the protocol.

 ^1..^9   A debug feature: prints 1 to 9 reports of the iteration of currents.
          Shows the interlaced step (marked p- U- V-) and the ordinary (p+ U+ V+).
          To understand what's printed, check with
            fgrep CDEBUG otes12i.f

 ^H       The table header is printed on the protocol

 ^M       The program waits for entries that modify the Spec_Area. C.f.
          oteu12.f and oteu18.f

 ^D       The depth array H(m,n) can be updated.

 ^E       Prompt after the next display of the elevation array

 ^F       The friction parameters FRIC(1..4) can be adjusted.

 ^V       The system asks for new monitor node position (enter at text prompter
          on graphic screen).

 ^W ^X    "when?" - the ending step will be printed on the protocol and the
          grasol status line.
          ^X: Grasol will prompt (cannot display the status then). Taken out of service

 ^W       Write the three arrays to file (E -> iun_save , Mu & Mv -> iun_save+1)
          iun_save is set with  call tteq_save2unit(i) . Default=91
          The arrays can be plotted using  elplot  and  uvplot
          The number of saving instances is 1 by default. It can be modified at the display prompter
          using c 7 #nsave

 ^S       The program stops after writing the dump file.

 ^Z       Some general purpose parameters. 
          Actual parameters will be printed in the log-file.
          New parameters can be entered at the prompter in the graphic window
          E.g. parameter 1 means the phase cut parameter (phase is shown in graphic trace of
          harmonic solutions.
          Or to re-enact advection at passive boundaries, enter Q 7 T (sets QGP(7)=.true.).
          See otes12i.f at "^Z - special purpose"

 ^Q       The program stops immediately.
 

Other user interactions concern screen graphics and tracing.

 ^A       Trace of active boundary data is initiated for the next time step.

 ^O       Trace of etd-o-o-area data is initiated for the next time step.

Graphic displays can be modified in a number of ways. Irregardless how OPT(2:2) was declared at call time...

 ^G       The elevation array will be displayed and prompt after display
          will be reactivated.

 ^P       The tide generating potential will be shown and prompt after
          display will be reactivated.

 ^T       The graphic trace is switched on and prompting after display
          will be reactivated. Time step for next graphics is set to 1.
 ^U       Like ^T, time step is unchanged, however.

A nice feature is that you can watch the harmonic solution as they (hopefully) converge.   Do the following:
From the outside, OC ^T
At the graphic prompter, enter first  c  and  18  to select phase, then I  and e.g.  100 for the time increment to redraw, finally  G  for go,
then watch.

If you want to show another constituent (provided it is enabled through calling parameter CTIDE), do
^T , enter  # at the graphic prompter (not mentioned in the menu) and type  1  for the second tide in progress.  

More details in the next chapter.

New features have been included in the OC mechanism:
   Control of model excitation of the ETD_TGP_SLOPE kind.
    Function UBR_FF (oteu18.f) will interpret the 'c <command-string>' argument and call  ETD_TGP_SLOPE(string).
  With blankspace between command symbol and argument, the parameter to OC must be enclosed in quotes.
     Underlining is supposed to emphasize the fact (we might change OC for more kindness to the user).

OC '@S <command-string>'

    e.g. for an est-west slope centred on grid index 145, height 1.0, half-wave length 350 units, tapered at twice the length,
    acting with a period of 30 hours, for the next 30 hours ahead (half-period but sine-squared!) 

OC '@S E:1.,145.,350.,2.'
OC '@S T!30.,30.'

    An aid for parameter specification is here: http://holt.oso.chalmers.se/hgs/OTEQ/etd_tgp_slope.nb (Mathematica notebook; see png-image (prefer to open it in a new tab/window)

OC '@E <file-unit,modulus>'

OC '@F <n>'           - sets subtype n (meaningless now that we've abolished VPEL) 
OC @f                 - recalls subtype scanning.
OC '@T <flags>'       - sets a new target string. If non-nil, sets it permanently (calls ISOFOR).
                        If nil, resumes with the flag set aside (default or a priori set with ISIFOR).
OC '@t <flags>'       - sets a new target string for only the next instance of GraSol.

OC @R

OC '@V <i>,<j>'

OC '@B <v>'

The Watchdog

In order to abort integration if the system turns out unstable, this feature surveys the solutions and warns (protocol), reduces the repeat interval of graphics to one step. When a severity threshold is exceeded, it will stop the process. Code is in oteu12.f . Watchdog options,  CALL...

WATCHDOG_CLIP(xl)     - essentially an illegal and worthless action: clips the array at these limits (-xl .. +xl)
WATCHDOG_MOD(n)       - how often the array is observed (n = modulus of time step number; if zero, analyse)
WATCHDOG_BITE(xx)     - stop when absolute value of any node value exceeds xx.
WATCHDOG_BARK(x)      - warn when absolute value of any node value exceeds x.
WATCHDOG_POINT(q1,q2) - if q1 is .true., set immediate reactivation of graphics according to q2. Activated with "bark".
WATCHDOG_STOP(q)      - if q is .true., the dog stops execution.
WATCHDOG_WHERE(i,j,q) - the node that caused the dog to bark. On return, q is .true. if the node indexes are non-zero.   

Graphic trace:

Table  GRAPHIC TRACE - Component numbers and the variable that is traced
To select the array, press the  f  or  c  key at the graphic prompter and enter a number:

0	Friction/damping scaling factor
1  2	Coriolis terms in U and V, respectively
3  4	Gradients of tide generating potentials along x and y directions, respectively
5  6	Advection terms along x and y directions, respectively
7  8	Eddy viscosity terms along x and y directions, respectively
9 10	Mass transport vector M = {U,V}
11 12	Current vector M/h
13 14	Friction force along x and y directions, respectively
15 16	dM/dt
17 18	Harmonic solution, amplitude (17) or phase (18). Select a specific constituent with the # key
20	HV, the sea depth, augmented with elevation under nonlin
21	(not finalised yet; called at the wrong place)  Show the tide generating potential (not the gradients). Problem is that the flag array used is type M, the TGP array is type Z.
n.u.
23 24	Mass transport vector at the interlaced steps

| Return to Displays | Return to Displays grasol prompter |

Graphic display prompter (GDP):

The display and prompting occurs in subroutine GRASOL (/home/hgs/Oload/p/gra/otes18.f)

<CR>       Pressing the Carriage-Return key satisfies the GDP.  TTEQ will continue.

I             Press "I" (Increment option) and define the number of time steps until the next display.

G  T      "Go" and "Text screen" modes are toggled modes (key "G" or "T"). Go means that
                 the prompter is skipped. (Regain control by e.g. sending   OC ^G  from the outside.)
                 Text screen should be selected if graphic mode is undesirable between consecutive maps.

S               Stop mode (S-option) implies skipping the display routine; you can re-enable
                  the display mode by sending  OC ^E, OC ^P, OC ^T or OC ^G, depending on
                  what you want to see.
                  Pressing "S" passes control to TTEQ.

d       Dump the elevation array to real-binary file. The system prompts for a file name.
        Enter a file name containing one `#´ character, and the dump will recur with every array shown.
        The `#´ character will be replaced by the step number.
        (careful! Request only one array variable for show!)
        Enter a `.´ character to stop dumping.  

r               The data range can be changed: Press "r" and enter a new value. The data range
                  may optionally be clipped against the color range; this option is always prompted for
                  before you are asked to enter the range value(s).  Press "R" and redefine the
                  data range to be one-sided, two-sided or general (-1, 0, +1). In the second case you need
                  to enter two values, for the lower and the upper range, respectively. 

                  Overrange colors are difficult to interpret. Lower-than-bottom is shown by
                  mixing black and a base color, higher-than-top by mixing base colors that
                  are two, three, ... intervals apart. The color numbers are derived with
                  the MOD function; thus, vastly-out-of-range data will still be colored
                  quite similar to inside-the-range data, and is hard to discern.
                  After changing the data range, the map is redrawn.

l  h       Press l to get low resolution,  h  to get double size pixels.
1  2       Synonymes:  1  and  2. Larger numbers will draw larger cells; maximum size is 7.
L  H       Press  L  or  H  to cause the screen to be refreshed while changing resolution.

a  A       Press  a  to redraw,  A  to refresh the screen.

V               Press  V  to redefine the target symbols for display.

^C             Pressing  ^C  at the GDP stops TTEQ; the routine requests confirmation before it will dive.

c  f       Press `c´ to get prompted for one of 10 integer parameters to set.
                  (Calling program uses the ISGN_GRASOL function to retrieve the actual setting)
                  Press `f´ to set the first parameter right-away. Parameter nr. ....
                  1  - ... select a component to show; cf  Table GRAPHIC TRACE.
                  After `c´, entering ...
                  2  - to set the terminating time step of the the on-going TTEQ cycle. The actual time step is shown in the purple status bar.
                  3 ... unused.
                  4 -  to revive the display at the time step specified at the next prompt. 

                  Selecting 17 or 18, a tide harmonic solution in the making, will re-activate the graphic screen at every zero-crossing
                  of the imaginary part of the Fourier factor.

#               Press "#" after selection of component 17 or 18 to request view of a specific harmonic solution. You can
                  watch the convergence of the solution. In the purple status bar you can check the exp(wt); if it is (1,0),
                  a harmonic cycle for the wave in question is complete and the solution relatively well-determined.
                  Enter  1 for CTIDE(1:2), 2 for CTIDE(4:5),  ntides+1  for the double-frequency nonlinear tide belonging to 1.
                  If you e.g. asked for two harmonic solutions, enter  3  and you'll see the double-frequency solution of
                  CTIDE(1:2) (e.g. M4  if  CTIDE = 'M2 O1  ') .

@               Press "@" to get prompted for a halting time. At the halting time the graphic display will be
                  revived and stay in prompt mode  (ithalt_grasol() function)    

/              Plan an Active Boundary Step experiment. Respond to the following prompts:
                  Start and end of step: How many time steps ahead (end: default=indefinite)
                  Step height (default: 1.0) Press ESC for defaulting. 

^S             Press "CTRL-S" to set up a SPLASH test. System prompts for location, strength, time and duration

Examples for starting up TTEQ:

Start from a zero state:

    using SETLTE              common         using LTE***

(3) CALL SETLTE (0,-1,                      CALL LTETIM (0,-1)
         FRIC,NF_cons,TF_relax,NF_end,      CALL LTEFRI (Fric,NF_cons,TF_relax,NF_end) 
         NRAMP,                             CALL LTERMP (NRAMP)
         Imon,Jmon,                         CALL LTEMON (Imon,Jmon)
         OPTION)                            CALL LTEOPT (OPTION)

(8)                    ITBegin = 0
                       ITEnd   = K*NRSUM            ! e.g. K = 6
                       CALL LTETIM (ITBegin, ITEnd) ! SOLVE call
                       CALL TTEQ   (...)
______________________________________________________________________
 

Resuming a previous solution at  t = T :

(1) Read arrays ZOTEP, H, FLZ, FLM

(2) CALL RTRLTE (N.save, NT.cont)   ! INIT-D calls
    CALL LTETIM (0,-1)              !
    CALL TTEQ   (...,IT,NRSUM,...)  !

(3) ITBegin = IT+1
    ITEnd   = IT+K*NRSUM            ! e.g. K = 6

(4) CALL LTEFRI (...)
    and, optionally, other LTE*** routines, incl. PARLTE

(5) CALL LTETIM (ITBegin, ITEnd)    ! SOLVE call
    CALL TTEQ   (...)

______________________________________________________________________

Log file messages

Printed at every semi-cycle of the leading harmonic,  t  being the number of steps since the epoch (which may be large if a late start time has been specified).

where the emphasized symbols designate:

Z - QABZ     = excitation by elevations at active boundaries
M - QABM     = excitation by currents    "    "       "
A - QADVEC   = application of advection term
E - QEDDY    = application of momentum Austausch term

I - QINTRMST = auxiliary current arrays are stepped at interstitial times
Q - QRIOF    = quadratic bottom friction is applied (during run-in phase or beyond)

IterFr       = the maximum number of iterations of friction since the last message.

< after SNR: = appears at a complete harmonic cycle of the leading tide (reliable harmonic solution)  

.bye