39.19 time_step_monitor

Option time_step_monitor computes instantaneous values of total kinetic energy^39.4 per unit volume averaged over the entire domain volume in units of gm/cm/sec². It also computes first and second moments of tracer quantities. The mean tracer is the first moment and tracer variance^39.5 is the second moment about the mean in units of tracer squared. Additionally, the quantity $\vert{\partial T /\partial t}\vert$ in units of deg C/sec (for n=1) and (grams of salt per grams of water)/sec (for n=2) averaged over the domain volume is computed. The explicit forms are given by

$$\frac{\rho_\circ}{2}\frac{1}{Vol^U}\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{imt-1}\sum_{n=1}^{2} u^2_{i,k,j,n,\tau}\cdot\Delta^U_{i,k,j}$$ <ke> = (39.248)

$$<t_{i,k,j,n,\tau}> \frac{1}{Vol^T}\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{imt-1} t_{i,k,j,n,\tau} \cdot \Delta^T_{i,k,j}$$ = (39.249)

$$tracer\_variance <t_{i,k,j,n,\tau}^2> - <t_{i,k,j,n,\tau}>^2$$ = (39.250)

$$<\vert\delta_\tau (t_{i,k,j,n,\tau})\vert> \frac{1}{Vol^T}\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{im... ...t_{i,k,j,n,\tau+1}-t_{i,k,j,n,\tau-1}\vert}{2\Delta\tau} \cdot \Delta^T_{i,k,j}$$ = (39.251)

where

$$<t_{i,k,j,n,\tau}^2> = \frac{1}{Vol^T}\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{imt-1} t_{i,k,j,n,\tau}^2 \cdot \Delta^T_{i,k,j}$$ (39.252)

and the volume elements for U cells and T cells are

$$\Delta^U_{i,k,j} umask_{i,k,j} \cdot\dxui\cdot\csuj\cdot\dyuj\cdot dzt_k$$ = (39.253)

$$\Delta^T_{i,k,j} tmask_{i,k,j}\cdot\dxti\cdot\cstj\cdot\dytj\cdot dzt_k$$ = (39.254)

The masks umask_i,k,j and tmask_i,k,j are 1.0on ocean U cells and T cells but 0.0 on land U cells and T cells. Also, the relation between j and jrow is as described in Section 14.2. The total volumes are constructed as

$$\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{imt-1} \Delta^U_{i,k,j}$$ Vol^U = (39.255)

$$\sum_{jrow=2}^{jmt-1}\sum_{k=1}^{km}\sum_{i=2}^{imt-1} \Delta^T_{i,k,j}$$ Vol^T = (39.256)

In addition to the above quantities, the iteration count from the elliptic solver is saved. When option netcdf is enabled, the output from this diagnostic has a NetCDF format and is written to file ts_integrals.yyyyyy.mm.dd.dta.nc. Otherwise, the output from this diagnostic may be written as ascii to the model printout or as 32 bit IEEE unformatted data to file ts_integrals.yyyyyy.mm.dd.dta. If option netcdf or time_step_monitor_netcdf is enabled, data is written in NetCDF format rather than in unformatted IEEE. The ``yyyyyy.mm.dd'' is a place holder for year, month, and day and this naming convention is explained further in Section 38.2. The interval between output is specified by variable tsiint and the control is specified by variable iotsi.