Clarify that Omega pressure fields are relative (gauge) pressure

All three pressure fields (SurfacePressure, PressureInterface,
PressureMid) are relative pressure — absolute pressure minus the
standard atmosphere (101325 Pa). This clarification is needed because:
- The CF standard name sea_water_pressure applies to absolute pressure,
  so it is removed and left blank for PressureInterface and PressureMid
- The TEOS-10 EOS expects relative pressure, consistent with how Eos.h
  already passes pressure (Pa2Db * Pressure with no AtmRefP offset)
- The z-tilde pseudo-height is 0 m at the sea surface under standard
  atmospheric forcing only when p is relative pressure

Changes:
- VertCoord.cpp: remove sea_water_pressure CF name, update long names
  and min valid values (-AtmRefP, since absolute pressure >= 0) for
  PressureInterface and PressureMid; clarify computePressure comment
- VertCoord.h: clarify computePressure declaration comment
- Eos.h: note that Pressure inputs to TEOS-10 functors are relative
- userGuide/OceanState.md: describe SurfacePressure as relative
  pressure, typically 0 Pa for standard atmospheric forcing
- userGuide/VertCoord.md: note that p in the pseudo-height formula is
  relative pressure; update PressureInterface/PressureMid descriptions
- devGuide/OceanState.md: note SurfacePressure is relative pressure

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: xylar

components/omega/doc/devGuide/OceanState.md

@@ -77,6 +77,9 @@ The `SurfacePressure` device array can be retrieved with:
 ```c++
 Array1DReal SurfPres = State->getSurfacePressure();
 ```
+`SurfacePressure` is **relative pressure** (gauge pressure, i.e., absolute pressure minus the
+standard atmosphere of 101325 Pa), so it is typically zero (0 Pa) for free-surface runs with
+standard atmospheric forcing.
 This is used by `VertCoord` to compute layer pressures; `VertCoord` receives the array pointer
 via `VertCoord::setSurfacePressure()` during `OceanState::init()`.
 

components/omega/doc/userGuide/OceanState.md

@@ -10,9 +10,12 @@ initial-condition file and written to restart files.
 The class contains a method to update the time levels for the state variables between timesteps.
 This involves a halo update, time level index update, and updating the `IOFields` data references.
 
-`SurfacePressure` represents the pressure (Pa) at the top of the ocean column.
+`SurfacePressure` represents the relative pressure (Pa) at the top of the ocean column,
+i.e., absolute pressure minus the standard atmosphere (101325 Pa).
 Unlike `NormalVelocity` and `PseudoThickness`, it does not carry multiple time levels.
 Because `SurfacePressure` is registered in the `State` field group, it is read from the
 initial-condition file and must be present there; it does not default to zero.
-For a free-surface ocean run the surface pressure is typically set to atmospheric pressure
-(~101325 Pa) in the initial-condition file.
+For a free-surface ocean run with standard atmospheric forcing, the surface pressure is
+zero (0 Pa) in the initial-condition file.
+For a coupled ocean–atmosphere run, `SurfacePressure` holds the anomaly of the atmospheric
+surface pressure from the standard atmosphere.

components/omega/doc/userGuide/VertCoord.md

@@ -4,7 +4,9 @@
 
 ### Overview
 
-Omega uses pseudo height, $\tilde{z} = \frac{p}{\rho_0 g}$,  as the vertical coordinate ([V1 governing equation document](omega-design-governing-eqns-omega1)).
+Omega uses pseudo height, $\tilde{z} = \frac{p}{\rho_0 g}$,  as the vertical coordinate ([V1 governing equation document](omega-design-governing-eqns-omega1)),
+where $p$ is **relative pressure** (gauge pressure, i.e., absolute pressure minus the standard atmosphere of 101325 Pa).
+With this definition, $\tilde{z} = 0$ at the sea surface under standard atmospheric forcing.
 In practice, $\tilde{z}$ is not computed directly.
 Instead, the model tracks and evolves the pseudo-thickness, $\tilde{h} = \Delta \tilde{z}$, defined as the difference between adjacent layer interfaces.
 The pseudo height is essentially a normalized pressure coordinate, with the advantage that it has units of meters.
@@ -27,8 +29,8 @@ Multiple instances of the vertical coordinate class can be created and accessed
 | ------------- | ----------- | ----- |
 | NVertLayers   | maximum number of vertical layers | - |
 | NVertLayersP1 | maximum number of vertical layers plus 1 | - |
-| PressureInterface | pressure at layer interfaces | force per unit area at layer interfaces | kg m$^{-1}$ s$^{-2}$ |
-| PressureMid | pressure at layer mid points | force per unit area at layer mid point | kg m$^{-1}$ s$^{-2}$ |
+| PressureInterface | relative pressure (gauge pressure) at layer interfaces | Pa |
+| PressureMid | relative pressure (gauge pressure) at layer midpoints | Pa |
 | GeomZInterface | geometric height of layer interfaces | m |
 | GeomZMid | geometric height of layer midpoint | m |
 | GeopotentialMid | geopotential at layer mid points | m$^2$/s$^2$|

components/omega/src/ocn/Eos.h

@@ -36,8 +36,10 @@ class Teos10Eos {
 
    //   The functor takes the full arrays of specific volume (inout),
    //   the indices ICell and KChunk, and the ocean tracers (conservative)
-   //   temperature, and (absolute) salinity as inputs, and outputs the
-   //   specific volume according to the Roquet et al. 2015 75 term expansion.
+   //   temperature, (absolute) salinity, and relative pressure (gauge pressure,
+   //   i.e., absolute pressure minus the standard atmosphere) as inputs, and
+   //   outputs the specific volume according to the Roquet et al. 2015 75 term
+   //   expansion.
    KOKKOS_FUNCTION void operator()(Array2DReal SpecVol, I4 ICell, I4 KChunk,
                                    const Array2DReal &ConservTemp,
                                    const Array2DReal &AbsSalinity,
@@ -353,7 +355,9 @@ class Teos10Eos {
    }
 
    /// Calculates freezing Conservative Temperature using TEOS-10 polynomial
-   /// (polynomial error in [-5e-4, 6e-4] K, from GSW package)
+   /// (polynomial error in [-5e-4, 6e-4] K, from GSW package).
+   /// P is relative pressure (gauge pressure in Pa, i.e., absolute pressure
+   /// minus the standard atmosphere).
    KOKKOS_FUNCTION Real calcCtFreezing(const Real Sa, const Real P,
                                        const Real SaturationFract) const {
       constexpr Real Sso = 35.16504;
@@ -482,8 +486,9 @@ class Teos10BruntVaisalaFreqSq {
 
    //   The functor takes the full arrays of squared Brunt-Vaisala frequency
    //   (inout) the index ICell, and the ocean tracers (conservative)
-   //   temperature, (absolute) salinity, pressure, specific volume as inputs,
-   //   and outputs the squared Brunt-Vaisala frequency.
+   //   temperature, (absolute) salinity, relative pressure (gauge pressure,
+   //   i.e., absolute pressure minus the standard atmosphere), and specific
+   //   volume as inputs, and outputs the squared Brunt-Vaisala frequency.
    KOKKOS_FUNCTION void operator()(Array2DReal BruntVaisalaFreqSq, I4 ICell,
                                    I4 KChunk, const Array2DReal &ConservTemp,
                                    const Array2DReal &AbsSalinity,

components/omega/src/ocn/VertCoord.cpp

@@ -330,14 +330,14 @@ void VertCoord::defineFields() {
    DimNames[1] = "NVertLayersP1";
 
    auto PressureInterfaceField = Field::create(
-       PressInterfFldName,                      // field name
-       "Pressure at vertical layer interfaces", // long name or description
-       "Pa",                                    // units
-       "sea_water_pressure",                    // CF standard Name
-       0.0,                                     // min valid value
-       std::numeric_limits<Real>::max(),        // max valid value
-       NDims,                                   // number of dimensions
-       DimNames                                 // dimension names
+       PressInterfFldName,                                       // field name
+       "Relative pressure (gauge pressure) at layer interfaces", // long name
+       "Pa",                                                     // units
+       "",                               // CF standard Name
+       -AtmRefP,                         // min valid value
+       std::numeric_limits<Real>::max(), // max valid value
+       NDims,                            // number of dimensions
+       DimNames                          // dimension names
    );
 
    auto GeomZInterfaceField = Field::create(
@@ -354,14 +354,14 @@ void VertCoord::defineFields() {
    DimNames[1] = "NVertLayers";
 
    auto PressureMidField = Field::create(
-       PressMidFldName,                        // field name
-       "Pressure at vertical layer midpoints", // long name or description
-       "Pa",                                   // units
-       "sea_water_pressure",                   // CF standard Name
-       0.0,                                    // min valid value
-       std::numeric_limits<Real>::max(),       // max valid value
-       NDims,                                  // number of dimensions
-       DimNames                                // dimension names
+       PressMidFldName,                                         // field name
+       "Relative pressure (gauge pressure) at layer midpoints", // long name
+       "Pa",                                                    // units
+       "",                               // CF standard Name
+       -AtmRefP,                         // min valid value
+       std::numeric_limits<Real>::max(), // max valid value
+       NDims,                            // number of dimensions
+       DimNames                          // dimension names
    );
 
    auto GeomZMidField = Field::create(
@@ -957,11 +957,12 @@ void VertCoord::setMasks() {
 } // end setMasks()
 
 //------------------------------------------------------------------------------
-// Compute the pressure at each layer interface and midpoint given the
-// PseudoThickness and SurfacePressure. Hierarchical parallelism is used with a
-// parallel_for loop over all cells and a parallel_scan performing a prefix sum
-// in each column to compute pressure from the top-most active layer to the
-// bottom-most active layer.
+// Compute the relative pressure (gauge pressure, i.e., absolute pressure minus
+// the standard atmosphere of 101325 Pa) at each layer interface and midpoint
+// given PseudoThickness and SurfacePressure (also relative). Hierarchical
+// parallelism is used with a parallel_for loop over all cells and a
+// parallel_scan performing a prefix sum in each column from the top-most active
+// layer to the bottom-most active layer.
 void VertCoord::computePressure(
     const Array2DReal &PseudoThickness, // [in] pseudo-thickness
     const Array1DReal &SurfacePressure  // [in] surface pressure

components/omega/src/ocn/VertCoord.h

@@ -269,9 +269,12 @@ class VertCoord {
 
    /// Sums the mass thickness times g from the top layer down, starting with
    /// the surface pressure
+   /// Computes the relative pressure (gauge pressure, i.e., absolute pressure
+   /// minus the standard atmosphere) at layer interfaces and midpoints by
+   /// summing mass thickness times g from the top layer down.
    void computePressure(
        const Array2DReal &PseudoThickness, ///< [in] pseudo-thickness
-       const Array1DReal &SurfacePressure  ///< [in] surface pressure
+       const Array1DReal &SurfacePressure  ///< [in] relative surface pressure
    );
 
    /// Sum the mass thickness times specific volume from the bottom layer up,