Important: Added new vertical stretching functional

[arango]

Added new vertical stretching option, Vstretching=5, based on a quadratic Legendre polynomial function that allows higher resolution near the surface developed by Souza et al. (2015). Many thanks to Joao Sousa and Brian Powell for coding and testing this new vertical stretching. For more documentation, please check ​WikiROMS or the publication reference.

• The new vertical stretching functional is coded in set_scoord.F:

  !
  !----------------------------------------------------------------------
  ! Stretching 5 case using a quadratic Legendre polynomial function
  ! aproach for the s-coordinate to enhance the surface exchange layer.
  !
  ! J. Souza, B.S. Powell, A.C. Castillo-Trujillo, and P. Flament, 2015:
  !   The Vorticity Balance of the Ocean Surface in Hawaii from a
  !   Regional Reanalysis.'' J. Phys. Oceanogr., 45, 424-440.
  !
  ! Added by Joao Marcos Souza - SOEST - 05/07/2012.
  !-----------------------------------------------------------------------
  !
        ELSE IF (Vstretching(ng).eq.5) THEN
          SCALARS(ng)%sc_w(N(ng))=0.0_r8
          SCALARS(ng)%Cs_w(N(ng))=0.0_r8
          DO k=N(ng)-1,1,-1
            rk=REAL(k,r8)
            rN=REAL(N(ng),r8)
            sc_w=-(rk*rk - 2.0_r8*rk*rN + rk + rN*rN - rN)/(rN*rN - rN)-  &
                 0.01_r8*(rk*rk - rk*rN)/(1.0_r8 - rN)
            SCALARS(ng)%sc_w(k)=sc_w
            IF (theta_s(ng).gt.0.0_r8) THEN
              Csur=(1.0_r8-COSH(theta_s(ng)*sc_w))/                       &
       &           (COSH(theta_s(ng))-1.0_r8)
            ELSE
              Csur=-sc_w**2
            END IF
            IF (theta_b(ng).gt.0.0_r8) THEN
              Cbot=(EXP(theta_b(ng)*Csur)-1.0_r8)/                        &
       &           (1.0_r8-EXP(-theta_b(ng)))
              SCALARS(ng)%Cs_w(k)=Cbot
            ELSE
              SCALARS(ng)%Cs_w(k)=Csur
            END IF
          END DO
          SCALARS(ng)%sc_w(0)=-1.0_r8
          SCALARS(ng)%Cs_w(0)=-1.0_r8
  !
          DO k=1,N(ng)
            rk=REAL(k,r8)-0.5_r8
            rN=REAL(N(ng),r8)
            sc_r=-(rk*rk - 2.0_r8*rk*rN + rk + rN*rN - rN)/(rN*rN - rN)-  &
                 0.01_r8*(rk*rk - rk*rN)/(1.0_r8 - rN)
            SCALARS(ng)%sc_r(k)=sc_r
            IF (theta_s(ng).gt.0.0_r8) THEN
              Csur=(1.0_r8-COSH(theta_s(ng)*sc_r))/                       &
       &           (COSH(theta_s(ng))-1.0_r8)
            ELSE
              Csur=-sc_r**2
            END IF
            IF (theta_b(ng).gt.0.0_r8) THEN
              Cbot=(EXP(theta_b(ng)*Csur)-1.0_r8)/                        &
       &           (1.0_r8-EXP(-theta_b(ng)))
              SCALARS(ng)%Cs_r(k)=Cbot
            ELSE
              SCALARS(ng)%Cs_r(k)=Csur
            END IF
          END DO
        END IF
  

  The new functional is similar to Vstretching=4, but with a quadratic instead or linearly varying fractional vertical coordinate, s.

• The Matlab scripts stretching.m, set_depth.m, and scoord.m were updated with the new vertical stretching option. The difference between Vstretchin=4 and Vstretching=5 is illustrated below.

For Vtransform=2 and Vstretching=4, we get almost 4 vertical levels in the top 50 m:

Contrarily, with Vtransform=2 and Vstretching=5, we double the number of vertical levels to 8 in the top 50 m:

Notice that the increased vertical resolution at the near-surface causes a loss of resolution at the bottom.

• All the input ocean_*.in scripts were modified to update the documentation about Vstretching.

---

Reference:

Souza, J. M., B. Powell, A. C. Castillo-Trujillo, and P. Flament, 2015: The Vorticity Balance of the Ocean Surface in Hawaii from a Regional Reanalysis, J. Phys. Oceanogr., 45, 424-440, doi:10.1175/JPO-D-14-0074.1.