Feature/skewness

manual/eqs/output.tex

@@ -310,6 +310,10 @@ \subsection{~Output parameters} \label{sub:outpars}
       \begin{equation} Q_{kk} = \frac{1}{E^2} \int_0^{f_{NK}} \int_0^{2\pi} 
       0.5 \left[ A(k,\theta)+ A(k,\theta+\pi)\right]^2 \frac{\sigma^2}{k C_g} \:\rd \theta  \: \rd  \sigma \: \label{eq:qkk}
       \end{equation}
+\item \textbf{SKW}  Skewness of surface elevation sampled at zero slope. This is the $\lambda_1$ parameter defined in \cite{Barrick&Lipa1985} or $\lambda_{3,0,0}$ in \cite{Srokosz1986}. It is computed from the second order correction to the surface elevation, using ECWAM code by P. Janssen.
+\item \textbf{EMB} this is  $-\gamma/8 = -(\lambda_{1,2,0}+\lambda_{1,0,2}-2 \lambda{0,1,1} \lambda{1,1,1})/8 (1-\lambda_{0,1,1]^2)$, such that the mean sea level of points with zero slope 
+is EMB$\times H_s$.
+\item \textbf{EMC} this is hte additional tracker bias coefficient equal to  $-\lambda_{3,0,0}/24$, which is specific to the choice of retracker, see the $J_z$ function in \cite{DeCarlo&Ardhuin2024}.
 \end{list}
 
 \item{Numerical diagnostics }

manual/manual.bib

@@ -3760,3 +3760,13 @@ @PHDTHESIS{Gagnaire-Renou2009
    year = 2010,
 }
 
+@ARTICLE{Srokosz1986,
+   author = "Meric A. Srokosz",
+   title = "On the joint distribution of surface elevation and slopes for a non linear random sea, with an application to radar altimetry",
+   journal = JGR,
+   volume = 91,
+   pages = "995--1006",
+   year = 1986,
+   keywords={altimeter;sea state bias},
+}
+

model/inp/ww3_ounf.inp

@@ -16,7 +16,7 @@ $ DPT CUR WND AST WLV ICE IBG TAU RHO D50 IC1 IC5 HS LM T02 T0M1 T01 FP
 $ DIR SPR DP HIG EF TH1M STH1M TH2M STH2M WN PHS PTP PLP PDIR PSPR PWS PDP
 $ PQP PPE PGW PSW PTM10 PT01 PT02 PEP TWS PNR UST CHA CGE FAW TAW TWA WCC
 $ WCF WCH WCM SXY TWO BHD FOC TUS USS P2S USF P2L TWI FIC ABR UBR BED
-$ FBB TBB MSS MSC DTD FC CFX CFD CFK U1 U2 WNM TOC
+$ FBB TBB MSS MSC DTD FC CFX CFD CFK U1 U2 WNM TOC MSS QP QKK SKW EMB EMC
 $
  N
  DPT HS FP T01

model/inp/ww3_shel.inp

@@ -212,10 +212,13 @@ $        8                          Spectrum parameters
 $   -------------------------------------------------
 $  F  F  8     1   MSS[X,Y]   MSS   Mean square slopes
 $  F  F  8     2   MSC[X,Y]   MSC   Spectral level at high frequency tail
-!  F  F  8     3   MSSD       MSD   Slope direction
-!  F  F  8     4   MSCD       MCD   Tail slope direction
-!  F  F  8     5   QP         QP    Goda peakedness parameter
-!  F  F  8     6   QKK        QKK   Wavenumber peakedness
+$  F  F  8     3   MSSD       MSD   Slope direction
+$  F  F  8     4   MSCD       MCD   Tail slope direction
+$  F  F  8     5   QP         QP    Goda peakedness parameter
+$  F  F  8     6   QKK        QKK   Wavenumber peakedness
+$  F  F  8     7   SKEW       SKW   Skewness of elevation for zero slopes
+$  F  F  8     8   EMBIA1     EMB   Mean sea level at zero slopes / Hs
+$  F  F  8     9   EMBIA2     EMC   Tracker bias for LRM least square altimetry
 $   -------------------------------------------------
 $        9                          Numerical diagnostics
 $   -------------------------------------------------

model/nml/ww3_ounf.nml

@@ -14,7 +14,7 @@
 !  UST CHA CGE FAW TAW TWA WCC WCF WCH WCM FWS
 !  SXY TWO BHD FOC TUS USS P2S USF P2L TWI FIC TOC
 !  ABR UBR BED FBB TBB
-!  MSS MSC WL02 AXT AYT AXY
+!  MSS MSC MSD MCD QP QKK SKW EMB EMC
 !  DTD FC CFX CFD CFK
 !  U1 U2
 !

model/nml/ww3_shel.nml

@@ -206,6 +206,9 @@
 !  F  F  8     4   MSCD       MCD   Tail slope direction
 !  F  F  8     5   QP         QP    Goda peakedness parameter
 !  F  F  8     6   QKK        QKK   Wavenumber peakedness
+!  F  F  8     7   SKEW       SKW   Skewness of elevation for zero slopes
+!  F  F  8     8   EMBIA1     EMB   Mean sea level at zero slopes / Hs 
+!  F  F  8     9   EMBIA2     EMC   Tracker bias for LRM least square altimetry
 !   -------------------------------------------------
 !        9                          Numerical diagnostics
 !   -------------------------------------------------

model/src/w3adatmd.F90

@@ -188,6 +188,7 @@ MODULE W3ADATMD
   !      MSCD      R.A.  Public   Direction of MSCX
   !      QP        R.A.  Public   Goda peakedness parameter.
   !      QKK       R.A.  Public   Spectral bandwidth (De Carlo et al. 2023)
+  !      SKEW      R.A.  Public   skewness lambda_3,0,0 (Srokosz 1986)
   !
   !      DTDYN     R.A.  Public   Mean dynamic time step (raw).
   !      FCUT      R.A.  Public   Cut-off frequency for tail.
@@ -475,9 +476,10 @@ MODULE W3ADATMD
     ! Output fields group 8)
     !
     REAL, POINTER         ::  MSSX(:),  MSSY(:),  MSSD(:),        &
-         MSCX(:),  MSCY(:),  MSCD(:), QKK(:)
+         MSCX(:),  MSCY(:),  MSCD(:), QKK(:), SKEW(:), EMBIA1(:), EMBIA2(:)
     REAL, POINTER         ::  XMSSX(:), XMSSY(:), XMSSD(:),       &
-         XMSCX(:), XMSCY(:), XMSCD(:), XQKK(:)
+         XMSCX(:), XMSCY(:), XMSCD(:), XQKK(:),                   &
+         XSKEW(:), XEMBIA1(:), XEMBIA2(:)    
     !
     ! Output fields group 9)
     !
@@ -613,7 +615,7 @@ MODULE W3ADATMD
        BEDFORMS(:,:), PHIBBL(:), TAUBBL(:,:)
   !
   REAL, POINTER           :: MSSX(:), MSSY(:), MSSD(:),           &
-       MSCX(:), MSCY(:), MSCD(:), QKK(:)
+       MSCX(:), MSCY(:), MSCD(:), QKK(:), SKEW(:), EMBIA1(:), EMBIA2(:)
   !
   REAL, POINTER           :: DTDYN(:), FCUT(:), CFLXYMAX(:),      &
        CFLTHMAX(:), CFLKMAX(:)
@@ -1265,7 +1267,9 @@ SUBROUTINE W3DIMA  ( IMOD, NDSE, NDST, D_ONLY )
     ALLOCATE ( WADATS(IMOD)%MSSX(NSEALM), WADATS(IMOD)%MSSY(NSEALM), &
          WADATS(IMOD)%MSCX(NSEALM), WADATS(IMOD)%MSCY(NSEALM), &
          WADATS(IMOD)%MSSD(NSEALM), WADATS(IMOD)%MSCD(NSEALM), &
-         WADATS(IMOD)%QKK(NSEALM), STAT=ISTAT )
+         WADATS(IMOD)%QKK(NSEALM), WADATS(IMOD)%SKEW(NSEALM),  &
+         WADATS(IMOD)%EMBIA1(NSEALM), WADATS(IMOD)%EMBIA2(NSEALM),  &
+              STAT=ISTAT )
     CHECK_ALLOC_STATUS ( ISTAT )
     !
     WADATS(IMOD)%MSSX   = UNDEF
@@ -1275,6 +1279,9 @@ SUBROUTINE W3DIMA  ( IMOD, NDSE, NDST, D_ONLY )
     WADATS(IMOD)%MSCY   = UNDEF
     WADATS(IMOD)%MSCD   = UNDEF
     WADATS(IMOD)%QKK    = UNDEF
+    WADATS(IMOD)%SKEW   = UNDEF
+    WADATS(IMOD)%EMBIA1 = UNDEF
+    WADATS(IMOD)%EMBIA2 = UNDEF
     call print_memcheck(memunit, 'memcheck_____:'//' W3DIMA 8')
     !
     ! 9) Numerical diagnostics
@@ -2281,6 +2288,24 @@ SUBROUTINE W3XDMA  ( IMOD, NDSE, NDST, OUTFLAGS )
       ALLOCATE ( WADATS(IMOD)%XQKK(1) )
     END IF
     !
+    IF ( OUTFLAGS( 8,  7) ) THEN
+      ALLOCATE ( WADATS(IMOD)%XSKEW(NXXX) )
+    ELSE
+      ALLOCATE ( WADATS(IMOD)%XSKEW(1) )
+    END IF
+    !
+    IF ( OUTFLAGS( 8,  8) ) THEN
+      ALLOCATE ( WADATS(IMOD)%XEMBIA1(NXXX) )
+    ELSE
+      ALLOCATE ( WADATS(IMOD)%XEMBIA1(1) )
+    END IF
+    !
+    IF ( OUTFLAGS( 8,  9) ) THEN
+      ALLOCATE ( WADATS(IMOD)%XEMBIA2(NXXX) )
+    ELSE
+      ALLOCATE ( WADATS(IMOD)%XEMBIA2(1) )
+    END IF
+    !
     WADATS(IMOD)%XMSSX   = UNDEF
     WADATS(IMOD)%XMSSY   = UNDEF
     WADATS(IMOD)%XMSSD   = UNDEF
@@ -2289,6 +2314,9 @@ SUBROUTINE W3XDMA  ( IMOD, NDSE, NDST, OUTFLAGS )
     WADATS(IMOD)%XMSCD   = UNDEF
     WADATS(IMOD)%XQP(1)  = UNDEF
     WADATS(IMOD)%XQKK    = UNDEF
+    WADATS(IMOD)%XSKEW   = UNDEF
+    WADATS(IMOD)%XEMBIA1 = UNDEF
+    WADATS(IMOD)%XEMBIA2 = UNDEF
     !
     IF ( OUTFLAGS( 9, 1) ) THEN
       ALLOCATE ( WADATS(IMOD)%XDTDYN(NXXX), STAT=ISTAT )
@@ -2903,6 +2931,9 @@ SUBROUTINE W3SETA ( IMOD, NDSE, NDST )
       MSCY   => WADATS(IMOD)%MSCY
       MSCD   => WADATS(IMOD)%MSCD
       QKK    => WADATS(IMOD)%QKK
+      SKEW   => WADATS(IMOD)%SKEW
+      EMBIA1  => WADATS(IMOD)%EMBIA1
+      EMBIA2  => WADATS(IMOD)%EMBIA2
       !
       DTDYN    => WADATS(IMOD)%DTDYN
       FCUT     => WADATS(IMOD)%FCUT
@@ -3242,6 +3273,9 @@ SUBROUTINE W3XETA ( IMOD, NDSE, NDST )
       MSCY   => WADATS(IMOD)%XMSCY
       MSCD   => WADATS(IMOD)%XMSCD
       QKK    => WADATS(IMOD)%XQKK
+      SKEW   => WADATS(IMOD)%XSKEW
+      EMBIA1 => WADATS(IMOD)%XEMBIA1
+      EMBIA2 => WADATS(IMOD)%XEMBIA2
       !
       DTDYN    => WADATS(IMOD)%XDTDYN
       FCUT     => WADATS(IMOD)%XFCUT

model/src/w3initmd.F90

@@ -2150,7 +2150,7 @@ SUBROUTINE W3MPIO ( IMOD )
          STMAXE, STMAXD, HMAXE, HCMAXE, HMAXD,     &
          HCMAXD, QP, PTHP0, PQP, PPE, PGW, PSW,    &
          PTM1, PT1, PT2, PEP, WBT, CX, CY,         &
-         TAUOCX, TAUOCY, WNMEAN, QKK
+         TAUOCX, TAUOCY, WNMEAN, QKK, SKEW, EMBIA1, EMBIA2
 #endif
 
 #ifdef W3_MPI
@@ -3406,6 +3406,48 @@ SUBROUTINE W3MPIO ( IMOD )
 #ifdef W3_MPIT
           WRITE (NDST,9011) IH, ' 8/06', IROOT, IT, IRQGO(IH), IERR
 #endif
+#ifdef W3_MPI
+        END IF
+#endif
+        !
+#ifdef W3_MPI
+        IF ( FLGRDALL( 8, 7) ) THEN
+          IH     = IH + 1
+          IT     = IT + 1
+          CALL MPI_SEND_INIT (SKEW (1),NSEALM , MPI_REAL, IROOT,   &
+               IT, MPI_COMM_WAVE, IRQGO(IH), IERR)
+#endif
+#ifdef W3_MPIT
+          WRITE (NDST,9011) IH, ' 8/07', IROOT, IT, IRQGO(IH), IERR
+#endif
+#ifdef W3_MPI
+        END IF
+#endif
+        !
+#ifdef W3_MPI
+        IF ( FLGRDALL( 8, 8) ) THEN
+          IH     = IH + 1
+          IT     = IT + 1
+          CALL MPI_SEND_INIT (EMBIA1  (1),NSEALM , MPI_REAL, IROOT,   &
+               IT, MPI_COMM_WAVE, IRQGO(IH), IERR)
+#endif
+#ifdef W3_MPIT
+          WRITE (NDST,9011) IH, ' 8/08', IROOT, IT, IRQGO(IH), IERR
+#endif
+#ifdef W3_MPI
+        END IF
+#endif
+        !
+#ifdef W3_MPI
+        IF ( FLGRDALL( 8, 9) ) THEN
+          IH     = IH + 1
+          IT     = IT + 1
+          CALL MPI_SEND_INIT (EMBIA2 (1),NSEALM , MPI_REAL, IROOT,   &
+               IT, MPI_COMM_WAVE, IRQGO(IH), IERR)
+#endif
+#ifdef W3_MPIT
+          WRITE (NDST,9011) IH, ' 8/09', IROOT, IT, IRQGO(IH), IERR
+#endif
 #ifdef W3_MPI
         END IF
 #endif
@@ -4653,6 +4695,48 @@ SUBROUTINE W3MPIO ( IMOD )
 #ifdef W3_MPIT
             WRITE (NDST,9011) IH, ' 8/06', IFROM, IT, IRQGO2(IH), IERR
 #endif
+#ifdef W3_MPI
+          END IF
+#endif
+          !
+#ifdef W3_MPI
+          IF ( FLGRDALL( 8, 7) ) THEN
+            IH     = IH + 1
+            IT     = IT + 1
+            CALL MPI_RECV_INIT (SKEW  (I0),1,WW3_FIELD_VEC, IFROM, IT,  &
+                 MPI_COMM_WAVE, IRQGO2(IH), IERR )
+#endif
+#ifdef W3_MPIT
+            WRITE (NDST,9011) IH, ' 8/07', IFROM, IT, IRQGO2(IH), IERR
+#endif
+#ifdef W3_MPI
+          END IF
+#endif
+          !
+#ifdef W3_MPI
+          IF ( FLGRDALL( 8, 8) ) THEN
+            IH     = IH + 1
+            IT     = IT + 1
+            CALL MPI_RECV_INIT (EMBIA1 (I0),1,WW3_FIELD_VEC, IFROM, IT,  &
+                 MPI_COMM_WAVE, IRQGO2(IH), IERR )
+#endif
+#ifdef W3_MPIT
+            WRITE (NDST,9011) IH, ' 8/08', IFROM, IT, IRQGO2(IH), IERR
+#endif
+#ifdef W3_MPI
+          END IF
+#endif
+          !
+#ifdef W3_MPI
+          IF ( FLGRDALL( 8, 9) ) THEN
+            IH     = IH + 1
+            IT     = IT + 1
+            CALL MPI_RECV_INIT (EMBIA2  (I0),1,WW3_FIELD_VEC, IFROM, IT,  &
+                 MPI_COMM_WAVE, IRQGO2(IH), IERR )
+#endif
+#ifdef W3_MPIT
+            WRITE (NDST,9011) IH, ' 8/09', IFROM, IT, IRQGO2(IH), IERR
+#endif
 #ifdef W3_MPI
           END IF
 #endif