diff --git a/src/Z4c/z4c.cpp b/src/Z4c/z4c.cpp
index 54de10f3..e134a87f 100644
--- a/src/Z4c/z4c.cpp
+++ b/src/Z4c/z4c.cpp
@@ -68,11 +68,19 @@ std::shared_ptr<StateDescriptor> Initialize(ParameterInput *pin) {
   Metadata m_constraint_vector({Metadata::Cell, Metadata::Metadata::Derived, Metadata::OneCopy}, std::vector<int>{3});
   z4c->AddField<constraint::H>(m_constraint_scalar);
   z4c->AddField<constraint::M>(m_constraint_vector);
+  z4c->AddField<constraint::Z>(m_constraint_scalar);
 
+  Metadata m_evolution_scalar({Metadata::Cell, Metadata::Metadata::Derived, Metadata::OneCopy});
+  Metadata m_evolution_vector({Metadata::Cell, Metadata::Metadata::Derived, Metadata::OneCopy}, std::vector<int>{3});
   Metadata m_evolution_rank2({Metadata::Cell, Metadata::Metadata::Derived, Metadata::OneCopy}, std::vector<int>{3,3});
-  z4c->AddField<evolution::At>(m_evolution_rank2);
- 
-  
+  z4c->AddField<evolution_z4c::chi>(m_evolution_scalar);
+  z4c->AddField<evolution_z4c::g>(m_evolution_rank2);
+  z4c->AddField<evolution_z4c::Khat>(m_evolution_scalar);
+  z4c->AddField<evolution_z4c::A>(m_evolution_rank2);
+  z4c->AddField<evolution_z4c::Gam>(m_evolution_vector);
+  z4c->AddField<evolution_z4c::Theta>(m_evolution_scalar);
+  z4c->AddField<evolution_z4c::alpha>(m_evolution_scalar);
+  z4c->AddField<evolution_z4c::beta>(m_evolution_vector);
 
   return z4c
 }
diff --git a/src/Z4c/z4c.hpp b/src/Z4c/z4c.hpp
index 710f85f2..585169f6 100644
--- a/src/Z4c/z4c.hpp
+++ b/src/Z4c/z4c.hpp
@@ -17,11 +17,11 @@ Breif: General header for Z4c formulation
        Bernuzzi & Hilditch (2010) and Hilditch et al. (2013).
        The Z4c system is comprised of dynamical variable:
        chi: Conformal factor (scalar)
-       gt : Induced 3-metric (rank-2)
-       Kh : Trace of extrinsic curvature (scalar)
-       At : Traceless of extrinsic curvature (rank-2)
+       g : Induced 3-metric (rank-2)
+       Khat : Trace of extrinsic curvature (scalar)
+       A : Traceless of extrinsic curvature (rank-2)
        Theta : Temporal projection of Z4 vector (scalar)
-       Gt : Conformaly-related function (3-vector)
+       Gam : Conformaly-related function (3-vector)
 
        In addtion, we follow typical gauge choice:
        Bona-Masso for lapse, alpha (scalar) \TODO :maybe 1+log?
@@ -49,15 +49,35 @@ Author : Hyun Lim
 
 namespace z4c { // fix consistencty with namespace everywhere
   namespace constraint{
-  VARIABLE(z4c.c, H);
-  VARIABLE(z4c.c, M);
+  VARIABLE(z4c.c, H); // Hamiltoninan constraint
+  VARIABLE(z4c.c, M); // Momentum constraint
+  VARIABLE(z4c.c, Z); // Z-vector constraint
   } // constraint
-  namespace evolution{
-  VARIABLE(z4c.c, At);
-  } // evolution
+  namespace evolution_z4c{
+  VARIABLE(z4c.c, chi); // Conformal factor
+  VARIABLE(z4c.c, g); // Induced 3 metric
+  VARIABLE(z4c.c, Khat); // Trace of extrinsic curvature
+  VARIABLE(z4c.c, A); // Traceless of extrinsic curvature
+  VARIABLE(z4c.c, Gam); // Conformally related function 
+  VARIABLE(z4c.c, Theta); // Temporal projection of Z4 vector
+  VARIABLE(z4c.c, alpha); // Lapse
+  VARIABLE(z4c.c, beta); // Shift
+  } // evolution_z4c
+  namespace evolution_adm{
+  VARIABLE(z4c.c, g); // Induced 3 metric
+  VARIABLE(z4c.c, K); // Extrinsic curvature
+  VARIABLE(z4c.c, psi); // Psi scalar function
+  } // evolution_adm
+  namespace matter_source{ // TODO : this is not really the varialbe. We may not want them as like this
+  VARIABLE(z4c.c, rho); 
+  VARIABLE(z4c.c, Si); 
+  VARIABLE(z4c.c, Sij);
+  } // matter_source
 
-// Prototype for package init
-std::shared_ptr<parthenon::StateDescriptor> Initialize(ParameterInput *pin);
+  // TODO: add psi4 for GW extraction
+
+  // Prototype for package init
+  std::shared_ptr<parthenon::StateDescriptor> Initialize(ParameterInput *pin);
 
 } // z4c