diff --git a/ocean_only/benchmark/MOM_parameter_doc.all b/ocean_only/benchmark/MOM_parameter_doc.all
index 3cfdced781..941c826902 100644
--- a/ocean_only/benchmark/MOM_parameter_doc.all
+++ b/ocean_only/benchmark/MOM_parameter_doc.all
@@ -465,6 +465,12 @@ THICKNESS_CONFIG = "benchmark"  !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module benchmark_initialize_thickness ===
+BENCHMARK_ML_DEPTH_IC = 50.0    !   [m] default = 50.0
+                                ! Initial mixed layer depth in the benchmark test case.
+BENCHMARK_THERMOCLINE_SCALE = 500.0 !   [m] default = 500.0
+                                ! Initial thermocline depth scale in the benchmark test case.
 TS_CONFIG = "benchmark"         !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/benchmark/MOM_parameter_doc.short b/ocean_only/benchmark/MOM_parameter_doc.short
index 9f1bc2b85d..cc137e295a 100644
--- a/ocean_only/benchmark/MOM_parameter_doc.short
+++ b/ocean_only/benchmark/MOM_parameter_doc.short
@@ -199,6 +199,8 @@ THICKNESS_CONFIG = "benchmark"  !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module benchmark_initialize_thickness ===
 TS_CONFIG = "benchmark"         !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/circle_obcs/MOM_parameter_doc.all b/ocean_only/circle_obcs/MOM_parameter_doc.all
index 47d44cc930..65997dfd86 100644
--- a/ocean_only/circle_obcs/MOM_parameter_doc.all
+++ b/ocean_only/circle_obcs/MOM_parameter_doc.all
@@ -470,6 +470,9 @@ DISK_RADIUS = 24.0              !   [kilometers]
 DISK_X_OFFSET = 0.0             !   [kilometers] default = 0.0
                                 ! The x-offset of the initially elevated disk in the
                                 ! circle_obcs test case.
+DISK_IC_AMPLITUDE = 5.0         !   [m] default = 5.0
+                                ! Initial amplitude of interface height displacements
+                                ! in the circle_obcs test case.
 VELOCITY_CONFIG = "zero"        ! default = "zero"
                                 ! A string that determines how the initial velocities
                                 ! are specified for a new run:
diff --git a/ocean_only/seamount/layer/MOM_parameter_doc.all b/ocean_only/seamount/layer/MOM_parameter_doc.all
index adce9c17ba..c952c3520c 100644
--- a/ocean_only/seamount/layer/MOM_parameter_doc.all
+++ b/ocean_only/seamount/layer/MOM_parameter_doc.all
@@ -459,6 +459,9 @@ THICKNESS_CONFIG = "seamount"   !
                                 !     USER - call a user modified routine.
 MIN_THICKNESS = 0.1             !   [m] default = 0.001
                                 ! Minimum thickness for layer
+INTERFACE_IC_QUANTA = 2048.0    !   [m-1] default = 2048.0
+                                ! The granularity of initial interface height values
+                                ! per meter, to avoid sensivity to order-of-arithmetic changes.
 TS_CONFIG = "seamount"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/seamount/rho/MOM_parameter_doc.all b/ocean_only/seamount/rho/MOM_parameter_doc.all
index faf4054445..11cbff9784 100644
--- a/ocean_only/seamount/rho/MOM_parameter_doc.all
+++ b/ocean_only/seamount/rho/MOM_parameter_doc.all
@@ -586,6 +586,9 @@ THICKNESS_CONFIG = "seamount"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+INTERFACE_IC_QUANTA = 2048.0    !   [m-1] default = 2048.0
+                                ! The granularity of initial interface height values
+                                ! per meter, to avoid sensivity to order-of-arithmetic changes.
 TS_CONFIG = "seamount"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/layer/MOM_parameter_doc.all b/ocean_only/sloshing/layer/MOM_parameter_doc.all
index ec63d24eeb..36cc7c0de6 100644
--- a/ocean_only/sloshing/layer/MOM_parameter_doc.all
+++ b/ocean_only/sloshing/layer/MOM_parameter_doc.all
@@ -434,6 +434,13 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
+SLOSHING_IC_AMPLITUDE = 75.0    !   [m] default = 75.0
+                                ! Initial amplitude of sloshing internal interface height
+                                ! displacements it the sloshing test case.
+SLOSHING_IC_BUG = True          !   [Boolean] default = True
+                                ! If true, use code with a bug to set the sloshing initial conditions.
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/layer/MOM_parameter_doc.short b/ocean_only/sloshing/layer/MOM_parameter_doc.short
index 13d53ec942..93dafec728 100644
--- a/ocean_only/sloshing/layer/MOM_parameter_doc.short
+++ b/ocean_only/sloshing/layer/MOM_parameter_doc.short
@@ -190,6 +190,8 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/rho/MOM_parameter_doc.all b/ocean_only/sloshing/rho/MOM_parameter_doc.all
index 64b2600cb4..2a4116393a 100644
--- a/ocean_only/sloshing/rho/MOM_parameter_doc.all
+++ b/ocean_only/sloshing/rho/MOM_parameter_doc.all
@@ -563,6 +563,13 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
+SLOSHING_IC_AMPLITUDE = 75.0    !   [m] default = 75.0
+                                ! Initial amplitude of sloshing internal interface height
+                                ! displacements it the sloshing test case.
+SLOSHING_IC_BUG = True          !   [Boolean] default = True
+                                ! If true, use code with a bug to set the sloshing initial conditions.
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/rho/MOM_parameter_doc.short b/ocean_only/sloshing/rho/MOM_parameter_doc.short
index 984c372756..23578b408c 100644
--- a/ocean_only/sloshing/rho/MOM_parameter_doc.short
+++ b/ocean_only/sloshing/rho/MOM_parameter_doc.short
@@ -237,6 +237,8 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/z/MOM_parameter_doc.all b/ocean_only/sloshing/z/MOM_parameter_doc.all
index b530a4f5aa..992b9c3723 100644
--- a/ocean_only/sloshing/z/MOM_parameter_doc.all
+++ b/ocean_only/sloshing/z/MOM_parameter_doc.all
@@ -517,6 +517,13 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
+SLOSHING_IC_AMPLITUDE = 75.0    !   [m] default = 75.0
+                                ! Initial amplitude of sloshing internal interface height
+                                ! displacements it the sloshing test case.
+SLOSHING_IC_BUG = True          !   [Boolean] default = True
+                                ! If true, use code with a bug to set the sloshing initial conditions.
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run:
diff --git a/ocean_only/sloshing/z/MOM_parameter_doc.short b/ocean_only/sloshing/z/MOM_parameter_doc.short
index 2f269deff8..e225ebc8cb 100644
--- a/ocean_only/sloshing/z/MOM_parameter_doc.short
+++ b/ocean_only/sloshing/z/MOM_parameter_doc.short
@@ -213,6 +213,8 @@ THICKNESS_CONFIG = "sloshing"   !
                                 !     soliton - Equatorial Rossby soliton.
                                 !     rossby_front - a mixed layer front in thermal wind balance.
                                 !     USER - call a user modified routine.
+
+! === module sloshing_initialization ===
 TS_CONFIG = "sloshing"          !
                                 ! A string that determines how the initial tempertures
                                 ! and salinities are specified for a new run: