diff --git a/src/parameterizations/lateral/MOM_Zanna_Bolton.F90 b/src/parameterizations/lateral/MOM_Zanna_Bolton.F90
index d9f5412f21..60a587fe64 100644
--- a/src/parameterizations/lateral/MOM_Zanna_Bolton.F90
+++ b/src/parameterizations/lateral/MOM_Zanna_Bolton.F90
@@ -72,6 +72,7 @@ module MOM_Zanna_Bolton
   real      :: ZB_large_scale_memory_const !< The non-dimensional factor for the memory time scale
                                !! for the velocity gradients that scales the dynamical time scale [nondim]
                                !! Typical range: 1-10
+  real      :: ZB_min_memory  !< The minimum eddy memory time scale; default: 0 [T  ~> s]
   real      :: ZB_max_memory  !< The maximum eddy memory time scale; default: 1 year [T  ~> s]
   real      :: DT             !< The baroclinic model time step [T  ~> s]
 
@@ -283,6 +284,9 @@ subroutine ZB_2020_init(Time, G, GV, US, param_file, diag, CS, use_ZB2020)
   call get_param(param_file, mdl, "ZB_MAX_MEMORY", CS%ZB_max_memory, &
                  "The maximal eddy memory time. Default is 1 year", units="s", scale=US%s_to_T, &
                   default=31536000.0)
+  call get_param(param_file, mdl, "ZB_MIN_MEMORY", CS%ZB_min_memory, &
+                 "The maximal eddy memory time. Default is 0", units="s", scale=US%s_to_T, &
+                  default=0.0)
   
   call get_param(param_file, mdl, "DT", CS%dt, &
                  "The (baroclinic) dynamics time step.", units="s", scale=US%s_to_T, &
@@ -816,6 +820,7 @@ subroutine step_forward_ZB_memory(u, v, h, G, GV, CS, eddy)
         else
           tau = CS%ZB_eddy_memory
         endif
+        tau = max(tau, CS%ZB_min_memory)
         CS%ZBtau_eddy(i,j,k) = tau
 
         ! Eulerian memory with implicit time stepping
@@ -833,6 +838,7 @@ subroutine step_forward_ZB_memory(u, v, h, G, GV, CS, eddy)
         else
           tau = CS%ZB_large_scale_memory
         endif
+        tau = max(tau, CS%ZB_min_memory)
         CS%ZBtau_large_scale(i,j,k) = tau
 
         ! Eulerian memory with implicit time stepping