diff --git a/include/aspect/postprocess/topography.h b/include/aspect/postprocess/topography.h
index 46f29389c9a..97598784ddc 100644
--- a/include/aspect/postprocess/topography.h
+++ b/include/aspect/postprocess/topography.h
@@ -65,6 +65,23 @@ namespace aspect
          * @}
          */
 
+        /**
+         * Serialize the contents of this class as far as they are not read
+         * from input parameter files.
+         */
+        template <class Archive>
+        void serialize (Archive &ar, const unsigned int version);
+
+        /**
+         * Save the state of this object.
+         */
+        void save (std::map<std::string, std::string> &status_strings) const override;
+
+        /**
+         * Restore the state of the object.
+         */
+        void load (const std::map<std::string, std::string> &status_strings) override;
+
       private:
         /**
          * Whether or not to produce text files with topography values
diff --git a/source/postprocess/topography.cc b/source/postprocess/topography.cc
index f555a391dd3..f975109125d 100644
--- a/source/postprocess/topography.cc
+++ b/source/postprocess/topography.cc
@@ -217,6 +217,44 @@ namespace aspect
 
 
 
+    template <int dim>
+    template <class Archive>
+    void Topography<dim>::serialize (Archive &ar, const unsigned int)
+    {
+      ar &last_output_time;
+    }
+
+
+
+    template <int dim>
+    void Topography<dim>::save (std::map<std::string, std::string> &status_strings) const
+    {
+      // Serialize into a stringstream. Put the following into a code
+      // block of its own to ensure the destruction of the 'oa'
+      // archive triggers a flush() on the stringstream so we can
+      // query the completed string below.
+      std::ostringstream os;
+      {
+        aspect::oarchive oa (os);
+        oa << (*this);
+      }
+
+      status_strings["Topography"] = os.str();
+    }
+
+
+
+    template <int dim>
+    void Topography<dim>::load (const std::map<std::string, std::string> &status_strings)
+    {
+      // see if something was saved
+      if (status_strings.find("Topography") != status_strings.end())
+        {
+          std::istringstream is (status_strings.find("Topography")->second);
+          aspect::iarchive ia (is);
+          ia >> (*this);
+        }
+    }
 
   }
 }