Add Foreign Keys To Table

I'm having difficulty finding the correct syntax to modify an existing
table. The modification is to add two columns, each a foreign reference to
the two key columns of another table.

The other table:

CREATE TABLE station_type (
sta_type VARCHAR(50),
secondary_type VARCHAR(50),
natural_indic BOOL,
PRIMARY KEY (sta_type, secondary_type)
);

When I try to alter the other table to add columns:
sta_type VARCHAR(50) REFERENCES station_type(sta_type) and
secondary_type VARCHAR(50) REFERENCES station_type(secondary_type)
I get syntax errors. For example,

alter table station_information add column sta_type varchar(50) references
station_type(sta_type);
ERROR: there is no unique constraint matching given keys for referenced
table "station_type"

alter table station_information add column sta_type varchar(50) not null
references station_type(sta_type);
ERROR: there is no unique constraint matching given keys for referenced
table "station_type"

alter table station_information add column sta_type varchar(50)
unique not null references station_type(sta_type);
NOTICE: ALTER TABLE / ADD UNIQUE will create implicit index
"station_information_sta_type_key" for table "station_information"
ERROR: there is no unique constraint matching given keys for referenced
table "station_type"

Reading the alter table document page for 9.x does not show me what I'm
doing incorrectly.

Rich