grünem
Grünem is the dative singular form of the German adjective grün (green) in the strong declension. It is used when no determiner precedes the noun and the noun is masculine or neuter. In other words, grünem marks both the dative case and the absence of a determiner, agreeing with a masculine or neuter noun such as in phrases like mit grünem Gras or in grünem Kleid.
In contrast, when a definite article is present, adjectives take weak endings. For example, dem grünen Mann
Grünem commonly appears in everyday German in contexts where the noun is not preceded by a determiner
Related concepts include the contrast with the weak declension (dem grünen Mann, dem grünen Haus) and with
See also: German grammar, adjective declension, color adjectives in German.