Ṛtu (Ritu) is one of the names of God Śiva (Siva) as described in Śivasahasranāmastotra (Sivasahasranamastotra; The Hymn of Thousand Names of Siva). In this śloka (sloka; verse) of Śivasahasranamastotra, such names of Śiva as Ṛtu(Ritu; Season), Saṁvatsara (Samvatsara; Year), Māsa(Masa; Month) Pakṣa(Paksha; Fortnight) — have been uttered all together. God Śiva is the manifestation of Kāla (Kala; the cosmic concept of Time); hence He is also known as Mahākāla. We divide that infinite and endless Time in small units like Ṛtu, Saṁvatsara, Māsa, Pakṣa and the like. Amongst these, Ṛtu is such an unit that is determined not only through the movement of the sun and the moon, but also according to the changes of climate consequently. Since Mahādeva(Kala) is the manifestation of Kāla, He is also embodied through thses units of Time — in this regard, He is also known as Ṛtu —
ṛtuḥ, samvatsaraḥ, māsaḥ, pakṣaḥ
sankhyāsamāpanaḥ ṛtvādi sankhyāsamaptirūpaḥ.
In Mahānārāyaṇopaniṣada (Mahanarayanopanishada), all measuring units of time — kalā, muhūrta, kāṣṭhā, ahorātra, ardhamāsa, pakṣa, māsa, saṁvatsara, ṛtu– are conceptualised as the manifestations of God Viṣṇu-Nārāyaṇa (Vishnu-Narayana)–
sarve nimeṣā jajñire vidytaḥ puruṣādadhi
kala muhurtāḥ kāṣṭhāścāhorāśca sarvaśaḥ.
ardhamāsā māsā ṛtavaḥ saṃvatsarasca kalpatam
sa āpaḥ pradughe ubhe ime antarīkṣamatho suvaḥ.
In the thought of Upaniṣad (Upanishad) , the Supreme Self is sometimes conceptualised as Viṣṇu, and sometimes as Rudra. Rudra-Śiva and Viṣṇu are One. So these units of measuring Kāla, are attributed to God Śiva, as His names, as mentioned in Śivasahasranāmastotra.
Mahanarayanopanisad (Jacob) 1.8-9.