The Jiazi 甲子and Bingyin丙寅 and Jimao 己卯 days are the, first, third, and 16th days of the sexagenary cycle used by the chinese to mark days. These rhymes, taken from the 正福堂 almanac published in Taiwan, allow you to predict the climate for the season from the weather on each of these days. The Jiazi rhyme is certainly very old-- it is collected in the Complete Poems of the Tang
1- 甲子日雨占Judgments on rain on Jiazi days.
春甲子雨，赤地千里。夏甲子雨，搖船入市；
秋甲子雨，禾生兩耳。冬甲子雨，牛羊凍死；
If it rains on a Jiazi day in Spring; scarlet earth for a thousand miles
If it rains on a Jiazi day in summer, boats will be rowed into market.
If it rains on a Jiazi day in autumn, the rice will generate two ears.
If it rains on a Jiazi day in winter, cows and goats will freeze to death。
(note. The version in the Quan Tang Shi is translated below. it has minor differences with the above https://zh.wikisource.org/zh-hant/占四時甲子雨. the poem notably has an extra line
春雨甲子，赤地千里。夏雨甲子，乘船入市。
秋雨甲子，禾頭生耳。冬雨甲子，牛羊凍死。
鵲巢下地，其年大水。
If it rains on a Jiazi day in Spring; scarlet earth for a thousand miles
If it rains on a Jiazi day in Summer, boats will be rowed into market.
If it rains on a Jiazi day in autumn, the rice will generate ears.
If it rains on a Jiazi day in winter, cows and goats will freeze to death。
If magpies nest on the ground, a great flood that year.
- 丙寅晴占 Judgments on a clear Bing Yin day
春丙寅晴，無水散秧。夏丙寅晴，乾死禾糧。
秋丙寅晴，晒穀上倉。冬丙寅晴，無雪無霜。
A clear Bingyin day in spring, there will be no water , and few seedlings of rice
A clear Bingyin day in summer, rice and cereals dry up and die
A clear Bingyin day in autumn, grains [will] be dried and laid up for storage
A clear Bingyin day in Winter, neither rain nor frost
- 己卯風占 Judgments on a Windy Jimao Day
春己卯風，樹上空。夏己卯風，禾頭空。
秋己卯風，水裡空。冬己卯風，欄裡空。
Wind on a Jimao day in spring, the tops of trees empty
Wind on a Jimao day in summer, the tops of rice empty.
Wind on a Jimao day in Autumn, water empty
Wind on a Jimao day in Winter, the shed empty