Map from Google - Incheon

In Incheon, Korean city, located in the northwest of the country, on the coast of the Yellow Sea and a short distance from the capital Seoul, the climate is continental, with cold but sunny winters, and hot, sultry and rainy summers, though tempered by the breeze. Like the rest of Korea the city is affected by the monsoon circulation: in winter the northwest cold currents will prevail, while in summer they will be replaced by the hot and humid currents of tropical origin. Spring and autumn are transitional periods, mild and pleasant, especially the month of October.
The climate is very similar to that of Seoul, although it is a bit milder (less cold in winter, less hot but more humid in summer), and less rainy, because of the location on the coast. For example, in January 2011 in Seoul the temperature has dropped down to -18 °C, in Incheon to -15 °C; in January 2016 it dropped to -18 °C in Seoul and -16 °C in Incheon; in August 2016 it reached 36.6 °C in Seoul and 34 °C in Incheon.
Here are the average temperatures.
Average temperatures - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDec
IncheonJFMAMJJASOND
Min (°C)-5-3281318222218114-3
Max (°C)241016212528292620125

In winter the average temperature is around freezing or a few degrees below; sunshine is quite common, and a cold wind blows from the Asian continent. On colder periods, the temperature remains below freezing during the day; in the worst moments the temperature can drop to -15 °C or below.
Although winter is a dry season, sometimes it can snow.
In winter and especially in spring (March to May, which is called yellow dust season) the city can be reached by yellow dust (HwangSa in Korean), coming from the desert of Mongolia and China (but in truth there is also a contribution given by local pollution), which forms a characteristic haze and brings breathing problems and eye irritation.
Spring is mild, but the rains increase gradually. The rainiest season, however, is summer, because the summer monsoon: from June to August, more than 700 millimetres of rain fall. The rains can sometimes be torrential. The worst month, the wettest and least sunny, is generally July. In summer there can also be periods of good weather, in which it can be very hot, with highs about 35 °C.
In Autumn, rainfall decreases, and by October the rains are quite rare. Here is the average precipitation.
Average precipitation - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDecYear
IncheonJFMAMJJASONDY
Prec. (mm)202040601001103202851555550201235
Days757791015128687102

In August, September and early October (more rarely in July), Incheon can be affected by typhoons, tropical cyclones of South-East Asia, although this area of Korea is less exposed than the southern coast.

Songdo

The amount of sunshine in Incheon is decent in winter, and also in spring and autumn (although lower than in the southern part of the country, as in Busan), and reaches its minimum in July, when cloudy skies prevail (the sunshine amount goes down to 35 %), because of the summer monsoon.

In Incheon, the sea is very cold in winter, but it warms up a lot in summer, reaching 24 °C in August.
Sea temperature - Incheon
IncheonJanFebMarAprMayJunJulAugSepOctNovDec
IncheonJFMAMJJASOND
Sea (°C)5558131722242319149