Are there interdisciplinary sciences which combine earth sciences (like geophysics, climatology, meteorology etc.) and computer science? or something like biotechnology which combine biology with several fields.
Pretty much all Earth Sciences combine deeply with computer sciences. In many areas where the underlying physical phenomena are not well understood, machine learning is often used, and numerical models are a very common tool in pretty much all fields in Earth Sciences.
I think some notable examples where Earth Science is working side by side with leading edge computer sciences are large scale numerical models. A large fraction of the work done by today's larger supercomputers is running atmospheric models for weather forecasting. Similar models are often run also for reanalysis of historic climate, long term climate evolution, oceanic currents, models of Earth's core and its magnetic field, mantle convection, and the list could go on and on.
Inverse modelling and tomography are also areas were leading edge computer sciences are applied to Earth Science problems. Such as reconstructing the structure of earth interior from seismic tomography, inverting for the basal conditions of glaciers, or in a more applied field; electric, seismic and magnetic tomograhies to find minerals and oil.
It terms of formally mixed fields, you can think of many, starting from my own field: Geophysics, where physics is used to understand the Earth system. Although, many geophysicist work in Planetary Sciences, where the same methods are applied to other bodies beside the Earth, of course they work shoulder to shoulder with astronomers and space scientists. And like that, there are many others, like Geochemistry, Biogeochemistry, Geomicrobiology, Biogeography, Chemical oceanography, and many others.