In aggregating climate data with satellite images for predicting crop yield, there are several models to use. Since you are using several variables and data types, I would recommend the use of the Geographically Weighted Regression (GWR). It could help you to estimate the crop yield and also quantify the corresponding climatic data required.

As defined in a cited reference, the Geographically Weighted Regression (GWR) is a spatial analysis technique that takes non-stationary variables into consideration (e.g., climate; demographic factors; physical environment characteristics) and models the local relationships between these predictors and an outcome of interest.

Please go through the attached article, I believe it would be useful .

Your concern is the period of data to be chosen. In this case for accurate prediction of crop yields data on satellite images and climatic parameters needs to be corresponding. That will depend on for how many days you want to predict the yield.

Another concern the methodology, wherein you can use the DSSAT model which allows the integration of satellite data with the climate data to improve upon the potential of yield prediction st regional scale.

Yield Forecasting and Spatial Analysis of Sunflower Productivity Using Geographic Information System

One important component for crop yield prediction is the distribution and amount of rainwater in an area over the seasons. This should be monitored carefully. For this reason I would like to recommend these data: https://gpm.nasa.gov/precip-apps. Get the data (for example as geotiff) and integrate the climate data into a long-term precipitation monitoring GIS, combined with DEM data to include orographic effects. Geologic and soil maps should be included as well as the ecologic services provided by ESRI.

You can download the Climatic data from the website for your study area, then you can applied the interpolation of your climate data, and then merging the satellite image with the interpolated layer, and find you requirements