Missing data

There are two datasets. One is the training data(290,000 observations) and the other is the testing data(60,000 observations). I need to use training data to fit a model to predict testing data. And the prediction should have 60,000 results. But both of them include a mount of missing data. If we delete all missing data, training data will still have 35,000 observations and testing data will have 15,000 observations. There is a variable rainfall. It was recorded once a week, which results in the missing data. So what should I do? Do I need to delete all missing data in training data to fit a model, then impute all missing data in testing data and use the model to predict?