If we can’t accurately predict the weather next week, how can we predict the climate in a hundred years?
Weather is not the same as climate. Weather deals with very short term variability as it pertains to a specific geographical area. As such weather deals with a very large amount of variability day-to-day and even hour to hour. Very few weather predictions go beyond a seven day forecast that predicts temperature and precipitation percentages.
While weather forecasting is about predicting conditions at a specific instance in time, climate is concerned with detecting trends over long periods of time and over very large areas. When discussing climate, weather variability represents the day-to-day noise beyond which the longer term trend can be detected.
Consider the Amazon rain forest, one of the wettest environments on the planet. While you may not be able to say from one day to the next what the exact temperature will be and whether it will rain or not, you can say you expect the forest to receive around 7 feet of rainfall during a given year and have an average daytime temperature of around 80 degrees Fahrenheit. The former is weather, the latter is climate. These latter conclusions are based on long term trends of that environment.
While much more complex, the Earth’s climate can be examined in a similar way. By examining how various influences have impacted the climate over long periods of time, we can predict how those influences will impact the climate in the future.