Look at the size and complexity of the system you are trying to model. Look at the total number of inputs and outputs there are for this system, and notice all those inputs and outputs tend to vary for many different reasons. Consider the feedbacks, both positive and negative, that have to be modeled. Climate models and weather models are very similar, but tracking a storm involves running a whole bunch of models at once, to see what they all come with, then adjusting for updated info. These models have to predict weather over an area, say a continent, for a couple weeks, pretty much. Climate models have to predict decades of weather for the entire planet. It's a higher order of difficulty because it requires far more computations for the much larger area covered and greater amount of time required.

I think its because there are so many variables in constructing an accurate model. Information has to be collected from around the world covering lots of things: Co2 footprint, emissions etc. These relationships have different linear, exponential lines, and have to be all compiled to estimate some data. Very complex! therefore higher computational power can make models more accurate and reliable.

"Most computer climate models are limited by available computational power. Why is so much computing power need?"

It is due to the "grid" layout of the models.

The GCM's all use a a grid pattern to represent the surface of the earth. Think of an image of the earth, and the pixels in the image. A model 'grid' is like this, the earth divided into pixels. This doesn't just happen in one image of the earth, it happens vertically too. Images (grid patterns) are stacked vertically to model layers in the atmosphere, and depths in the ocean.

The models work by knowing certain starting information about each pixel. Time is considered in incremental steps. From the starting point, each pixcel is compared to what's known about its neighbours (vertically and horizontally), and new values are estimated for it for the next time increment. The model calculates all the new values for every pixcel in every image based on its surrounding pixels (horizontally and vertically). when completed it starts over on the next time increment.

The huge processing load comes from trying to improve the 'resolution' of the model. If you have only a few pixels in your picture, then you have a poor quality image. If you double the number of pieces in each direction then you get a better image, but you have four times the number of pixels. In the GCM's the images are stacked, so to double you resolution you end up with eight times the number of pixels you must compare to all its neighbours. Similarly, to improve the resolution over time you need to use small time increments. If you want to improve your model by improving the time snapshots from four per day to one per hour, you have just multiplied the total processing load six-fold.

The huge processing load is due to trying to improve model resolution, both spatial and temporal.

Modellers want to improve the resolution for very a very simple reason. A grid cell size of for example 1deg lat and long at the equator represents an area on the ground of 110 km in each direction (68 miles). The grid technique assumes that the value for each variable for the grid cell is distributed evenly over the whole grid cell area. This is clearly a very poor representation of what's actually happening... so modellers want to improve resolution, but that comes with a geometric increase in processing load.

The above answers pretty much sum it up. To summarize, there are an outrageous number of variables that go into predicting climate patterns. If we had a computing system that could handle them all we could predict daily weather patterns.

A man lights a match in Colorado, USA. That affects the globe. There are an infinite amount of variables such as this.

Yes but they are highly accurate and we must stop using petroleum.