The greenhouse effect is the primary determinant of Earth's average temperature and therefore of climate. But there are lesser, but still significant factors;
The Sun's brightness varies enough to effect climate.
The Sun's 11 and 22 year sunspot cycle is well known. Sunspots have been observed for thousands of years. Apparently there were no sunspots between 1645 and 1715, a cool period known as the Maunder Minimum. It is known that the Sun emits slightly less energy when there are no sunspots.
The Earth's albedo can change and effect climate.
Definition of Albedo
Albedo is the fraction of light (or heat) that is reflected by a body or surface. A white body has high albedo, a black body has low albedo.
Albedo is a measure of "whiteness" or reflectivity. Albedo, albino and albumen derive from the same Latin word, albus, meaning white. Albedo values range from 0 to 1. Virgin snow has an albedo of 0.95, a lump of coal has an albedo of 0.1. At 0.84, the planet Venus shines so brightly because it is as white as snow. At 0.113, the moon's albedo is similar to a lump of coal. The Moon would be much brighter if it were covered with snow.
Agricultural land has a higher albedo than the forest that existed in the past. Ice covered water has much higher albedo than open water. Soot from coal burning and diesel engines has lowered the albedo of the whole Earth.
Aerosols effect climate.
Natural examples of aerosols are pollen and salt crystals from windblown seawater. Soot and sulfates from coal burning and diesel engines are anthropogenic examples of aerosols. Soot can cause heating when it lands on snow. Aerosols block some sunlight and thus cause surface cooling. Sulfate aerosols are highly reflective which leads to cooling. Aerosols can have a strong effect on both heating and cooling.
Aerosols also effect cloud formation.
Climate and weather are chaotic.
Weather prediction beyond a few days very difficult. Meteorologists say that weather is subject to the "butterfly effect." What they mean is that small things seem to have large effects.
This snapshot of the behavior of a double pendulum illustrates chaotic behavior. The plot would look very different if the initial conditions were only slightly different.  An explanation and an animated version of this plot may be found here . Real weather is much more complicated than a double pendulum.
Climate exhibits metastability.
Stable State 1(drought)
Stable State 2(wet period)
Climate may seem stable but a seemingly small event can tip climate to a new regime. A wet period lasting many years might be followed by a dry period also lasting many years. The transition between the two states may be sudden. There are many examples of metastability. The El Niño Southern Oscillation is one; the monsoon cycle of India is another. 
Climate exhibits negative and positive feedback
Here is an example of negative feedback. Carbon dioxide concentration increases and stimulates plant growth enough to remove some carbon dioxide from the atmosphere. Negative feedback reduces variations in either direction.
Here is an example of positive feedback. The ice covering the Arctic Ocean melts a little during the summer and refreezes during the winter. An unusually warm summer results in more ice free water. This decreases the albedo and increases the amount of heat absorbed by the water. This increases melting. The effect increases next year because the winter ice is thinner and melts sooner next summer. Positive feedback amplifies variations in either direction.
Here is a hypothetical example of extreme positive feedback also called "runaway." Large areas of northern Eurasia and northern Canada are covered by permafrost. Large amounts of organic matter are buried in the permafrost. This organic matter would release large quantities of the greenhouse gasses methane and carbon dioxide if the permafrost thawed. This would initiate a "positive feedback loop" that would go something like this:
1) Some permafrost melts.2) Bacterial action releases methane and carbon dioxide.3) Some methane is lost in upper atmosphere.4) Some carbon dioxide is taken up by plants.5) But the warmer ocean absorbs less carbon dioxide.6) Enough methane and carbon dioxide remains to cause more global warming.7) Go to step 1.
Ocean currents profoundly effect climate.
The Gulf Stream carries warm water from the tropics to the North Atlantic. The climate of Europe, Scandinavia and Iceland would be much colder without the Gulf Stream. This fact is the "scientific" basis to the movie, The Day After Tomorrow. Yet the Gulf Stream is only a segment of the Great Ocean Conveyor Belt. It is known that in the past the Great Ocean Conveyor Belt has taken different routes and has even stopped. 
Volcanic gas and dust effects climate. 
The Icelandic volcano Laki exploded in 1783. The following winter was the coldest ever recorded in the United States--about 4.8°C below a 225 year average. Europe also experienced an abnormally severe winter. Benjamin Franklin correctly guessed that gas and dust from Laki were responsible.
The Indonesian volcano Tamboro exploded in 1815 and launched 150 cubic kilometers of material into the atmosphere. A similar thing happened in 1883 when the volcano Krakatoa exploded. Both years were known as "years without summers." Mount Pinatubo in the Philippines blew its top in 1991. The gas and dust lowered the average global temperature by about 0.5°C. The effects of volcanic events last only a few years.
The largest volcanic event of the past million years occurred 73,000 years ago. That is when another Indonesian volcano known as Toba erupted with enough force to send more than 2500 cubic kilometers of volcanic material into the atmosphere.
The gas emitted by volcanoes is mainly sulfur dioxide, which accounts for most of the global cooling associated with volcanoes. Volcanic dust plays a smaller role. Coal burning also produces sulfur dioxide and dust. The study of volcanoes provides insights into the impact of coal burning.
Sulfur dioxide combines with water to produce small drops of sulfuric acid. These small drops produce a haze, also called an aerosol, which has a high albedo. The aerosol reflects sunlight, resulting in cooling. Sulfur dioxide also produces acid rain.
The Earth spins on an axis which is pointed at the North Star. The Earth moves around the Sun in a nearly circular path that lies in the plane of the ecliptic. The Earth's spin axis is tilted by 23.5 degrees. This is what causes seasons. The Northern Hemisphere tilted toward the Sun during Summer. The Northern Hemisphere is tilted away from the Sun in Winter. The effect is very pronounced near the poles.
Imagine what it would be like if the Earth's spin axis were tilted 90 degrees. The Earth's seasons would become violent. At the North Pole, the Sun would be almost directly overhead for months and it would get hot enough to boil the ocean. At the South Pole, there would be no Sun and the oceans would freeze. The poles would switch places 6 months later. The huge temperature differences would cause storms dwarfing anything on today's Earth.
The Earth's distance to the Sun varies over the course of a year because the Earth's orbit is not circular but elliptical. Earth's orbit is said to be eccentric. The Earth receives more energy on January 2 when the Earth is closest to the Sun and less energy 6 months later when the Earth is furthest from the Sun. The difference is 7.0%. The effect is to moderate Northern Hemisphere seasons and to accentuate Southern Hemisphere seasons.
The tilt of Earth's axis and the eccentricity of Earth's orbit around the Sun have varied in the past. These variations are called Milankovitch cycles and they can be accurately calculated. For example, in 10,500 years the Earth will be furthest from the Sun on January 2. Milankovitch cycles are not well understood, but it is clear they have profound effects on the Earth's climate.
The Earth's surface varies markedly in the ability to store heat. A desert is very cold at night and very hot during the day because only a thin layer of sand is available to store heat. A deep ocean does not have large daily temperature changes because a deep ocean stores a lot of heat. Places near oceans have little seasonal temperature changes. Places with large seasonal temperature changes are usually very far from oceans.
Some parts of the ocean circulate very slowly which means that some parts of the ocean responds slowly to global warming.
Global air circulation 
Low altitude air movements carry heat from one place to another. The Santa Anna winds are an example of this. People in Southern California usually enjoy a pleasant climate because of the westerly winds that blow across the Pacific Ocean. But once in a while the wind blows from the East bringing very hot and dry air to the region. Low altitude air movements can also carry water from one place to another.
High altitude air movements are usually called jet streams. They occur at altitudes that jet aircraft fly. Jet streams strongly influence the movements of weather systems.
It must be obvious by now. Weather prediction and climate prediction is complicated. The Earth is a complex thing.
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