Occasionally on social media when someone posts in opposition to the notion of human caused climate change I respond. No one's mind is ever changed. I contend that, at this point, if you doubt human caused climate change you are either woefully ignorant or have a world view that simply cannot admit the possibility. You will not change your mind because you cannot change your mind.
When I was a kid I read Isaac Asimov's "The Universe" and it fascinated me because he not only gave information about what scientists think about the structure of the universe, but also gave some notion of the evidence that led us to believe these things. I'm no Asimov, but I thought I might go through some of the ways that scientists have used to peer into the climate past and to project the future. Many of the papers that discuss these things are behind paywalls, so I'm going to rely on more public links. Click on the links only if you want more information. The sources I have used tend to provide references that you can explore for even more information.
In all of this: observations are limited, observations often include only a few locations on a very large planet, there are uncertainties in measurements, over long time spans continents drift ... Despite this, there are enough measurements using a variety of techniques and theoretical underpinnings so that the general picture is quite clear and compelling.
First there are the "How do we know" questions. The "how" of what we know of climate depends on the time frame.
Recent Times (hundreds of years)
For recent times we have direct measurements of weather. This includes temperature (air and sea) and precipitation. There are also direct measurements of longer term indicators like sea level (though sea level is an inference based on statistical averages of a large number of measurements). Vegetation records and blooming information also give information. We also have counts of the number of hurricanes...
Even simple measurements like temperature have complexities. Each temperature record is taken at a single time and place using a particular technique. Over time the surroundings change as do the methods of recording the change. A measurement may have been taken in an open field in 1903 using a mercury thermometer. The same location today may be in the middle of an urban area with the temperature taken by a thermocouple.
The longest temperature record goes back to 1659 in Central England. It shows temperature for only about 400 years and only in a single area. Sea surface temperatures have been taken since the time of the US revolutionary war. Early ocean temperatures were measured by putting a thermometer in a bucket of water drawn from the ocean. Starting in the 1960s, temperatures were automatically recorded at the intake ports of large ships. More recently, buoys have been deployed to measure temperatures, but they differ in design and sensing methods.
The scarcity of data and differing techniques mean that adjustments and inferences have to be made to convert these individual observations into a coherent and meaningful world wide data set. For example, canvas buckets cool ocean water, insulated buckets less so. Measurements near a ship engine room tend to have warmer results. Luckily, when people publish data sets, they also publish the adjustments so that other people can check the assumptions, apply different adjustments, and check to see what the results are.
Individual observations indicate "weather" (more immediate) at a single location, but we are interested in climate (longer term) over the planet. To bridge the gap, scientists have created models and simulations. Modeling complex phenomena is difficult and tricky, but models can be checked against current and know past conditions to see how well they do. To cut to the chase, the models have gotten pretty good at simulation and predictions over time spans of decades. There are many large scale computer models for the climate (in the 10s, not the 100s or 1000s). This computer modeling work has been an ongoing effort for at least four decades. During this time period several things have occurred to increase the accuracy of the modeling. First, the computers of today are literally one million times faster and can handle a million times more data. That means simulations that used to take 11 days to run can now be run in one second. A year's simulation in the 1970s can be run in half an hour. Second, techniques of modeling have improved (smaller voxels at temperature boundaries, incorporation of aerosols from volcanos into the models, better ocean heat modeling...). Third, we are measuring a lot more by deploying more weather stations, ocean buoys, weather balloons....
http://www.ocean-sci.net/12/925/2016/
https://www.technologyreview.com/s/543546/why-climate-models-arent-better/
https://phys.org/news/2017-07-framework-accounts-conflicting-global-temperature.html
By comparing different indicators over time we can see if the measurement records tell a coherent story. If they don't, it indicates something wrong with the measurements or our understanding of the climate. Over the years, we have been able to create a theoretical understanding that pretty well corresponds to the observed record.
Over the near term, the last century or so, virtually all the data points in a single direction. The earth is warming pretty quickly. We can see this in measurements of air and ocean temperature, total volume of ice, earlier spring blooming, movement of habitats and migrations of animals ... The "hockey stick" graph of temperatures is real and correct.
https://www.nature.com/nclimate/journal/vaop/ncurrent/full/nclimate3325.html
https://en.wikipedia.org/wiki/Hockey_stick_graph
https://en.wikipedia.org/wiki/List_of_large-scale_temperature_reconstructions_of_the_last_2,000_years
Thousands of Years
Each year a tree forms a new ring. The size of the ring provides an indication of temperature and moisture at the location where the tree grew. In locations where dead tree trunks are available, living trees form the initial line in a chain of trees. Patterns of thin and thick at the outer edges of a dead tree may match the inner patterns on a living tree so the tree ring timeline can be extended. There are places where we have a tree ring record up to 4000 years.
If the recent pattern of rings on a particular species of tree can be matched to the weather patterns in the local historical record, we can use this correlation to start constructing plausible past weather patterns. This gives a climate measure for the location.
https://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets/tree-ring
Coral has some of the same attributes as tree rings. Regular patterns of growth can be detected. Oxygen isotopes in coral layers can also be used as climate indicators. Uranium/Thorium ratios can be used to date the coral samples.
http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=4467119&fileOId=4467197
We can also look at changes in the landscape to see patterns of deposition that indicate climate. This includes evidence of glaciation, ancient sea levels, pollen in sediment...
Thousands to Millions of Years
All climate measurements must rely on something that is different between warm climates and cool climates. One thing we have gotten good at in the past century is measuring the relative quantities of different isotopes of elements. The chemical properties of an element largely depend on the number of protons in the atom (its atomic number), but the weight of the atom also depends on the number of neutrons. In some circumstances the weight makes a difference. Isotopes are elements with the same atomic number but different atomic weights.
One important link between temperature and isotopes comes from the water evaporation cycle. Most oxygen is O16, but some is O18, which contains two extra neutrons. Both O16 and O18 are stable. O18 requires slightly more energy to evaporate and also tends to rain out slightly sooner than O16. These processes occur today and can be measured. As the earth cools, more water is stored in glaciers and ice caps. This water evaporated then snowed onto the land. The O18 tends to rain out earlier (at lower latitudes) so the snow tends to be depleted in O18. As O16 enriched snow enters the ice caps, it leaves the ocean. That means the oceans tend to have slightly higher O18 levels when the earth is cooler. The same process is true for deuterium, a heavier isotope of hydrogen.
http://www.iceandclimate.nbi.ku.dk/research/strat_dating/annual_layer_count/ice_core_dating/
https://en.wikipedia.org/wiki/Oxygen_isotope_ratio_cycle
This gives us two complimentary ways to measure ancient temperatures. We can look at the O18/O16 ratios in ice cap cores. We can also measure ocean O18/O16 ratios in the ocean using sediments high in calcite (CaCO3). because the calcite was formed by microorganisms that got one of the calcite oxygen atoms from the sea water in which they lived, the sediment reflects the O18/O16 ratios when the organism lived.
The ice core data goes back at least 740,000 years. Sediment data can be used for a much longer time span (at least hundreds of millions of years).
Note that we have current confirmation of the theory and two different sources of data: ice and sediment. This gives the data some real credibility, particularly since the very recent data is confirmed by other means.
https://en.wikipedia.org/wiki/Oxygen_isotope_ratio_cycle
http://cdiac.esd.ornl.gov/trends/temp/domec/domec.html
https://www.researchgate.net/profile/Hugh_Jenkyns/publication/252408787_New_oxygen_isotope_evidence_for_long-term_Cretaceous_climate_change_in_the_Southern_Hemisphere/links/571b621008ae6eb94d0d6405.pdf
Why does climate change?
Looking at the deduced climate over the past millions of years we can say pretty definitely that climate has changed drastically over time. The question of why is frightfully difficult. Moreover, small changes in one thing or another can, over time, create big changes in climate. The basic principle is that the temperature of the planet depends on its internal heat, the amount of energy entering the system (mostly from the sun) and the amount of heat leaving the planet (mostly reflected light). The earth's atmosphere acts as a blanket, keeping the earth warmer than it would be without the atmosphere.
The sun has day to day differences in output, 11 year cycles of sunspots and a long term trend (hundreds of millions of years) of increasing energy output. The earth's orbit changes as does its axis of tilt. Volcanos put large amounts of reflective particles into the atmosphere, reflecting more of the sun's energy into space. Snow and clouds reflect more light than land or ocean. Clouds block heat. In fact, water vapor and clouds are the most powerful heat trapping substances for the earth, accounting for about three quarters of all heat trapping.
https://www.giss.nasa.gov/research/briefs/schmidt_05/
The oceans have a huge thermal mass and there is large scale heat transport through the oceans and between the ocean and the air. Ocean currents carry much of this heat and transport depends on the positions of the landmass. Over eons continental drift can affect climate. The ocean circulation also depends on salt concentrations and large amounts of fresh water melting may interrupt planet wide ocean circulation. If planet wide ocean heat circulation is interrupted, there may be larger temperature differences between lower and higher latitudes. This may cause more snow to persist at higher latitudes and increase the reflectivity of the planet as a whole.
Scientists have been trying to tease the affects apart. The further back in time you go, the more difficult it becomes and the more speculative the conclusions.
Carbon Dioxide
This is the measure that has become controversial for political and monetary reasons. Despite the perceived controversy, we know a lot about the basic heat processes of the earth and there is no real controversy among the scientists who actually study climate. The physical response of CO2 to light is well known and can be easily measured. The effect of CO2 is to take infrared heading out of the planet and reflect some portion of it back in. This is not a huge effect, but part of it takes affect above the level of water vapor and provides another insulating layer for the planet.
The most immediate indicator of CO2 as a possible cause of temperature rises comes from a simple correlation over the past century. Of course simple correlation means little to nothing, and over extremely long periods of time (hundreds of millions of years) the relationship between CO2 levels and temperature are tenuous at best. That said, in an extremely complex system it is difficult to find causes and effects. Our best hope is to look at recent conditions where we have more measurements and the ability to test hypotheses directly. For the recent past, CO2 as a driver is quite well established.
The affects of CO2 have been directly measured. On the land, direct measurements of the wavelengths captured by CO2 have been measured and found to be increasing in conjunction with the increasing concentrations of CO2 in the atmosphere. The corresponding measurements from space show the opposite affect. As CO2 increases, the amount of light radiated by the planet in the range that CO2 absorbs goes down. That is, we have directly measured the greenhouse imbalance caused by increasing CO2.
https://www.skepticalscience.com/co2-temperature-correlation-intermediate.htm
http://newscenter.lbl.gov/2015/02/25/co2-greenhouse-effect-increase/
https://www.eumetsat.int/cs/idcplg?IdcService=GET_FILE&dDocName=pdf_conf_p50_s9_01_harries_v&allowInterrupt=1&noSaveAs=1&RevisionSelectionMethod=LatestReleasedhttp://science.sciencemag.org/content/289/5477/270
Theoretical attempts to assign quantitative amounts to different drivers of temperature are rapidly maturing. These point to the same conclusion, in the current situation CO2 is the main driver of increasing global temperature.
https://www.ipcc.ch/publications_and_data/ar4/wg1/en/spmsspm-human-and.html
Why do We Care?
This section is a little different. Even if the climate is changing, why should we care? After all, climate has changed drastically in the past and life on earth has survived. Even faced with mass extinctions, life has recovered. Devastating changes in climate have set the stage for new types of life to thrive and become dominant.
The earth and life on earth will survive climate change. Technological human society may not. In any number of areas, we are currently engaged in unsustainable practices. As Herbert Stein pointed out "If something cannot go on forever, it will stop." Our human life spans are relatively short and it is easy perceive the world we live in now as not much different than the world we were born in. Over spans of centuries it is easy to see the drastic changes.
Because the world is large and has been around a long time, we can unsustainably use some resources for a very long time. We probably have centuries of fossil fuels left. A few centuries is a very short time when we consider the millions of years it took to accumulate these reserves, but for humans it means we don't have to worry about having enough fossil fuels for many generations of human life.
When agriculture emerged there were probably fewer than twenty million people on earth. We hit the one billion mark around 1800. It took 123 years to get to two billion. Currently we are adding a billion each couple decades. This population increase requires a concomitant increase in resource use. When the European settlers first reached North America cod were so numerous that it was joked you could walk across the ocean on the backs of cod. In 1992 the cod fishery collapsed and it was estimated that it's biomass was one percent of its earlier levels.
When European settlers got to the U.S. Pacific Northwest the size and expanse of the forests were breathtaking. It seemed a resource that could not be exhausted. The forest is still vast, but satellite images show the incredible level of human exploitation.
There is good reason to say that we have entered a new geologic era, the anthropocene, where the dominant force shaping the planet is humans. Humans now move more earth than natural geologic processes. All of the worlds great aquifers are being emptied for agriculture. Many of them will cease to be productive within a couple of generations. Biologists tell us we are on the brink of a sixth great extinction of species. That is, an event on the scale of the extinction of the dinosaurs. This time it is being caused by human intervention in the environment.
Humans are an extremely adaptable species, but we rely on the web of life around us as well as incredibly complex and fragile systems of technology and trade. Rapid changes in either ecology or collapse of technological webs may exceed our ability to respond while maintaining our technological society. We are already seeing large scale human misery, but many people refuse to acknowledge there is even a problem. We are headed toward a world wide failure of systems that is unprecedented in human existence.
For me, the terrible part is that, collectively, we understand what is happening and if we take action we can enter a golden age of human existence and restored ecological health. We know many of the problems and we know some of the solutions. For example, E.O. Wilson has made the excellent suggestion that we set aside roughly half the earth as a preserve outside of human intervention. The preserve must be connected and contain many of the most biologically productive areas. This seems like a large and undoable task but, surprisingly, his analysis shows that it is not. The simple act of making contraception readily available to everyone (with no coercion) is probably sufficient to keep human population in check. Movement away from burning carbon is not only do-able it is probably inevitable for cost reasons, yet the fossil fuel industries fight tooth and nail to keep the burning going. World wide, democracy and concern for the average citizen is diminishing while power is being concentrated in the hands of people and institutions whose main concern is preserving and expanding their wealth and control.
https://www.amazon.com/Half-Earth-Our-Planets-Fight-Life/dp/1631492527/ref=sr_1_1?ie=UTF8&qid=1499277232&sr=8-1&keywords=half+earth+e.o.+wilson
http://nymag.com/daily/intelligencer/2017/07/climate-change-earth-too-hot-for-humans.html
https://www.youtube.com/watch?v=Kxryv2XrnqM
https://qz.com/871907/2016-was-the-year-solar-panels-finally-became-cheaper-than-fossil-fuels-just-wait-for-2017/
http://www.npr.org/sections/thetwo-way/2017/07/05/535596277/all-new-volvo-models-will-be-electric-or-hybrid-starting-in-2019
https://www.equalitytrust.org.uk/about-inequality/impacts