# Climate Simulation Data

Climate simulation data (referred to here as climate datasets) represents many different types of physical, chemical, and biological variables, such as temperature, wind speed, humidity, CO2 density, etc. Climate simulation data is three (or four) dimensional – latitude, longitude (and potentially height/depth), plus time. Usually, the spatial scale is in the order of 10s of kilometres, and the time-step is somewhere between five minutes and hourly, although paleo-climate models may use annual time steps. This data is often aggregated to daily, monthly, or annual values. Figure 5: An example of a set of annual maximum near-surface air temperatures from a single climate simulation. There is one value per spatial grid cell, per year.
## How we use Climate Data

Given a climate dataset e.g., annual maximum temperatures, a time series is retrieved by combining the available time steps and plotting the data for a location or multiple locations over time. Trend (if it exists) can be determined from these plots as well as substantial inter-annual variability, or noise. This noise, while it confounds a clear view of the trend, is important as it defines the envelope of probable annual values.
## Density Functions

Density functions can be used to represent the distribution of probabilities of a given variable. Since all exclusive probabilities must sum to one, a probability density function's integral will sum to one. This also means that for any given threshold, you can calculate the probability of an event occurring below that threshold by calculating the area under the graph to the left of that threshold (x), and you can also know that the probability of an event above that threshold is the inverse (1-x). The Probability Density Function (PDF) represents the relative likelihood of each value on the x-axis (temperatures in this example) occurring. The Cumulative Density Function (CDF), is derived from the PDF and it represents the probability of an event occurring lower than each x-axis value. The Survival Function (SF) is defined as the inverse, or 1 - CDF and therefore represents the probability of an event occurring higher than each x-axis value, or above a given threshold. In the case of extreme weather events, this allows the model to determine the likelihood of an event occurring at both the high and low ends. Both the CDF and the SF are particularly useful as they allow physical values, e.g. temperature thresholds, to be mapped to probabilities and back. The PDF does not allow this as there are multiple x-values that match a given probability.
## Calculating Annual Exceedance Probability (AEPs) and Severities

To calculate the Annual Exceedance Probability (AEP), i.e., the probability of an event occurring in any given year, the same method is used to shift the SF in the same way as the PDF. Changes in AEPs are defined by keeping the severity threshold constant, and following the change in probability. To determine the change in severity for a given probability threshold, probabilities or return frequencies are kept constant, and the contours of probability are followed.