The Democratic Republic of Congo’s forests contain 22 billion to 24 billion tons of carbon, equivalent to more than double the greenhouse gases emitted last year.

United Nations Reducing Emissions from Deforestation and Degradation (REDD) Program Countries and communities are paid for keeping land in forest. This helps slow the growth of carbon dioxide in the atmosphere Financial entities representing polluting countries and corporations buy carbon credits to offset their emissions Money for carbon credits is given to countries and communities to keep land forested for a set amount of time

How many trees in the world? How would you determine the number of trees on Earth? What are some of the reasons why you might come up with different answers? 3.04 trillion Of these trees, approximately 1.39 trillion exist in tropical and subtropical forests, with 0.74 trillion in boreal regions and 0.61 trillion in temperate regions. Based on our projected tree densities, we estimate that over 15 billion trees are cut down each year, and the global number of trees has fallen by approximately 46% since the start of human civilization.

How many trees in the world? 3 trillion trees Issues What is a tree? Size? Woody shrubs? Sampling: Where? How? Technological constraints: availability of satellite data, computational demands Time frame: For what time is data available? Is the resolution of the predictions of number of trees useful?

Methods Assembled database of forest plots (450,000 plots) from all over the world. Number of trees and density was known for each plot Variables measured for each of these forest plots: Topography: elevation, slope, aspect (as northness and eastness), Climate: annual mean temperature, temperature annual range, annual precipitation, Ecological: leaf area index (LAI), proportion of urban and/or developed land cover Mapped the entire surface of the Earth according to these topographic, climatic, and ecological variables Associated tree count data from plots for entire surface based on these variables

Sampling bias Develops when the procedures used to select the sample tend to favor the inclusion of individuals of the population with certain characteristics. The method of selecting samples causes it to differ from the population Picking study sites based on how easy it is to access and sample is an example of sampling bias.

The location of where plots originated from to determine the number of trees. More plots were in developed countries and in certain biomes – a sampling bias, but one that could not be avoided.

Sampling error Sampling error is the error caused by observing a sample instead of the whole population The act of sampling introduces uncertainty in inferences simply because a sample is only a representation of the population. Sampling bias is related to the designation of what to sample, sampling error is the inherent random component

Diagonal lines perfect correspondence between predicted and observed points By plotting the actual count of forest plots, with what was predicted, the scientists get an idea of sampling error, i.e. how well sample plots were representative of the conditions in which trees occur over the globe,

Inferential statistics Branch of statistics that addresses how we can make generalization and predictions based on sampling. Two “laws” must be followed for inferential statistics to work: Law of large numbers Central limits theorem

Law of large numbers Strength of inference depends on the amount of information available...i.e. how many observations you make. More is better. Consider a coin toss: 3 tries (1/3 tails) 100 tries (50/50 tails) Limited by time, effort, cost

Central limits theorem Describes how means of a sample tend to converge toward the population mean as more samples are drawn. In other words, the more times you ‘draw’ samples, and calculate a mean, the closer you will get to the overall mean Limited by time, effort, cost

Sampling To avoid sampling error, i.e. to insure that you are zeroing in on a true cross-section of the target population (plants, people, etc) Use a formal sampling design if applicable Avoid drawing too few samples Aim to have multiple observations in each sample Incorporate a random component to the sampling

Sampling Number of samples drawn Number of observations in each sample http://onlinestatbook.com/stat_sim/sampling_dist/index.html

Sampling impervious land cover

Sample area All instructions for sampling will be provided in class.

To submit Excel file of data observations Upload into Canvas under assignments. Create a group in Excel before uploading your file. Be prepared to report on your final percent value for impervious cover.