"Average" Rainfall in Arizona

 NOAA National Water Prediction Service reports daily, weekly, monthly, seasonal, and yearly accumulated precipitation and the totals can compared to "normal".  Their data access website states that normal precipitation is defined as the 30-year PRISM normal from 1981-2010.  The Parameter-elevation Regressions on Independent Slopes Model (PRISM) climate mapping system developed at Oregon State University are considered the most detailed, highest-equality spatial climate datasets currently available.

But is the average still the same in the 16 years since 2010?

Methods

I downloaded total accumulated precipitation for water years ending September 30 for the last 10 years.  Unfortunately, the files for many of the years were corrupted and I was only able to look at the three years from October 2022-Oct 2025.  

I clipped the rasters to the Southwest US and took the mean for each grid cell.

Results

Over the last three years, some areas of the Southwest have had 50% of normal precipitation, and other areas have had 150% of normal. 

NOAA NWPS % of normal 2023-2025

Color key:

Zooming in to the area around Prescott, Arizona:

NOAA NWPS % of normal 2023-2025

Conclusions

Most of the area around Prescott is between 85-95% of normal (medium orange), confirming the presence of long-term drought.  Areas less than 75% of normal (dark orange/red) include much of the Bradshaw mountains around Prescott, the Dugas area along I-17, the Mogollon Rim - east of Payson and from Sedona to Ash Fork, and the south slopes of the San Francisco mountains around Flagstaff.

However, there are significant areas between 115 and 125% of normal (light green), including some areas above 125% of normal (dark green).  These above-average areas include the Juniper mountains and Upper Verde River, the Santa Maria river near I-93, a bit of Sedona and Schnebly Hill to Mormon Lake, and the north side of the San Francisco mountains. 

This shows how spatially heterogeneous average rainfall can be, and how a simple description of a state as being in drought or not can be misleading. For example, the excellent Drought Aware web app from Esri shows broad swaths of Arizona currently in drought, but my analysis shows that there is likely much more spatial variability.  

Climate Change Belief Tree

An article in Nautilus magazine analogizes beliefs about climate change to branches on a tree.  I like that the tree diagram emphasizes the unity of thinking about climate change, even if we may be on different branches.  Also, I think it is OK for one person's beliefs to span different branches: belief about the future does not need to be certain but can be probabilistic and can change from one day to the next. 

Diagram and original article by Summer Praetorius.

The article concludes: "What if instead of feeling threatened by differences in opinion, we were to reconceptualize them in much the same way a tree will distribute a canopy to collect as much sunlight as possible—as a multi-pronged approach to getting the job done? In the same sense that both fast and slow processes contribute to Earth change, both steady progress and immediate local action will contribute to climate solutions. Let’s take stock of our pace and work together, thankful there is someone else to fill the space we can’t. After all, we are not lone trees, but a living, connected forest, and balance is essential for stability."

Bayesian Statistics

A recent post by Scientific American writer and blogger John Hogan got me thinking about Bayesian statistics again.

My favorite explanation of Bayesian statistics was by Nate Silver in The Signal and The Noise.  The basic approach involves incorporating prior estimates of probability into new measures of probability.  The opposing approach, which does not rely on prior knowledge, is termed "Frequentist" statistics and is exemplified Fisher's standard test used with p=0.05 (which implies that a given result would occur "by chance" only 5 in every 100 such tests).

Hogan uses the standard example of cancer tests to illustrate the importance and power of Bayesian thinking, but an astute commenter points out that the real power of Bayesian thinking comes when used in a process that tests, updates probabilities, and tests again, so that each test incorporates the learning from previous tests.

Silver offered a similar example in his book, but a review in the New Yorker points out that Silver got it wrong.   In Silver's case, he applies Bayesian statistics to the probability that global warming is occuring.  But the prior probability is estimated, and Bayesian approaches only improve on standard statistics when prior probabilities are well known.  So while Silver does present a rational means of updating beliefs, since the original belief is not based on statistical data, the resulting analysis cannot be called statistically valid.

Both the New Yorker review and Hogan's thoughts highlight the inherent power of confirmation bias to trump any statistical test, even Bayesian tests.

Psychometric Factor Analysis of Risk Perception: Dread Risk and Unknown Risk

Risks are perceived based on their qualities.

Micromorts can be used as an "objective" statistical approximation of risk.

"Substance X causes cancer in animals...."

Consider two statements, S1 and S2: S1: ‘‘Would you agree or disagree that the way an animal reacts to a chemical is a reliable predictor of how a human would react to it?’’

The second statement, S2, is a little more specific: ‘‘If a scientific study produces evidence that a chemical causes cancer in animals, then we can be reasonably sure that the chemical will cause cancer in humans.’’

How did you respond? How would a scientist respond?

from P. Slovic, ‘‘Trust, Emotion, Sex, Politics, and Science: Surveying the Risk-Assessment Battlefield,’’ in Environment, Ethics, and Behavior, M. H. Bazerman, D. M. Messick, A. E. Tenbrunsel, and K. A. Wade-Benzoni (eds.) (San Francisco, New Lexington, 1997), pp. 277–313.

Granger Causality

"Biodemography of human ageing"

This article in the March 25th 2010 issue of Nature magazine confounds the rest of that issue's Insight Review of human ageing. For someone not versed in the field of demographic statistics used in this article, the graphs and conclusions are unique. By examining a kind of running average of life expectancy, the author is able to talk about the continuing increase in life expectancy.

"Humans will continue to suffer senescence -- but the process is not intractable. Mortality has been postponed considerably as a result not of revolutionary advances in slowing the process of ageing but of ongoing progress in improving health. If progress in reducing mortality continues at the same pace....then in countries with high life expectancies most children born since the year 2000 will celebrate their 100th birthday -- in the twenty-second century. "

"Brawling Over Mammography"

An interesting debate about the problem of false-positives in medical testing. Obviously, everyone wants to be tested "just in case", but a sensible policy would favor plausibility testing; everyone is not equally likely to have every disease. This article from the February 19, 2010 issue of Science, details the situation surrounding the release of a report by the U.S. Preventive Services Task Force that ran afoul of political accusations of "medical rationing". For women age 40-49 years with no other risk factors, the odds that a positive mammogram is actually due to cancer, rather than a false-positive test, is only about 2%. In other words, for every one breast cancer detection, 50 women are told that they have tested positive on their mammogram.

Inequality and Wealth

The unlinking of Top 1% income from all those below them is simultaneous of another trend which is hard to measure, and often overlooked: increasingly, health and human hapiness have stopped tracking GDP and wealth. Correlation, or causation? Would greater equality lead to higher standard of living? Why? In the 1960's President Kennedy stated that a "rising tide would lift all boats," which was generally true, but something changed in the early 1980's.

http://www.huffingtonpost.com/2009/08/14/income-inequality-is-at-a_n_259516.html

Americans throw away more food than most people consume

According to a paper by Kevin Hall et al in PLoS, Americans waste about 1,400 Calories a day, about as much as is needed to feed an average adult in much of the world. They arrived at this figure by calculating the total number of food calories produced on farmland in America (plus imports, minus exports) and compared this to the total calories consumed by Americans. Although we Americans are doing our best to consume large amounts of food, we still end up throwing away or otherwise wasting enough food every day to feed another person.

Climate Change, by U.S. State

The climate is always changing, and here are the last 30 year averaged trends.



You can also see how the seasons are changing.

Bankfull Discharge

Bankfull Discharge is (often) defined as the average high flow of a river that recurs about every two and a half years. Sometime bankfull discharge can be easily determined from the high water mark and local topography, whereas in other cases it is somewhat of an abstraction. Here's a chart of the yearly high flow (in CFS), for the Red River, near Questa NM, since 1915. It gives a good idea of the variability inherent to streamflow. What do you think the bankfull discharge is?