Condisdering Maximum Weekly Maximum Temperature

Introduction

It has always struck me as a little bit odd that we use a simplistic measure of mean temperature when discussing anthropogenic global warming (AGW; aka "climate change") and the oft-times draconian policy proposals to combat and/or mitigate its effects. In fisheries management out here in the interior western United States where bull trout (Salvelinus confluentus) occur, we have been required to use a more sophisticated approach. Bull trout are the most temperature-limited salmonid in this area, and water temperature can restrict their occurrence and persistence. Because they are so sensitive, because their range has been reduced over the past few millennia by warming water temperatures associated with natural climate climate change, and because land management actions by federal agencies can affect their viability, they have been listed as "threatened" under the Endangered Species Act. Before listing, various stream temperature metrics were used to evaluate and monitor suitability for bull trout, but the states concerned have now settled primarily on a metric called "Maximum Weekly Maximum Temperature" (or MWMT), calculated as the average maximum temperature over seven consecutive days. The established criterion varies among states, but in Idaho the criterion is presently 10°C in the months of July, August, and September. (The Environmental Protection Agency is, I think, considering revising this value; it is too low and difficult to attain naturally in pristine streams in Idaho occupied by bull trout*.) But the concept behind the metric seems to be a good one as it tracks both maximum daily temperature and duration at high, potentially deleterious temperatures. 

A Sample Case

On the Payette National Forest, we had been monitoring stream temperatures sine 1993, about the time Hobo^® brand portable, lightweight data loggers from Onset^® products became readily available. These were early days and precise field protocols for monitoring deployment had not been well established, but they still helped us learn what the temperature regime was in various streams. Official protocols were developed on the Forest by 2002**, which were improved, standardized, and made available by the Rocky Mountain Research Station in 2005***. As I assembled our database and built SAS routines to summarize data, I wrote a routine to calculate MWMT for all the cataloged streams we were monitoring and produced a Forest-wide report in 2007†. A graphic from that report is reproduced here:

There is another report with updated data through 2022 but it is not available to the public. I have recently obtained the Forest's stream monitoring data via FOIA for another project, but I decided to validate my methods by creating a similar graphic using an R-Studio†† script:

It's difficult to compare these charts directly because the newer post does not include any data before 1998. I am not quite sure why these data were not included in my FOIA request, but conversations with USFS data analyst involved with the latest reporting suggested that some older data were probably unreliable, and my Q-Q plot shows several probable outliers before 2000. This is clearly evident in this plot showing a normal distribution after eliminating these points:

 

Air Temperatures

This MWMT approach also seems potentially suitable for monitoring air temperatures. Most long-established temperature monitoring stations collect daily maximum temperatures, so it would be relatively easy to calculate at individual stations; using anomalies, it may be suitable for global indices as well. I am not prepared to suggest it as a replacement for modern monitoring methods, although I distrust systems that depend on modeled adjustments to the data actually collected. Using MWMT may help circumvent this problem because maximum temperature is measured, outliers would likely be naturally excluded (although specific analysis of outliers, if they are used, should be individually handled as the researcher deems appropriate), and missing data will just naturally be skipped (obviously, this would muddy the concept of "weekly" but would likely have a trivial effect on robustness).

On the other side of the coin, the approach does reduce the visibility of overall trends in temperature determined by annual or monthly averages because it significantly reduces the number of data points analyzed. In my opinion, this may well be less important than the fact that it targets the limiting factor of whether a station is heating for an extended period. For example, a year may be unusually warm on average when low temperatures are rising and/or when there are long periods of warm, but not excessive, temperatures. 

Whatever the pros and cons, I think that multifaceted analyses of data with a variety of methods is a better way to understand reality than limiting our analyses to a restricted set of mostly similar methods as the "official" climate monitoring outfits do. I think the approach deserves a look for air temperatures, so I give it a shot here.

Case Study

I am starting this with the weather station with which I am most familiar, the Global Historical Climatology Network (GHCN) station in New Meadows, Idaho. I wrote an extensive review of its movements and locations over time and have posted several investigations of its temperature data here, here, and here (some mention of the station in combination with other nearby stations is in a few other posts, as well). Relevant information about the station can be found in those posts. (Note that NOAA's Historical Observing Metadata Repository [HOMR] was in its infancy then, but it is still flawed with respect to this station).

Methods

Mean Maximum Weekly Temperature can be easily computed with a spreadsheet using the "AVERAGE" and "MAX" functions: You simply take a 7-day running average of the maximum temperatures (Tmax) and then find the maximum value. This obviously requires asome pre-processing to organize the data and manually extract the Tmax data from the NOAA station downloads and hand-work programming the spreadsheet, compiling the data by year in an additional spreadsheet or worksheet, and then creating simple graphics. I preferred to create an R-Studio script to sift through the downloaded GHCN data, find Tmax for each day, compute a 7-day running average, and find the maximum value for each year. The annual maxima were then plotted and fitted to various statistical models (linear, loess, harmonic, etc.) and put in context with ambient CO2 from Law Dome and Mauna Loa I also computed a 30 year baseline average for the period 1951-1980 (the period NASA GISS uses†††) in order to compute annual anomalies to provide a graph of trends in anomalies.

The first graphical analysis is simply a plot of MWMT over time:

This, unlike a simple plot of Tmax over time shown in a previous post, exhibits a non-significant but possibly increasing trend. Casual inspection, however, suggests an underlying oscillation that can be seen a little more easily with a LOESS model:

Pursuing this train of thought a little farther, a harmonic regression (sine wave oscillation) can be fit to the data: 

This oscillation has approximately the same wavelength as I've fit to the Atlantic Multidecadal Oscillation AMO, not shown) but with opposite phase. This is somewhat surprising because the Pacific Decadal Oscillation (PDO) would be thought to have more impact in this area; perhaps the two interact in ways that I am unable to model, and perhaps the latter has more impact on precipitation than temperature. Interesting questions that someone else may find intriguing enough to investigate. Whatever the case, air MWMT is apparently unrelated to atmospheric CO2:

Relation to Streams

Fisheries biologists in land management situations are most concerned about stream temperatures, as discussed above. It is well known that air temperature is an important determinant of stream temperature and of concern with respect to climate change and it's effect on fishes‡ (although it can be modified by other factors like ground water recharge and shading or lack thereof). The stream discussed above, Grouse Creek, is approximately 32 miles northeast of the New Meadows GHCN station, but I have just enough data to see if their temperatures correlate. In fact, they do as this linear model shows:

One might expect a better fit with a stream closer to the GHCN station, but I have not attempted that at this point because this is the stream with the longest data record that I have processed to date.

Summary

 

This post represents a an attempt to look at air temperature using a method that is common and, in some cases legally required, for stream temperatures. It is not a definitive work; it is intended to propose that more study of whether this approach might be useful in temperature monitoring in relation to climate change. It has the benefit of using measured temperatures rather than modeled (i.e., adjusted or "corrected") ones and does not require simple (Tmax + Tmin)/2 daily averages‡‡. It appears that it may reveal underlying patterns in temperature over time and trends that may not appear from simple monthly or annual averages. The potential relation to nearby stream temperatures may also provide a way to further help understand stream temperature changes in relation to watershed management and climate change.

This is a preliminary and cursory look at a potential temperature monitoring method; anyone with comments can offer them to me on X (@rln_nelson).

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* See e.g. Hillman, T.W.; Essig, D. 1998. Review of Bull Trout Temperature Requirements: a Response to the EPA Bull Trout Temperature Rule. Unpublished report prepared for Idaho Division of Environmental Quality. Boise, ID: BioAnalysts, Inc. 74p. and Nelson, R.L.; Burns, D.C. 2006. Statistical Summary and Comparisons of Stream Temperatures on the Payette National Forest. Preliminary Working Draft. Unpublished Report. McCall, ID: U.S. Department of Agriculture, Forest Service, Payette National Forest, Fisheries Program. 104p.

** Anonymous. Suggested protocol for use of HoboTemp™ Thermographs. (Revised 30 May 2002).

***  Nelson, R.L.; Burns, D.C. 2006. Statistical Summary and Comparisons of Stream Temperatures on the Payette National Forest. Preliminary Working Draft. Unpublished Report. McCall, ID: U.S. Department of Agriculture, Forest Service, Payette National Forest, Fisheries Program. 104p.

† Dunham, J., G. Chandler, R. Reiman, and D. Martin. 2005. Measuring Stream Temperature with Digital Data Loggers: A User’s Guide. Gen. Tech. Rep. RMRS-GTR-150WWW. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 15 p.

†† https://posit.co/solutions/data-science/

†† https://data.giss.nasa.gov/gistemp/faq/#q101

‡ See e.g. Mosheni & Stefan 1999, Stream temperature/air temperature relationship: a physical interpretation, Journal of Hydrology, 218:128-141.(https://www.sciencedirect.com/science/article/abs/pii/S0022169499000347)

‡‡ There are questions about the reliability of this method, though it is usually regarded as satisfactory for monitoring changes in global average temperature (GAT).