A Better Heat Index Chart

The Heat Index (HI) is a familiar concept, often encountered in the media on hot summer days. The popular understanding of this concept is simply that humidity, not just temperature, affects a person’s experience of heat.

The U.S. National Weather Service (NWS), of the National Oceanic and Atmospheric Administration (NOAA), produces charts that state HI corresponding to a certain temperature and relative humidity (RH) or dew point (DP). I wanted to use those charts, with certain refinements, for purposes of a certain project. This post describes how I proceeded. The finished spreadsheet is available at Kiwi6 and in my Google Drive public folder.

Background

According to Fabbri (2015, p. 10), Houghten and Yagloglous (1923) commenced the scientific study of comfortable temperature with the concept of “effective temperature,” focusing on temperature, humidity, and wind speed. Other studies followed. Fanger (1967) introduced the subjective study of related phenomena, using the responses of human study participants, seated in a climate-controlled room, to calculate “thermal comfort.” But the most frequently mentioned modern study is that of Steadman (1979). Steadman assumed a person 5’7″ tall, weighing 148 lbs., wearing clothing of a specified resistance to transfer of heat and moisture (i.e., pants and a short-sleeved shirt, except in severe heat), engaged in walking outdoors at about 3.1 MPH (and, if sweating, not dripping sweat), with a 5.8 MPH wind assumed, in effect, to be blowing from various directions.

Steadman’s work was refined by Rothfusz (1990), who boiled down those assumptions into a formula that NOAA now cites, along with several adjustments and alternatives. But the formula does not drive the NOAA HI table; the process actually went in reverse, starting with Steadman’s table and resulting in what Rothfusz called an “ersatz” formula that tried to approximate it (with errors of ± 1.3°F — see Moore, 2010). I found other versions of the formula (see e.g., NPL, HabyAZO Sensors, vCalc, SaltWiki, NMR Lab), but since they, too, were derivative of the NOAA values, it did not seem necessary or even advisable to master and use them.

Contrary to Steadman’s assumptions, most people are not 5’7″ tall, weighing 148 lbs., wearing long pants on warm summer days, and walking with (or into) a 5.8 MPH wind. Moreover, Steadman did not (practically speaking, could not) take account of the many other factors that could affect personal heat experience (e.g., wearing a hat or sunblock, walking under direct sunshine versus cloud cover, being elderly or menopausal, taking medications, drinking alcohol, being on or near a bright or reflective surface). Ogunsote (2002) observed that measurements of personal heat experience could include performance tests, physiological tests, and mental assessment tests. Mohan et al. (2014) suggested that thermal comfort can be assessed using rational, empirical, and direct indices: that is, based on equations, assessment of individuals’ responses, or direct measurement of environmental variables. Yan (2008) cites a number of such efforts, including the Corrected Effective Temperature, New Effective Temperature, Temperature-Humidity Index, Summer Simmer Index, Humiture (and Humidex), Wet-Bulb Globe Temperature Index, Relative Strain Index, Predicted 4-hourly Sweat Rate Index, and Belding-Hatch Heat Index. As Yan indicates, these too have their assumptions. For instance, the Predicted 4-hourly Sweat Rate Index assumes a physically fit young man exerting in specified conditions. Morabito et al. (2014) took the approach of using deaths of elderly people during heat waves to identify the most effective HI predictor, and concluded that the Universal Thermal Climate Index (UTCI) might be superior.

Note that these remarks pertain to outdoor exposure. Indoors, the variables may be fewer and more controlled. AZO Sensors suggested that indoor comfort has been defined, not only by HI, but also by the International Organization for Standardization (ISO; see ISO 7730, “Ergonomics of the Thermal Environment”) and the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). Diagrams offered by AZO Sensors implied greater sophistication in the ASHRAE conceptualization, with overlapping but not identical spheres for ideal summer and winter indoor temperatures. On the other hand, a comfort calculator provided by Healthy Heating illustrated that ISO 7730 took account of a half-dozen of Steadman’s factors (e.g., activity level, clothing). When the indoor context involves work, the conditions may be subject to regulatory scrutiny. For example, Fidler et al. (1988) responded to complaints of excess rates of heart disease, among employees at a Goodrich tire manufacturing plant in Opelika, AL, and found wet bulb temperatures up to nine degrees above recommended levels.

The main point of these paragraphs — aside from providing a sense of the kinds of efforts that have been made to create a good heat index — is that heat index calculations can provide useful general guidelines, but are not a matter of precise science. The kind of research I might have found most persuasive would have been social science research establishing areas in which people generally agree (that e.g., wearing a hat in direct sunlight provides a sense of cooling equal to a five degree drop in the temperature). It seemed there had been some such research, but not enough to arrive at any definitive conclusions regarding the subjective experience of heat.

Improving Upon NOAA’s Charts

My review of background information (above) suggested that NOAA’s HI charts incorporated various assumptions that would not fully apply to most people in most situations — but also that those charts were generally accepted and not profoundly flawed. It seemed likely that these charts would continue to be widely used, and that it would be difficult to improve upon them significantly without devoting a career to it.

It did appear, however, that some minor improvements were feasible. One improvement, apt to be appreciated more by researchers than by the general public, would be to make the contents of those charts available in spreadsheet form, so as to facilitate related calculations. A search seemed to indicate that no such spreadsheets were currently available.

Note that the NOAA DP and RH charts I used, such as the one shown here, were extended from the smaller ones favored by NOAA (for e.g., RH). The extensions included more detail and also values for lower DP and RH values. Regarding those lower values, note that the left sides of these extended charts provided HI values that were actually lower than the air temperature. This was consistent with the fact that low humidity would tend to have a cooling effect (Robbins, 2016; Moore, 2010).

Another improvement to these NOAA charts would be to correct certain apparent errors and irregularities. The apparent errors I noticed were that (1) NOAA’s DP HI chart specified HI = 120 when DP = 48 and T = 122 — an error, it seemed, as HI values all around that one were lower; and (2) that chart specified HI = 78 when DP = 40 and T = 80, where HI values on both sides were 79. As an example of irregularity, consider other values shown for T = 122. Up to DP = 62, the HI values rises by no more than one or two degrees for each additional 2°F rise in dewpoint. But then, at DP = 64, HI suddenly lurches four points higher. There does not appear to be a reason for that: at DP = 66, HI rises by only one point. Or consider the sequential values for T = 114, DP = 56 through 70 (even numbers only): 113, 114, 115, 118, 119, 121, 124, 125. Why the big leap from 115 to 118, the calm spot, and then another leap from 121 to 124? To correct for such irregularities, I found that a moving average of five values (including two on either side) produced a table with much smoother transitions from one DP increment to the next, departing by more than 0.4 degree from the original value only in a few instances of patent irregularity, and even then only slightly.

Another possible improvement — for, again, the researcher, as distinct from the consumer seeking a summary chart — was to interpolate missing values. The DP chart provided increments for every other degree (e.g., DP = 4, 6, 8 . . .). To facilitate lookup of any value, it seemed advisable to insert values for every degree, interpolating the average of the values immediately before and after. I did this on the basis of the moving average table. The resulting table still had a few anomalies, but they appeared to be in terms of tenths of degrees, and largely at the DP extremes.

I repeated those steps with NOAA’s RH HI chart. I added a query feature to the resulting DP/RH HI spreadsheet, and used that to compare this spreadsheet’s values against the results from NOAA’s HI calculator. I did that with spot checks for air temperatures of 80, 90, 100, 110, and 120°F, with DP and RH = 10, 30, 50, 70, and 90. I had to compare the results for DP/RH = 10 and 30 against the extended NOAA DP and RH charts (such as the one shown above); the NOAA calculator warned that it could not accurately address those. In turn, the calculator did provide values for some high temperature/RH combinations that were left blank in the NOAA chart, but those were rare in the real world. For example, the highest temperature recorded in 2016 in Europe and Asia, according to one database I was working with, was 126.7°F, where the NOAA chart topped out at 126°F. (In that case, DP was only 58.4). Otherwise, where these checks did not produce errors due to exceeding the values provided in the NOAA charts, the values in the spreadsheet varied from those charts by only a few tenths of a point, consistent with my decision to reduce irregularities between values. Within the spot checks just mentioned, there were two exceptions:

  • At 120°F, DP = 50, the NOAA calculator produced a value that was a full 1°F higher than the value in the spreadsheet — but the spreadsheet was consistent with the NOAA chart (above).
  • At 120°F, DP = 90, the NOAA calculator and the NOAA chart agreed on HI = 172. The spreadsheet varied, preferring the value of 173.6 as being more consistent with surrounding values.

It appeared, in short, that the spreadsheet captured the values provided by the NOAA chart and calculator, for practical purposes; that it captured those values more consistently and with a few errors removed; and that its results were available in a form that would facilitate lookups.

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