20231228Exhibit 3.pdf

Intermountain Gas Company
Historical Temperature Climate Report
2023 – 2028
Exhibit No. 3
1
Historical Temperature Climate Report
Prepared for
Intermountain Gas Company
January 26, 2021
By Russell J. Qualls, Ph.D., P.E.
Climate Consultant
2
Historical Temperature Climate Report
Prepared for Intermountain Gas Company
By Russell J. Qualls, Ph.D., P.E.
INTRODUCTION
This report provides estimates of design air temperature values that are likely to be equaled or
exceeded (in a “colder than” sense) in a year, with specified probabilities of occurrence and
with specified average return periods. The estimates are made for monthly and annual daily-
average temperatures, and for annual minimum daily average temperatures, at seven locations
in Southern Idaho used by Intermountain Gas Company (IGC) in its gas supply and storage
calculations. The estimated values are intended to assist IGC in developing its Integrated
Resource Plan (IRP).
This report arose out of discussions with representatives of IGC regarding what information was
most needed for development of the IRPs, and provides an update to similar earlier reports
(Qualls, 2007, 2017; Molnau, 1994). Each of these reports relied upon probability distributions
generated from historical temperature values measured at or near the seven Southern Idaho
IGC calculation locations, and included the Normal Distribution (“NORM”; symmetric bell-
shaped distribution) and the Pearson Type III Distribution (“PIII”; a skewed distribution which
can represent asymmetric data and converges to the Normal distribution for symmetric data).
Selecting design temperatures from values generated by these probability distributions is
preferable over using individual observations, such as the coldest observed daily average
temperature, because exceedance probabilities corresponding to values obtained from the
probability distributions are known. This enables IGC to choose a design temperature, from
among a range of values, which corresponds to an exceedance probability that IGC considers
appropriate for the intended use.
Each successive report incorporates temperature data which occurred and was measured after
the completion of the earlier reports. In addition, this report includes temperature data from
as much of the entire Period Of Record (POR) at each location as was deemed reliable. This
extends the data pool for each location backward in time, making each dataset much larger
(i.e., covering a longer time period) than in the preceding reports. This has some statistical
advantages. First, it allows one to assess with greater confidence how well a particular
distribution represents the observed data, and secondly, it generally narrows the range of
uncertainty associated with a given probabilistic temperature value. This report includes
analyses introduced in the 2017 report, which quantify the goodness-of-fit of each probability
distribution and the range of uncertainty of each estimated value. These additional analyses
include:
3

1) Running hypothesis tests on each probability distribution fitted, to assess whether it
should be accepted as a good descriptor of the data (Chi-Squared Test)
2) Calculation of the 90% confidence interval for each probabilistic temperature estimate.
There is a 90% probability that the endpoints of the confidence interval, known as upper
and lower confidence limits, encompass the true probabilistic temperature value.

Further discussion of these additional analyses is provided in Appendix B.

The contents of this report may be compared with Intermountain Gas Company’s
Integrated Resource Plan (IRP) to estimate probabilities associated with design values
presented there.
DATA
The data used in this report were either provided by Lori Blattner or Landon Barber of IGC, or
obtained directly from the National Centers for Environmental Information (NCEI, formerly
National Climate Data Center, NCDC). The data consist of daily observed maximum and
minimum temperatures, and/or daily averages calculated as the mean of the daily maximum
and minimum values. Table 1 provides the IGC Zone ID, location name, and starting Water Year
for the data. A Water Year (WY) begins on October 1st, and ends on September 30th of the
following year, and is numbered by the year in which it ends. That is, the 1905 Water Year for
Caldwell begins on October 1, 1904 and ends on September 30, 1905. A Water Year groups all
winter months of a particular season together. The analysis for each station extends to the end
of the 2020 Water Year (September 30, 2020).
Table 1: Weather Station Zones, Locations, and Starting Water Year (WY)
Zone ID Location Starting WY
350 Caldwell 1905
450 Boise 1941
500 Hailey 1909
600 Twin Falls 1906
700 Rexburg 1908
750 Idaho Falls 1949
800 Pocatello 1939

Most long-term weather stations include occasional changes such as instrument replacements
or changes, or station moves. The data used in this analysis span these changes. Some of these
changes have occurred in the past 30 years, so the Molnau (1994) and Qualls (2007, 2017)
reports, and the data currently used by IGC have some of these changes embedded in them, as
would the current analysis even if it was limited to the past 30 years.
4

RESULTS
For each IGC location, results calculated over the POR at each station from data aggregated at
the annual time scale are presented in this section, and results with greater detail including
monthly analyses and additional figures are presented in the appendices. “Annual” in this
report refers to a Water Year. Table 2 presents POR summaries and statistics of station data
and values of exceedance temperatures for annual mean daily average temperatures and
annual minimum daily average temperatures. Exceedance temperatures are presented for a
range of return periods (T=2, 5, 10, 20, 50 and 100 years) and their corresponding exceedance
probabilities, calculated by fitting both Normal (NORM) and Pearson Type III (PIII) distributions
to observed data from each IGC location. With the addition of only 5 years’ data since the
previous report, the resulting values do not change substantially.

POR summaries and statistics of the data are presented in the top third of Table 2. In this
section, the statistics are calculated from the annual values at a given station over the number
of years available for that station. For the annual mean daily average temperature shown in
the left half of Table 2, the POR mean at each station ranges from a low value of 43 °F (Station
700) to high value of 52 °F (Station 450) across the different locations. This is shown in the first
Table 2: Annual Station data and exceedance temperatures based on NORM and PIII Distributions (°F)
350 450 500 600 700 750 800 350 450 500 600 700 750 800
51 52 43 49 43 44 47 10 10 -1 6 -6 -5 0
1.6 1.7 1.6 1.7 1.8 1.7 1.4 9.7 8.8 7.3 8.3 8.0 7.8 8.0
0.1 -0.1 0.2 0.3 0.0 -0.4 -0.1 -0.5 -0.6 -0.3 -0.3 -0.2 -0.3 -0.3
55 56 49 54 48 48 50 28 27 13 24 16 10 15
48 48 39 45 38 39 43 -18 -16 -23 -15 -27 -23 -18
116 80 111 115 113 72 82 116 80 111 115 113 72 82
T P
2 0.5 51 52 43 49 43 44 47 10 10 -1 6 -6 -5 0
5 0.2 50 50 42 47 41 43 46 2 3 -7 -1 -13 -11 -7
10 0.1 49 50 41 47 40 42 45 -3 -1 -10 -4 -16 -15 -10
20 0.05 49 49 41 46 40 41 45 -6 -4 -13 -7 -19 -17 -13
50 0.02 48 48 40 45 39 41 44 -10 -8 -16 -11 -22 -21 -16
100 0.01 48 48 40 45 39 40 44 -13 -10 -18 -13 -25 -23 -18
T P
2 0.5 51 52 43 49 43 44 47 11 11 -1 7 -6 -4 1
5 0.2 50 50 42 47 41 43 46 2 3 -7 0 -13 -11 -6
10 0.1 49 50 41 47 40 42 45 -3 -1 -11 -5 -16 -15 -10
20 0.05 49 49 41 46 40 41 45 -7 -5 -14 -8 -20 -18 -13
50 0.02 48 48 40 46 39 40 44 -13 -10 -17 -12 -23 -22 -17
100 0.01 48 48 40 45 39 40 43 -16 -14 -20 -15 -26 -24 -20
Min
No Years
Station
Mean
Std Dev
Skew
Max
Normally Distributed Exceedance Temperatures Normally Distributed Exceedance Temperatures
PIII Distributed Exceedance Temperatures PIII Distributed Exceedance Temperatures
Annual Mean Daily Average Temperature Annual Minimum Daily Average Temperature
5

row below the station number, labeled “Mean”. In the second row below the station number,
the relatively small standard deviation shows that the collection of annual mean temperatures
do not spread out very far around the POR mean at each station. This can also be seen in the
relatively small difference between the Max and Min values in the fourth and fifth rows below
the station numbers, which represent the largest and smallest annual mean daily average
temperature for each station. The Max and Min values differ by no more than 10 °F at any of
the stations.
Because the spread of the annual mean daily average temperatures is small at each station, the
exceedance temperatures for different return periods also fall within a fairly narrow range, as
shown for the normal distribution in the left half of the middle third of Table 2. For example, at
station 350, the two-year return period exceedance temperature is 51 °F and the 100-year
return period exceedance temperature is only 3 °F colder at 48 °F. Furthermore, the asymmetry
is small as shown by the small value of the skew coefficients for the annual mean daily average
temperatures, in the third row below the station numbers in Table 2. As a result, the PIII
distribution nearly converges to the normal distribution and in most cases they give the same
result for each return period (e.g., the 100-year return period event is the same or only slightly
different between the NORM and PIII distributions for a given station; compare left half of
middle and lower thirds of Table 2).
In addition, the small spread of the annual mean daily average temperatures indicates that the
calculated exceedance values can be accepted with high certainty. Ninety percent confidence
intervals have been calculated for the different return period exceedance temperatures at each
station and for both the Norm and PIII distributions. Upper and lower Confidence Limits (CL
values) are given in tables in Appendix A. For the annual mean daily average temperatures,
Figure 1 shows the values of the 100-year exceedance temperature and their upper and lower
CLs for the NORM and PIII distributions at each station.
The range of the CLs around the 100-year return period value at each station is small, less than
1 °F at most stations, and the results are similar between the Norm and PIII distributions for a
given station. The CLs are even smaller for exceedance temperatures with shorter return
periods than 100 years. Thus, the exceedance temperatures for the annual mean daily
temperatures given in Table 2 can be accepted with a high degree of confidence. The annual
minimum daily average temperatures, summarized in the right half of Table 2, have a much
higher degree of variability. This is expected because these data and statistics come from the
single lowest daily average temperature observation from each year, in contrast to the annual
mean daily average temperatures discussed above which are comprised of the mean of a full
year’s worth of daily values. Averaging, as in the case of the annual mean temperatures,
centralizes the results and reduces variability. The difference between the behavior of the
6

annual minimum and annual mean daily average temperatures is clearly visible in the time
series plots of each of these variables for each station shown in Appendix A. The upper line is
the annual mean and the lower line is the annual minimum over the POR for a given station.
The greater variability of the annual minimums is readily apparent.

Summary statistics for the annual minimum daily average temperatures given in the left half of
Table 2 reflect its greater variability. The standard deviation of the annual minimums is much
larger than that for the annual means, and many of the stations exhibit large negative skew.
The large standard deviation indicates that the uncertainty of the exceedance values of annual
minimum temperatures is larger than it was for the annual mean temperatures, consequently
the range of the confidence limits for the minimum temperatures is much wider. This is shown
in Figure 2 for the 100-year return period minimum temperatures, where the CLs span a range
from 3.5 to 7.2 ˚F. The large negative skew suggests that the PIII distribution should provide a
more realistic estimate of the minimum annual daily average exceedance temperatures than
would the NORM distribution. Results of Chi-Square tests of the “goodness-of-fit” of the NORM
and PIII distributions for each station generally confirm this as discussed in Appendix B.
For the T-year return period exceedance values of annual minimum daily average temperature,
the PIII distribution provides better estimates than the NORM distribution, and the true values
of the exceedance temperatures could be several degrees larger or smaller than the values
provided in Table 2 owing to the inherent uncertainty of this variable.

36.0
38.0
40.0
42.0
44.0
46.0
48.0
50.0
Norm PIII Norm PIII Norm PIII Norm PIII Norm PIII Norm PIII Norm PIII
350 450 500 600 700 750 800
Te
m
p
e
r
a
t
u
r
e

(
°F)
Station and Probability Distribution
Figure 1. 100-Year Annual Mean Daily Average Temperature
Upper CL
Lower CL
T-Yr Temp
7

Although estimated annual Tavg exceedance temperatures are very similar between the Norm
and PIII distribution, for monthly Tavg and annual minTavg exceedance temperatures there are
a number of cases where the PIII distribution represents the data better than does the Norm
distribution and where the exceedance temperatures and confidence limits differ between the
two distributions. For this reason, to simplify the selection process, it is recommended that the
PIII exceedance temperatures be used in general. Where both distributions provide similar
results it doesn’t matter, and where they differ, PIII is usually more representative of the data.
Routinely using the PIII values will avoid accidentally using the Norm exceedance temperatures
when they are not representative of the observations. Further explanation is provided in
Appendix B.
Multi-Year Time Horizon Probabilities
Probabilities of equaling or exceeding an event at least once during a multi-year period can be
calculated based on the return period, T. Average Return Period T and annual exceedance
probability have a reciprocal relationship, P=1/T. The exceedance probabilities, P, correspond
to the likelihood of observing temperatures less than or equal to the indicated value in any
single year. In order to apply these numbers over a multi-year time horizon, one should
calculate the probability PJ that the temperature will be less than the specified threshold at
least once during the J-year period. PJ may be calculated as PJ = (1-(1-P)J). Values of PJ for J
equal to 5, 10, and 15 years are given in Table 3.
The single-year exceedance probability of 0.033 which appears in the third row up from the
bottom is the approximate exceedance probability corresponding to using the coldest day
-30.0
-25.0
-20.0
-15.0
-10.0
-5.0
No
r
m
PI
I
I
No
r
m
PI
I
I
No
r
m
PI
I
I
No
r
m
PI
I
I
No
r
m
PI
I
I
No
r
m
PI
I
I
No
r
m
PI
I
I
350 450 500 600 700 750 800
Te
m
p
e
r
a
t
u
r
e

(
°F)
Station and Probability Distribution
Figure 2. 100-Year Annual Minimum Daily Average Temperature
Upper CL
Lower CL
T-Yr Temp
8

observed in a T=thirty-year period as the peak design day. Thus, the likelihood that a
temperature colder than the 0.033 or 3.3% exceedance temperature will be observed at least
once in the next five years is 0.16 or 16%, as shown in the 5-year (J=5) column. Similarly, there
is only a 5% chance of having a temperature occur at least once that is colder than the P=0.01
exceedance temperature (i.e., the T=100-year event) within a 5-year span.

Table 3. Multi-Year Exceedance Probabilities corresponding to different time horizons (J=5,
10, and 15 years) for different values of single-year exceedance probability.
Single-Year Multi-Year Exceedance Probabilities, PJ
T P J=5 J=10 J=15
2 0.5 0.97 0.999 0.99997
5 0.2 0.67 0.89 0.96
10 0.1 0.41 0.65 0.79
20 0.05 0.23 0.40 0.54
30 0.033 0.16 0.29 0.40
50 0.02 0.10 0.18 0.26
100 0.01 0.05 0.10 0.14

SUMMARY
T-year exceedance temperature values for monthly and annual daily average Temperatures
(Tavg) and annual minimum daily average temperatures (minTavg) have been estimated for
seven stations across Southern Idaho by fitting Normal and PIII distributions to long-term
observations from the stations. Results for annual Tavg and minTavg are presented in Table 2
and Figures 1 and 2 above and in Appendix A, which also includes results for monthly Tavg.
For annual Tavg exceedance temperatures, results are similar between the Norm and PIII
distribution estimates. For monthly Tavg and annual minTavg, results are often substantially
different owing primarily to skew in the distribution of the data so that the PIII distribution
provides a superior estimate of exceedance temperatures. The χ2 (Chi-Squared) test applied to
the results generally confirms that PIII is as good as or better than the Norm distribution.
Because PIII usually provides a better estimate when results differ between the Norm and PIII
distributions, it is recommended to use the PIII results from this report. When the Norm and
PIII estimates are similar, this produces no negative consequences. However, when they differ,
routinely using the PIII results avoids accidentally using the less accurate results from the Norm
distribution.
A measure of uncertainty of the exceedance temperatures is given by 90% confidence limits in
Figures 1 and 2 above, and in tables given for each station in Appendix A.
9

REFERENCES CITED

Benjamin, J.R. and C.A. Cornell, Probability, Statistics and Decision, for Civil Engineers, McGraw-
Hill, New York, 1970.

Chow, V.T., D.R. Maidment, and L. W. Mays, Applied Hydrology, McGraw-Hill, 1988.

Devore, J.L., Probability and Statistics for Engineering and the Sciences, 2nd Ed., Brooks/Cole,
Monterey, CA, 1987.

Haan, C.T., Statistical Methods in Hydrology, Iowa State University Press, Ames, Iowa, 1977.

Interagency Advisory Committee on Water Data (now combined into Advisory Committee on
Water Information), Guidelines for determining flood flow frequency, Bulletin 17B,
http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html, 1981.

Lapin, L.L., Probability and Statistics for Modern Engineering, Brooks/Cole, Monterey, CA, 1983.

Pearson, E.S. and H.O. Hartley (eds.), The Biometrica Tables for Statisticians, vol. 1, 3rd ed.,
Biometrica, 1966.

Qualls, R.J., 30 Year Climate Report prepared for Intermountain Gas Company, July 5, 2007.

Qualls, R.J., Historical Temperature Climate Report prepared for Intermountain Gas Company,
May 9, 2017.

10

Appendix A
Detailed Station Results
Detailed data and statistics for each station are presented in both tabular and graphic form in
this appendix. Information for each station is grouped together on a series of four pages in
order of station number. Each page lists the station number and name at the top. The first
page for each station lists the starting and ending water year, followed by a table similar to the
top one-third of Table 2 in the main body of the report, except that it contains data for one
station only, and contains monthly results for the mean daily average temperature, in addition
to annual results. In these pages Tavg refers to the monthly or annual mean daily average
temperature; minTavg refers to annual minimum daily average temperature. The results in the
last two columns are identical to those in Table 2 for the respective station. The left figure
shows time series over the period of record (POR) of annual values of Tavg and minTavg. These
time series plots illustrate how the data vary from year to year throughout the period of record,
and the difference in variability between Tavg and minTavg. The two figures on the right present
the annual data sorted by magnitude for Tavg (upper) and minTavg (lower).
The second and third pages for each station give tables of exceedance temperatures and Upper
and Lower Confidence Limits (CLs) for the Norm and PIII distributions, respectively. As in the
tables at the top of the first page for each station, monthly and annual values are included for
Tavg, and annual values for minTavg. The exceedance temperature values for annual Tavg and
minTavg given in these tables are the same as those given in Table 2 in the main body of this
report.
The fourth page for each station shows the exceedance temperatures and CLs graphically for
annual values of Tavg and minTavg for the Norm and PIII distributions. Each graph presents
results for the full range of return periods analyzed in this report, that is, 2, 5, 10, 20, 50 and
100 years. Each left/right pair of figures can be compared to see the influence of fitting a
Normal versus PIII distribution to the data. Tavg is presented in the top pair of figures, and
minTavg is presented in the bottom pair.
Weather Station Zones, Locations, and Starting Water Year (WY)
Zone ID Location Starting WY
350 Caldwell 1905
450 Boise 1941
500 Hailey 1909
600 Twin Falls 1906
700 Rexburg 1908
750 Idaho Falls 1949
800 Pocatello 1939
Station: 350 Caldwell
Water Years (WY) Starting: 1905 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 51.0 39.1 30.9 29.3 35.8 43.7 51.0 58.9 66.5 74.4 71.8 62.2 51.3 9.8
Sx 2.6 3.2 4.7 5.7 4.4 2.9 3.0 3.2 3.1 2.7 2.8 2.9 1.6 9.7
Skew 0.13 ‐0.30 ‐0.76 ‐0.62 ‐0.79 ‐0.15 0.17 0.03 0.41 0.01 0.29 0.15 0.10 ‐0.50
Max 59.5 45.3 41.7 42.1 43.6 49.8 58.9 66.2 75.3 80.4 79.9 70.7 55.3 28.0
Min 44.6 29.0 12.5 13.1 20.5 34.7 44.6 51.8 60.5 66.7 66.1 55.4 47.9 ‐18.0
n (years) 116 116 116 116 116 116 116 116 116 115 116 116 116 116
Tavg (˚F)
‐30
‐20
‐10
0
10
20
30
40
50
60
1900 1920 1940 1960 1980 2000 2020
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Year
Caldwell Annual Temperatures
Tavg minTavg
46
48
50
52
54
56
1 11 21 31 41 51 61 71 81 91 101 111
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Sorted Tavg (annual)
‐30
‐20
‐10
0
10
20
30
1 11 21 31 41 51 61 71 81 91 101 111
Te
m
p
e
r
a
t
u
r
e

(
°
F
)
Sorted minTavg (annual)
Station: 350 Caldwell
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.0 39.1 30.9 29.3 35.8 43.7 51.0 58.9 66.5 74.4 71.8 62.2 51.3 9.8
5 0.2 48.8 36.4 26.9 24.5 32.1 41.2 48.5 56.3 63.9 72.1 69.5 59.8 50.0 1.7
10 0.1 47.7 35.1 24.9 22.0 30.1 39.9 47.2 54.9 62.5 71.0 68.2 58.5 49.3 ‐2.6
20 0.05 46.7 33.9 23.2 19.9 28.5 38.9 46.2 53.7 61.3 70.0 67.2 57.4 48.7 ‐6.1
50 0.02 45.6 32.6 21.3 17.6 26.7 37.7 45.0 52.4 60.1 68.9 66.0 56.2 48.1 ‐10.1
100 0.01 44.9 31.7 20.0 16.1 25.5 36.9 44.1 51.6 59.2 68.2 65.3 55.4 47.6 ‐12.8
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.4 39.5 31.4 30.0 36.3 44.0 51.4 59.3 66.9 74.7 72.2 62.6 51.5 11.0
5 0.2 49.2 36.9 27.6 25.3 32.7 41.6 48.9 56.7 64.3 72.5 69.8 60.2 50.2 2.9
10 0.1 48.1 35.5 25.6 22.9 30.8 40.4 47.7 55.4 63.0 71.4 68.6 58.9 49.5 ‐1.1
20 0.05 47.2 34.4 24.0 20.9 29.3 39.4 46.7 54.3 61.9 70.5 67.7 57.9 49.0 ‐4.5
50 0.02 46.2 33.2 22.2 18.7 27.6 38.2 45.5 53.1 60.7 69.4 66.6 56.8 48.4 ‐8.2
100 0.01 45.5 32.4 21.0 17.3 26.4 37.5 44.8 52.3 59.9 68.7 65.9 56.1 48.0 ‐10.7
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 50.7 38.7 30.3 28.7 35.3 43.3 50.7 58.6 66.1 74.1 71.5 61.9 51.1 8.7
5 0.2 48.4 36.0 26.3 23.7 31.4 40.8 48.1 55.8 63.4 71.8 69.0 59.4 49.7 0.2
10 0.1 47.2 34.5 24.1 21.0 29.4 39.4 46.7 54.3 61.9 70.5 67.7 58.0 49.0 ‐4.3
20 0.05 46.2 33.3 22.3 18.8 27.6 38.3 45.6 53.1 60.7 69.5 66.6 56.9 48.4 ‐8.1
50 0.02 45.0 31.9 20.2 16.3 25.7 37.0 44.3 51.7 59.4 68.3 65.4 55.6 47.7 ‐12.3
100 0.01 44.3 31.0 18.8 14.6 24.4 36.1 43.4 50.8 58.4 67.5 64.5 54.7 47.3 ‐15.2
Tavg
Upper Confidence Limit
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Lower Confidence Limit
Station: 350 Caldwell
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.0 39.3 31.5 29.9 36.4 43.7 51.0 58.9 66.3 74.4 71.7 62.2 51.3 10.6
5 0.2 48.8 36.5 27.2 24.8 32.3 41.2 48.5 56.3 63.8 72.1 69.4 59.8 50.0 2.0
10 0.1 47.7 35.0 24.6 21.8 29.9 39.9 47.3 54.9 62.6 71.0 68.3 58.5 49.3 ‐3.0
20 0.05 46.8 33.6 22.3 19.1 27.7 38.7 46.3 53.8 61.7 70.0 67.4 57.6 48.8 ‐7.4
50 0.02 45.8 32.1 19.5 15.8 25.0 37.4 45.2 52.5 60.8 68.9 66.5 56.5 48.2 ‐12.6
100 0.01 45.2 31.0 17.4 13.5 23.0 36.6 44.5 51.7 60.1 68.2 65.9 55.8 47.8 ‐16.3
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.4 39.8 32.2 30.8 37.0 44.2 51.4 59.4 66.8 74.8 72.1 62.6 51.5 12.1
5 0.2 49.3 37.0 28.0 25.8 33.1 41.7 49.0 56.8 64.4 72.6 69.9 60.3 50.2 3.6
10 0.1 48.2 35.6 25.6 22.9 30.8 40.4 47.9 55.5 63.2 71.5 68.8 59.1 49.6 ‐1.1
20 0.05 47.4 34.3 23.4 20.4 28.7 39.4 46.9 54.5 62.4 70.6 68.0 58.2 49.1 ‐5.2
50 0.02 46.5 32.9 20.8 17.4 26.2 38.2 45.9 53.3 61.5 69.6 67.1 57.2 48.5 ‐10.0
100 0.01 45.9 31.9 18.9 15.3 24.4 37.4 45.3 52.5 60.9 68.9 66.6 56.5 48.2 ‐13.4
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 50.6 38.8 30.8 29.1 35.7 43.3 50.5 58.4 65.8 74.0 71.3 61.7 51.0 9.1
5 0.2 48.3 35.9 26.4 23.7 31.5 40.7 48.0 55.7 63.2 71.6 68.9 59.2 49.7 0.2
10 0.1 47.1 34.2 23.6 20.5 28.9 39.2 46.6 54.2 62.0 70.4 67.7 57.9 48.9 ‐5.2
20 0.05 46.1 32.8 21.0 17.5 26.5 38.0 45.6 53.0 61.0 69.3 66.7 56.8 48.4 ‐10.0
50 0.02 45.0 31.1 17.9 13.9 23.5 36.5 44.4 51.6 59.9 68.1 65.7 55.6 47.7 ‐15.8
100 0.01 44.3 29.9 15.6 11.4 21.3 35.6 43.6 50.6 59.2 67.3 65.0 54.8 47.3 ‐19.8
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Tavg
Station: 350 Caldwell
46
47
48
49
50
51
52
2 5 10 20 50 100
Te
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Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
10
15
2 5 10 20 50 100
Te
m
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(
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F
)
Return Period, T (years)
Normal Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
10
15
2 5 10 20 50 100
Te
m
p
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r
a
t
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(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
46
47
48
49
50
51
52
2 5 10 20 50 100
Te
m
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r
a
t
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(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
Station: 450 Boise
Water Years (WY) Starting: 1941 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 52.4 39.8 31.3 29.9 36.1 43.0 49.8 58.2 66.3 75.3 73.5 64.0 51.7 10.3
Sx 3.1 3.6 4.5 5.9 4.2 3.2 2.9 3.0 3.3 3.3 3.0 3.4 1.7 8.8
Skew 0.14 ‐0.54 ‐1.36 ‐0.73 ‐0.75 ‐0.11 0.07 0.01 0.24 0.05 ‐0.08 ‐0.18 ‐0.09 ‐0.59
Max 59.8 47.2 38.4 41.0 43.9 49.7 56.7 64.3 75.9 83.1 78.7 71.4 55.6 27.0
Min 45.1 27.6 12.6 10.3 23.2 35.9 43.8 52.1 59.3 65.0 67.2 56.2 47.6 ‐15.5
n (years) 80 80 80 80 80 80 80 80 80 80 80 80 80 80
Tavg (˚F)
‐20
‐10
0
10
20
30
40
50
60
1940 1960 1980 2000 2020
Te
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Year
Boise Annual Temperatures
Tavg minTavg
46
48
50
52
54
56
1 11 21 31 41 51 61 71
Te
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Sorted Tavg (annual)
‐20
‐10
0
10
20
30
Te
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(
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Sorted minTavg (annual)
Station: 450 Boise
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 52.4 39.8 31.3 29.9 36.1 43.0 49.8 58.2 66.3 75.3 73.5 64.0 51.7 10.3
5 0.2 49.7 36.7 27.6 24.9 32.6 40.3 47.4 55.7 63.5 72.5 70.9 61.2 50.3 2.9
10 0.1 48.3 35.2 25.6 22.3 30.7 38.9 46.1 54.3 62.1 71.1 69.6 59.7 49.5 ‐0.9
20 0.05 47.2 33.9 24.0 20.2 29.2 37.7 45.0 53.2 60.9 69.9 68.5 58.4 48.9 ‐4.1
50 0.02 45.9 32.4 22.2 17.8 27.5 36.4 43.8 52.0 59.6 68.6 67.3 57.0 48.2 ‐7.7
100 0.01 45.1 31.4 20.9 16.1 26.3 35.5 43.0 51.2 58.7 67.7 66.5 56.1 47.8 ‐10.1
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 52.8 40.3 32.0 30.8 36.8 43.4 50.2 58.6 66.7 75.7 73.9 64.5 51.9 11.6
5 0.2 50.2 37.3 28.3 25.9 33.3 40.8 47.8 56.1 64.0 73.0 71.4 61.7 50.5 4.3
10 0.1 48.9 35.8 26.4 23.4 31.5 39.4 46.6 54.9 62.7 71.7 70.2 60.3 49.8 0.7
20 0.05 47.8 34.6 24.9 21.4 30.1 38.4 45.6 53.9 61.6 70.6 69.1 59.1 49.3 ‐2.3
50 0.02 46.7 33.3 23.2 19.1 28.5 37.1 44.5 52.7 60.3 69.3 68.0 57.8 48.6 ‐5.6
100 0.01 45.9 32.4 22.1 17.6 27.4 36.3 43.8 52.0 59.5 68.5 67.2 57.0 48.2 ‐7.8
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.9 39.2 30.7 29.1 35.5 42.5 49.4 57.8 65.8 74.8 73.1 63.5 51.4 9.0
5 0.2 49.2 36.1 26.8 23.9 31.9 39.7 46.9 55.1 63.0 72.0 70.4 60.6 50.0 1.4
10 0.1 47.7 34.4 24.7 21.1 29.9 38.2 45.5 53.7 61.4 70.4 69.0 59.0 49.2 ‐2.7
20 0.05 46.5 33.0 22.9 18.8 28.2 36.9 44.3 52.5 60.1 69.1 67.8 57.6 48.5 ‐6.2
50 0.02 45.1 31.4 20.9 16.1 26.3 35.5 43.0 51.2 58.7 67.7 66.4 56.1 47.8 ‐10.1
100 0.01 44.1 30.4 19.6 14.3 25.1 34.6 42.2 50.3 57.7 66.7 65.5 55.1 47.3 ‐12.7
Lower Confidence Limit
Tavg
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 450 Boise
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 52.3 40.1 32.3 30.6 36.7 43.0 49.8 58.2 66.1 75.2 73.5 64.1 51.7 11.2
5 0.2 49.7 36.9 28.2 25.3 32.8 40.3 47.4 55.7 63.5 72.5 71.0 61.2 50.3 3.3
10 0.1 48.4 35.0 25.4 22.0 30.5 38.8 46.1 54.3 62.2 71.1 69.6 59.6 49.5 ‐1.3
20 0.05 47.3 33.4 22.7 19.1 28.4 37.6 45.1 53.3 61.1 70.0 68.4 58.3 48.9 ‐5.4
50 0.02 46.2 31.4 19.3 15.6 25.9 36.2 44.0 52.0 60.0 68.7 67.1 56.7 48.1 ‐10.3
100 0.01 45.4 30.0 16.8 13.0 24.1 35.3 43.2 51.2 59.3 67.8 66.3 55.6 47.6 ‐13.8
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 52.9 40.7 33.1 31.8 37.5 43.6 50.3 58.7 66.7 75.8 74.1 64.8 52.0 12.8
5 0.2 50.3 37.6 29.0 26.5 33.7 40.9 47.9 56.3 64.2 73.2 71.6 61.9 50.6 5.1
10 0.1 49.1 35.9 26.4 23.4 31.5 39.6 46.8 55.0 62.9 71.9 70.3 60.4 49.9 0.7
20 0.05 48.1 34.3 24.0 20.7 29.6 38.4 45.8 54.0 62.0 70.8 69.2 59.2 49.3 ‐3.0
50 0.02 47.1 32.6 20.9 17.5 27.3 37.2 44.8 52.9 60.9 69.6 68.0 57.7 48.6 ‐7.5
100 0.01 46.4 31.3 18.6 15.2 25.7 36.3 44.1 52.2 60.3 68.8 67.3 56.8 48.2 ‐10.6
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 51.7 39.4 31.5 29.5 35.9 42.4 49.2 57.6 65.5 74.6 73.0 63.5 51.4 9.5
5 0.2 49.0 36.1 27.2 23.9 31.9 39.6 46.7 55.0 62.7 71.8 70.3 60.4 49.9 1.3
10 0.1 47.5 34.0 24.1 20.4 29.3 38.0 45.3 53.5 61.3 70.2 68.8 58.7 49.0 ‐3.7
20 0.05 46.4 32.2 21.2 17.1 27.0 36.6 44.2 52.3 60.1 68.9 67.5 57.2 48.3 ‐8.3
50 0.02 45.0 30.0 17.3 13.1 24.2 35.0 42.9 50.9 58.9 67.5 66.0 55.4 47.5 ‐13.8
100 0.01 44.2 28.4 14.4 10.2 22.1 34.0 42.0 50.0 58.0 66.5 65.0 54.2 47.0 ‐17.8
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 450 Boise
46
47
48
49
50
51
52
53
2 5 10 20 50 100
Te
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(
˚
F
)
Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐20
‐15
‐10
‐5
0
5
10
15
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
Normal Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
46
47
48
49
50
51
52
53
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐20
‐15
‐10
‐5
0
5
10
15
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
Station: 500 Hailey
Water Years (WY) Starting: 1910 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 46.0 32.7 22.0 19.6 24.1 32.2 42.6 51.5 58.9 67.6 65.9 56.9 43.4 ‐1.0
Sx 3.0 3.9 4.4 4.7 5.0 4.3 3.5 3.0 2.7 2.5 2.5 3.1 1.6 7.3
Skew ‐0.04 ‐0.2 ‐0.1 ‐0.4 ‐0.1 0.0 0.0 0.2 0.5 ‐0.3 ‐0.2 ‐0.4 0.2 ‐0.3
Max 53.4 41.3 32.6 30.1 36.6 43.4 51.6 58.8 66.4 76.1 71.2 62.4 48.7 12.9
Min 37.8 22.1 9.4 6.0 10.4 20.3 34.3 44.7 54.4 58.3 60.4 49.4 39.4 ‐22.5
n (years) 111 111 111 111 111 111 111 111 111 111 111 111 111 111
Tavg (˚F)
‐30
‐20
‐10
0
10
20
30
40
50
60
1900 1920 1940 1960 1980 2000 2020
Te
m
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t
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(
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F
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Year
Hailey Annual Temperatures
Tavg minTavg
36
38
40
42
44
46
48
50
1 11 21 31 41 51 61 71 81 91 101 111
Te
m
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Sorted Tavg (annual)
‐30
‐20
‐10
0
10
20
1 11 21 31 41 51 61 71 81 91 101 111Te
m
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Sorted minTavg (annual)
Station: 500 Hailey
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.0 32.7 22.0 19.6 24.1 32.2 42.6 51.5 58.9 67.6 65.9 56.9 43.4 ‐1.0
5 0.2 43.5 29.4 18.3 15.6 19.9 28.6 39.7 49.0 56.6 65.5 63.8 54.3 42.1 ‐7.1
10 0.1 42.1 27.7 16.3 13.5 17.7 26.8 38.2 47.7 55.4 64.4 62.7 53.0 41.4 ‐10.3
20 0.05 41.0 26.3 14.7 11.8 15.9 25.2 36.9 46.6 54.4 63.5 61.8 51.8 40.8 ‐13.0
50 0.02 39.8 24.7 12.9 9.9 13.8 23.5 35.5 45.4 53.3 62.4 60.8 50.6 40.1 ‐15.9
100 0.01 39.0 23.6 11.7 8.6 12.4 22.3 34.6 44.6 52.5 61.7 60.1 49.7 39.7 ‐17.9
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.4 33.1 22.6 20.1 24.7 32.8 43.1 51.9 59.3 67.9 66.2 57.3 43.6 ‐0.1
5 0.2 43.9 29.9 18.9 16.3 20.6 29.2 40.2 49.4 57.0 65.8 64.2 54.7 42.3 ‐6.1
10 0.1 42.6 28.3 17.0 14.3 18.5 27.4 38.7 48.1 55.8 64.8 63.1 53.4 41.6 ‐9.2
20 0.05 41.6 26.9 15.5 12.7 16.7 26.0 37.5 47.1 54.9 63.9 62.3 52.4 41.1 ‐11.7
50 0.02 40.4 25.4 13.8 10.9 14.8 24.3 36.2 46.0 53.8 62.9 61.3 51.2 40.4 ‐14.5
100 0.01 39.6 24.5 12.7 9.7 13.5 23.2 35.3 45.2 53.1 62.3 60.7 50.4 40.0 ‐16.3
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.7 32.2 21.5 19.0 23.5 31.7 42.2 51.1 58.6 67.3 65.6 56.5 43.2 ‐1.8
5 0.2 43.0 28.8 17.6 14.9 19.1 28.0 39.2 48.5 56.2 65.1 63.5 53.9 41.8 ‐8.2
10 0.1 41.6 27.0 15.6 12.7 16.8 26.0 37.6 47.2 54.9 63.9 62.3 52.4 41.1 ‐11.6
20 0.05 40.4 25.5 13.8 10.9 14.9 24.3 36.2 46.0 53.9 63.0 61.3 51.2 40.5 ‐14.4
50 0.02 39.1 23.8 11.9 8.8 12.6 22.5 34.7 44.7 52.7 61.8 60.2 49.9 39.8 ‐17.6
100 0.01 38.2 22.6 10.6 7.4 11.2 21.2 33.7 43.8 51.8 61.1 59.5 49.0 39.3 ‐19.8
Lower Confidence Limit
Tavg
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 500 Hailey
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.0 32.8 22.1 19.9 24.2 32.2 42.6 51.4 58.7 67.7 66.0 57.1 43.4 ‐0.5
5 0.2 43.5 29.4 18.3 15.7 19.9 28.6 39.7 49.0 56.6 65.5 63.9 54.4 42.1 ‐6.9
10 0.1 42.1 27.6 16.3 13.4 17.7 26.8 38.2 47.8 55.6 64.3 62.7 52.8 41.4 ‐10.5
20 0.05 41.0 26.0 14.6 11.4 15.8 25.2 37.0 46.8 54.8 63.2 61.7 51.5 40.9 ‐13.6
50 0.02 39.7 24.2 12.6 9.0 13.7 23.5 35.6 45.8 54.0 62.0 60.6 49.9 40.3 ‐17.2
100 0.01 38.9 23.0 11.3 7.3 12.2 22.4 34.7 45.1 53.5 61.1 59.8 48.8 39.9 ‐19.7
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.5 33.4 22.8 20.6 24.9 32.9 43.2 51.9 59.2 68.1 66.4 57.6 43.6 0.6
5 0.2 44.0 30.1 19.1 16.5 20.8 29.4 40.3 49.5 57.1 66.0 64.3 54.9 42.3 ‐5.7
10 0.1 42.7 28.4 17.2 14.3 18.6 27.6 38.9 48.3 56.1 64.8 63.2 53.5 41.7 ‐9.1
20 0.05 41.7 26.9 15.6 12.4 16.9 26.2 37.7 47.5 55.4 63.8 62.3 52.2 41.2 ‐12.0
50 0.02 40.5 25.3 13.8 10.3 14.9 24.6 36.5 46.5 54.6 62.7 61.2 50.7 40.7 ‐15.3
100 0.01 39.7 24.1 12.6 8.8 13.6 23.6 35.6 45.9 54.1 61.9 60.5 49.7 40.3 ‐17.6
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.6 32.2 21.4 19.1 23.4 31.6 42.1 50.9 58.3 67.3 65.6 56.6 43.1 ‐1.7
5 0.2 42.9 28.7 17.5 14.8 18.9 27.8 39.0 48.4 56.0 65.0 63.4 53.8 41.7 ‐8.3
10 0.1 41.4 26.7 15.3 12.3 16.5 25.8 37.4 47.1 55.0 63.7 62.1 52.1 41.0 ‐12.2
20 0.05 40.2 25.0 13.4 10.1 14.4 24.1 36.1 46.0 54.1 62.6 61.0 50.6 40.5 ‐15.6
50 0.02 38.8 23.0 11.3 7.5 12.1 22.2 34.6 44.9 53.2 61.2 59.8 48.9 39.8 ‐19.6
100 0.01 37.9 21.7 9.8 5.6 10.5 21.0 33.5 44.2 52.6 60.2 58.9 47.6 39.4 ‐22.4
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 500 Hailey
39
40
41
42
43
44
2 5 10 20 50 100
Te
m
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a
t
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˚
F
)
Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
Normal Annual Minimum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
39
40
41
42
43
44
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
Station: 600 Twin Falls
Water Years (WY) Starting: 1906 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 49.5 37.8 29.3 27.7 32.9 40.2 47.6 55.8 63.5 71.5 69.2 60.0 48.8 6.4
Sx 3.0 3.4 4.5 5.3 4.7 3.2 3.1 3.0 3.0 2.9 2.7 2.9 1.7 8.3
Skew 0.1 ‐0.5 ‐0.6 ‐0.7 ‐0.3 ‐0.1 0.0 0.2 0.5 ‐0.3 0.1 ‐0.1 0.3 ‐0.3
Max 58.5 44.7 40.0 40.3 42.6 48.9 55.4 63.8 73.5 79.5 77.1 66.6 54.3 24.0
Min 41.8 26.8 12.8 7.8 19.4 30.8 40.4 49.6 57.0 60.9 63.6 53.1 44.6 ‐14.5
n (years) 114 115 114 115 115 115 113 114 114 115 115 115 115 115
Tavg (˚F)
‐20
‐10
0
10
20
30
40
50
60
1900 1920 1940 1960 1980 2000 2020
Te
m
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a
t
u
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(
˚
F
)
Year
Twin Falls Annual Temperatures
Tavg minTavg
42
44
46
48
50
52
54
56
1 11 21 31 41 51 61 71 81 91 101 111
Te
m
p
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r
a
t
u
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(
˚
F
)
Sorted Tavg (annual)
‐20
‐10
0
10
20
30
1 11 21 31 41 51 61 71 81 91 101 111
Te
m
p
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r
a
t
u
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(
˚
F
)
Sorted minTavg (annual)
Station: 600 Twin Falls
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 49.5 37.8 29.3 27.7 32.9 40.2 47.6 55.8 63.5 71.5 69.2 60.0 48.8 6.4
5 0.2 47.0 35.0 25.5 23.2 28.9 37.4 44.9 53.2 61.0 69.1 67.0 57.5 47.4 ‐0.7
10 0.1 45.7 33.5 23.5 20.8 26.8 36.0 43.5 51.9 59.7 67.8 65.8 56.2 46.7 ‐4.3
20 0.05 44.6 32.3 21.9 18.9 25.1 34.9 42.4 50.8 58.6 66.8 64.8 55.2 46.1 ‐7.4
50 0.02 43.4 30.9 20.0 16.7 23.2 33.5 41.1 49.5 57.4 65.6 63.7 54.0 45.4 ‐10.8
100 0.01 42.6 30.0 18.8 15.3 21.9 32.7 40.3 48.7 56.6 64.8 63.0 53.2 45.0 ‐13.0
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 49.9 38.2 29.9 28.3 33.5 40.5 47.9 56.1 63.9 71.8 69.5 60.4 49.0 7.4
5 0.2 47.4 35.4 26.1 23.9 29.5 37.9 45.3 53.6 61.4 69.5 67.3 57.9 47.6 0.5
10 0.1 46.2 34.0 24.2 21.7 27.6 36.5 44.0 52.3 60.2 68.3 66.2 56.7 46.9 ‐3.1
20 0.05 45.1 32.9 22.7 19.8 25.9 35.4 42.9 51.3 59.2 67.3 65.3 55.7 46.4 ‐5.9
50 0.02 44.0 31.6 20.9 17.8 24.1 34.2 41.7 50.1 58.0 66.2 64.3 54.5 45.7 ‐9.1
100 0.01 43.2 30.7 19.8 16.4 22.9 33.4 40.9 49.3 57.3 65.4 63.6 53.8 45.3 ‐11.3
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 49.2 37.4 28.8 27.0 32.3 39.8 47.2 55.4 63.2 71.2 68.9 59.6 48.6 5.4
5 0.2 46.6 34.5 24.9 22.4 28.2 37.0 44.5 52.7 60.6 68.7 66.6 57.1 47.2 ‐1.9
10 0.1 45.2 32.9 22.8 19.9 26.0 35.5 43.0 51.3 59.2 67.3 65.3 55.7 46.4 ‐5.8
20 0.05 44.0 31.6 21.0 17.9 24.2 34.2 41.8 50.1 58.0 66.2 64.3 54.6 45.8 ‐9.0
50 0.02 42.7 30.1 19.0 15.5 22.1 32.8 40.4 48.8 56.7 65.0 63.1 53.3 45.0 ‐12.7
100 0.01 41.8 29.1 17.7 14.0 20.7 31.9 39.5 47.9 55.9 64.1 62.3 52.4 44.5 ‐15.1
Lower Confidence Limit
Tavg
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 600 Twin Falls
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 49.5 38.1 29.8 28.3 33.1 40.2 47.5 55.6 63.3 71.7 69.2 60.1 48.7 6.8
5 0.2 47.0 35.1 25.7 23.5 29.0 37.5 44.9 53.2 61.0 69.1 67.0 57.5 47.4 ‐0.5
10 0.1 45.7 33.4 23.3 20.6 26.7 36.0 43.6 51.9 59.9 67.7 65.8 56.2 46.7 ‐4.6
20 0.05 44.7 31.9 21.3 18.0 24.7 34.8 42.4 51.0 59.1 66.5 64.9 55.1 46.2 ‐8.1
50 0.02 43.5 30.1 18.8 14.9 22.4 33.4 41.2 49.9 58.3 65.1 63.9 53.8 45.7 ‐12.2
100 0.01 42.7 28.8 17.0 12.7 20.8 32.5 40.4 49.2 57.8 64.2 63.3 52.9 45.3 ‐15.0
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 50.0 38.6 30.5 29.1 33.9 40.7 48.0 56.1 63.7 72.1 69.6 60.5 49.0 8.1
5 0.2 47.5 35.7 26.5 24.4 29.8 38.0 45.4 53.7 61.5 69.6 67.4 58.0 47.7 0.9
10 0.1 46.3 34.0 24.2 21.6 27.6 36.6 44.2 52.5 60.5 68.3 66.4 56.8 47.1 ‐2.9
20 0.05 45.3 32.6 22.3 19.2 25.8 35.5 43.1 51.6 59.7 67.2 65.5 55.7 46.6 ‐6.2
50 0.02 44.2 31.0 20.0 16.4 23.7 34.2 42.0 50.6 59.0 65.9 64.6 54.5 46.1 ‐10.0
100 0.01 43.5 29.8 18.4 14.3 22.2 33.4 41.2 50.0 58.5 65.0 64.0 53.7 45.7 ‐12.6
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 49.0 37.6 29.1 27.4 32.4 39.7 47.0 55.2 62.8 71.2 68.7 59.6 48.5 5.5
5 0.2 46.4 34.5 24.9 22.5 28.1 36.8 44.3 52.6 60.4 68.6 66.4 57.0 47.1 ‐2.1
10 0.1 45.0 32.6 22.3 19.4 25.6 35.3 42.8 51.3 59.3 67.1 65.2 55.5 46.4 ‐6.5
20 0.05 43.9 30.9 20.0 16.6 23.5 34.0 41.6 50.2 58.4 65.8 64.3 54.3 45.8 ‐10.3
50 0.02 42.6 29.0 17.3 13.1 20.9 32.5 40.3 49.0 57.5 64.2 63.2 52.9 45.2 ‐14.8
100 0.01 41.8 27.6 15.3 10.6 19.2 31.4 39.3 48.3 56.9 63.2 62.4 51.9 44.8 ‐18.0
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 600 Twin Falls
44
45
46
47
48
49
50
2 5 10 20 50 100
Te
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a
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Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐20
‐15
‐10
‐5
0
5
10
2 5 10 20 50 100
Te
m
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r
a
t
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(
˚
F
)
Return Period, T (years)
Normal Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
44
45
46
47
48
49
50
2 5 10 20 50 100
Te
m
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r
a
t
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(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐20
‐15
‐10
‐5
0
5
10
2 5 10 20 50 100
Te
m
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a
t
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(
˚
F
)
Return Period, T (years)
PIII Annual Minimum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
Station: 700 Rexburg
Water Years (WY) Starting: 1908 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 44.9 31.9 21.0 18.4 22.5 31.8 42.9 52.1 59.5 66.9 64.7 55.9 42.8 ‐5.9
Sx 3.1 4.1 4.8 5.5 5.9 5.0 3.4 2.9 2.7 2.4 2.6 2.9 1.8 8.0
Skew ‐0.2 ‐0.1 0.0 ‐0.4 ‐0.3 ‐0.3 ‐0.1 0.0 0.1 ‐0.1 0.0 ‐0.3 0.0 ‐0.2
Max 51.8 42.5 33.7 32.3 36.0 42.4 50.7 58.3 66.5 73.3 70.3 62.2 48.3 16.0
Min 36.7 21.7 11.8 ‐0.1 6.2 17.7 33.1 46.0 52.5 58.4 58.9 47.5 37.6 ‐27.5
n (years) 112 111 112 113 113 113 113 113 113 112 112 112 113 113
Tavg (˚F)
‐40
‐30
‐20
‐10
0
10
20
30
40
50
60
1900 1920 1940 1960 1980 2000 2020Te
m
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(
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Year
Rexburg Annual Temperatures
Tavg minTavg
36
38
40
42
44
46
48
50
1 11 21 31 41 51 61 71 81 91 101 111
Te
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(
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F
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Sorted Tavg (annual)
‐30
‐20
‐10
0
10
20
1 11 21 31 41 51 61 71 81 91 101 111
Te
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(
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Sorted minTavg (annual)
Station: 700 Rexburg
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 44.9 31.9 21.0 18.4 22.5 31.8 42.9 52.1 59.5 66.9 64.7 55.9 42.8 ‐5.9
5 0.2 42.3 28.4 17.0 13.7 17.5 27.6 40.1 49.6 57.2 64.8 62.6 53.4 41.2 ‐12.6
10 0.1 40.9 26.6 14.9 11.3 14.9 25.4 38.6 48.3 56.0 63.8 61.4 52.1 40.4 ‐16.1
20 0.05 39.8 25.2 13.1 9.3 12.8 23.6 37.3 47.3 55.0 62.9 60.5 51.1 39.8 ‐19.1
50 0.02 38.5 23.5 11.2 7.1 10.4 21.5 35.9 46.1 53.9 61.9 59.4 49.9 39.0 ‐22.3
100 0.01 37.7 22.4 9.9 5.6 8.8 20.1 35.0 45.3 53.2 61.2 58.7 49.1 38.5 ‐24.5
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.2 32.4 21.6 19.0 23.2 32.4 43.3 52.4 59.8 67.2 65.0 56.2 43.0 ‐4.9
5 0.2 42.7 29.0 17.6 14.5 18.3 28.3 40.5 50.0 57.6 65.2 62.9 53.8 41.5 ‐11.5
10 0.1 41.4 27.3 15.6 12.2 15.9 26.2 39.1 48.8 56.4 64.1 61.8 52.6 40.7 ‐14.9
20 0.05 40.3 25.9 14.0 10.3 13.8 24.4 37.9 47.8 55.5 63.3 60.9 51.6 40.1 ‐17.7
50 0.02 39.2 24.3 12.1 8.2 11.6 22.5 36.6 46.7 54.5 62.4 59.9 50.5 39.4 ‐20.7
100 0.01 38.4 23.3 10.9 6.8 10.1 21.2 35.7 45.9 53.8 61.7 59.3 49.7 38.9 ‐22.8
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 44.5 31.4 20.4 17.7 21.8 31.2 42.5 51.7 59.2 66.6 64.4 55.5 42.6 ‐6.8
5 0.2 41.8 27.8 16.3 12.9 16.7 26.8 39.6 49.2 56.8 64.5 62.2 53.0 41.0 ‐13.8
10 0.1 40.4 25.9 14.0 10.4 13.9 24.5 38.0 47.8 55.5 63.3 61.0 51.6 40.1 ‐17.5
20 0.05 39.2 24.3 12.2 8.2 11.6 22.6 36.6 46.7 54.5 62.4 60.0 50.5 39.4 ‐20.6
50 0.02 37.8 22.5 10.1 5.8 9.1 20.4 35.1 45.4 53.3 61.3 58.8 49.2 38.6 ‐24.2
100 0.01 36.9 21.3 8.7 4.2 7.3 18.9 34.1 44.6 52.5 60.6 58.1 48.4 38.0 ‐26.5
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Lower Confidence Limit
Tavg
Station: 700 Rexburg
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.0 32.0 21.0 18.8 22.8 32.0 43.0 52.1 59.4 66.9 64.7 56.0 42.8 ‐5.6
5 0.2 42.3 28.5 17.0 13.9 17.6 27.7 40.1 49.6 57.2 64.8 62.6 53.5 41.2 ‐12.5
10 0.1 40.9 26.6 14.9 11.1 14.8 25.3 38.5 48.3 56.1 63.7 61.4 52.0 40.4 ‐16.3
20 0.05 39.6 25.0 13.2 8.7 12.3 23.2 37.2 47.2 55.1 62.8 60.5 50.8 39.8 ‐19.5
50 0.02 38.2 23.2 11.3 5.8 9.4 20.8 35.7 46.0 54.1 61.7 59.4 49.4 39.0 ‐23.2
100 0.01 37.3 22.0 10.1 3.8 7.4 19.2 34.7 45.2 53.5 61.0 58.7 48.4 38.6 ‐25.7
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.4 32.6 21.7 19.6 23.7 32.8 43.5 52.6 59.9 67.3 65.1 56.5 43.1 ‐4.4
5 0.2 42.8 29.2 17.8 14.8 18.7 28.5 40.7 50.1 57.7 65.3 63.0 54.0 41.6 ‐11.2
10 0.1 41.5 27.4 15.8 12.2 15.9 26.2 39.2 48.9 56.6 64.2 61.9 52.6 40.8 ‐14.7
20 0.05 40.3 25.9 14.3 9.9 13.6 24.3 38.0 47.9 55.7 63.3 61.0 51.5 40.2 ‐17.7
50 0.02 39.0 24.3 12.5 7.3 10.9 22.1 36.6 46.8 54.8 62.3 60.1 50.2 39.5 ‐21.1
100 0.01 38.2 23.2 11.3 5.4 9.1 20.6 35.7 46.0 54.2 61.7 59.4 49.2 39.1 ‐23.4
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 44.5 31.3 20.2 17.9 21.9 31.3 42.5 51.7 59.0 66.5 64.3 55.6 42.5 ‐6.9
5 0.2 41.7 27.7 16.0 12.8 16.5 26.7 39.4 49.1 56.7 64.4 62.1 52.9 40.9 ‐14.1
10 0.1 40.2 25.7 13.8 9.8 13.4 24.1 37.7 47.7 55.5 63.2 60.8 51.4 40.0 ‐18.1
20 0.05 38.8 23.9 12.0 7.2 10.7 21.9 36.3 46.5 54.4 62.1 59.8 50.0 39.3 ‐21.6
50 0.02 37.3 22.0 9.9 4.0 7.5 19.2 34.7 45.1 53.3 61.0 58.6 48.4 38.5 ‐25.7
100 0.01 36.2 20.6 8.5 1.8 5.3 17.4 33.6 44.2 52.6 60.2 57.9 47.3 38.0 ‐28.5
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 700 Rexburg
37
38
39
40
41
42
43
44
2 5 10 20 50 100
Te
m
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(
˚
F
)
Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐30
‐25
‐20
‐15
‐10
‐5
0
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
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(
˚
F
)
Return Period, T (years)
Normal Annual Minimum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
37
38
39
40
41
42
43
44
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
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(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐30
‐25
‐20
‐15
‐10
‐5
0
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
Station: 750 Idaho Falls
Water Years (WY) Starting: 1949 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 45.5 32.7 21.7 19.4 24.5 34.7 44.2 53.1 61.0 68.6 66.9 57.5 44.2 ‐4.7
Sx 2.9 3.8 4.7 6.2 6.4 4.7 2.9 2.6 2.5 2.2 2.3 3.0 1.7 7.8
Skew ‐0.2 ‐0.2 ‐0.4 ‐0.1 ‐0.3 ‐0.9 ‐0.1 0.2 0.5 ‐0.9 0.0 ‐0.4 ‐0.4 ‐0.3
Max 52.6 40.0 30.0 32.8 36.9 42.9 50.1 59.9 67.5 72.4 71.6 64.2 48.1 10.1
Min 36.9 23.7 10.0 4.2 7.1 17.7 37.5 47.5 56.6 59.8 62.6 49.8 39.0 ‐23.0
n (years) 72 72 72 72 72 72 72 72 72 72 72 72 72 72
Tavg (˚F)
‐30
‐20
‐10
0
10
20
30
40
50
1940 1960 1980 2000 2020
Te
m
p
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r
a
t
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(
˚
F
)
Year
Idaho Falls Annual Temperatures
Tavg minTavg
36
38
40
42
44
46
48
50
1 11 21 31 41 51 61 71
Te
m
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r
a
t
u
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(
˚
F
)
Sorted Tavg (annual)
‐30
‐20
‐10
0
10
20
1 11 21 31 41 51 61 71
Te
m
p
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r
a
t
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(
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F
)
Sorted minTavg (annual)
Station: 750 Idaho Falls
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.5 32.7 21.7 19.4 24.5 34.7 44.2 53.1 61.0 68.6 66.9 57.5 44.2 ‐4.7
5 0.2 43.1 29.5 17.8 14.3 19.2 30.7 41.8 50.9 58.8 66.8 65.0 55.1 42.8 ‐11.2
10 0.1 41.9 27.8 15.7 11.5 16.4 28.7 40.6 49.7 57.7 65.8 64.0 53.8 42.1 ‐14.7
20 0.05 40.8 26.5 14.0 9.3 14.0 27.0 39.5 48.8 56.8 65.1 63.2 52.7 41.5 ‐17.5
50 0.02 39.6 24.9 12.1 6.8 11.4 25.0 38.4 47.7 55.8 64.2 62.2 51.5 40.8 ‐20.7
100 0.01 38.9 23.9 10.9 5.1 9.7 23.8 37.6 47.0 55.1 63.6 61.6 50.7 40.3 ‐22.8
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.0 33.2 22.4 20.4 25.5 35.4 44.7 53.5 61.4 68.9 67.2 58.0 44.5 ‐3.5
5 0.2 43.6 30.1 18.6 15.3 20.2 31.5 42.3 51.3 59.3 67.2 65.3 55.5 43.1 ‐9.9
10 0.1 42.4 28.6 16.6 12.7 17.6 29.6 41.1 50.2 58.2 66.3 64.4 54.3 42.4 ‐13.2
20 0.05 41.4 27.3 15.0 10.6 15.4 28.0 40.1 49.3 57.3 65.5 63.6 53.3 41.8 ‐15.8
50 0.02 40.3 25.9 13.3 8.3 13.0 26.2 39.1 48.3 56.4 64.7 62.8 52.2 41.2 ‐18.8
100 0.01 39.6 24.9 12.1 6.8 11.4 25.0 38.4 47.7 55.8 64.2 62.2 51.5 40.8 ‐20.7
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.1 32.1 21.0 18.5 23.6 34.0 43.8 52.7 60.6 68.3 66.5 57.1 44.0 ‐5.9
5 0.2 42.6 28.8 16.9 13.1 18.0 29.9 41.3 50.4 58.4 66.4 64.5 54.5 42.5 ‐12.7
10 0.1 41.2 27.0 14.7 10.2 14.9 27.6 39.9 49.1 57.2 65.4 63.5 53.1 41.7 ‐16.4
20 0.05 40.1 25.5 12.9 7.7 12.4 25.8 38.8 48.1 56.2 64.5 62.6 51.9 41.1 ‐19.5
50 0.02 38.8 23.8 10.8 5.0 9.5 23.6 37.5 46.9 55.0 63.5 61.6 50.6 40.3 ‐23.0
100 0.01 37.9 22.7 9.4 3.1 7.6 22.2 36.7 46.1 54.3 62.9 60.9 49.7 39.8 ‐25.3
Lower Confidence Limit
Tavg
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 750 Idaho Falls
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.6 32.8 22.0 19.6 24.9 35.4 44.3 53.0 60.8 68.9 66.9 57.7 44.3 ‐4.3
5 0.2 43.1 29.5 17.9 14.3 19.3 31.1 41.8 50.8 58.8 67.0 65.0 55.1 42.9 ‐11.1
10 0.1 41.8 27.8 15.6 11.5 16.2 28.4 40.5 49.8 57.9 65.7 64.0 53.7 42.0 ‐14.9
20 0.05 40.7 26.3 13.5 9.1 13.5 26.0 39.5 48.9 57.2 64.6 63.2 52.4 41.3 ‐18.1
50 0.02 39.4 24.5 11.1 6.4 10.3 23.0 38.2 48.0 56.5 63.2 62.2 50.9 40.4 ‐21.8
100 0.01 38.5 23.4 9.5 4.5 8.1 20.8 37.4 47.3 56.0 62.2 61.6 49.8 39.8 ‐24.3
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 46.2 33.5 22.9 20.8 26.2 36.3 44.8 53.5 61.3 69.3 67.3 58.3 44.7 ‐2.8
5 0.2 43.7 30.3 18.9 15.6 20.6 32.1 42.4 51.4 59.3 67.4 65.5 55.7 43.2 ‐9.5
10 0.1 42.5 28.7 16.7 13.0 17.7 29.6 41.2 50.4 58.5 66.3 64.5 54.4 42.4 ‐13.0
20 0.05 41.5 27.3 14.8 10.8 15.2 27.3 40.2 49.6 57.8 65.2 63.8 53.2 41.8 ‐15.9
50 0.02 40.3 25.8 12.7 8.3 12.4 24.6 39.1 48.7 57.2 64.0 62.9 51.9 41.0 ‐19.3
100 0.01 39.5 24.7 11.2 6.6 10.4 22.7 38.4 48.2 56.8 63.1 62.4 50.9 40.4 ‐21.5
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 45.0 32.1 21.1 18.4 23.7 34.5 43.7 52.5 60.3 68.5 66.4 57.1 44.0 ‐5.8
5 0.2 42.4 28.6 16.8 12.8 17.7 30.0 41.1 50.2 58.2 66.4 64.4 54.4 42.5 ‐13.0
10 0.1 41.0 26.7 14.2 9.7 14.3 27.0 39.7 49.0 57.2 65.1 63.3 52.8 41.5 ‐17.1
20 0.05 39.7 25.0 11.9 7.0 11.2 24.3 38.5 48.0 56.4 63.8 62.4 51.4 40.7 ‐20.7
50 0.02 38.2 23.0 9.2 3.9 7.7 20.8 37.1 47.0 55.6 62.3 61.3 49.7 39.7 ‐25.0
100 0.01 37.2 21.7 7.3 1.8 5.2 18.3 36.1 46.3 55.1 61.1 60.6 48.5 39.0 ‐27.9
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 750 Idaho Falls
38
39
40
41
42
43
44
45
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
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(
˚
F
)
Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐30
‐25
‐20
‐15
‐10
‐5
0
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
Normal Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
38
39
40
41
42
43
44
45
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐30
‐25
‐20
‐15
‐10
‐5
0
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
Station: 800 Pocatello
Water Years (WY) Starting: 1939 Ending: 2020
minTavg
Month Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
Mean 47.9 35.2 26.1 24.0 29.2 37.3 45.6 54.2 62.4 71.0 69.3 59.4 46.9 0.2
Sx 3.1 3.6 4.5 5.9 5.3 3.7 2.9 2.8 2.8 2.3 2.2 2.7 1.4 8.0
Skew ‐0.04 ‐0.33 ‐0.47 ‐0.42 ‐0.44 ‐0.53 0.14 0.18 0.58 ‐0.93 ‐0.32 ‐0.53 ‐0.10 ‐0.26
Max 55.3 42.4 34.5 36.2 38.6 44.2 52.4 61.4 69.6 75.1 73.5 65.6 50.3 15.0
Min 39.2 25.8 11.4 5.1 16.9 27.5 39.0 48.5 57.3 61.1 62.9 51.8 43.4 ‐17.5
n (years) 81 81 81 82 82 82 82 82 82 82 82 82 82 82
Tavg (˚F)
‐20
‐10
0
10
20
30
40
50
60
1920 1940 1960 1980 2000 2020
Te
m
p
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r
a
t
u
r
e
s

(
˚
F
)
Year
Pocatello Annual Temperatures
Tavg minTavg
42
44
46
48
50
52
1 11 21 31 41 51 61 71 81
Te
m
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a
t
u
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e

(
˚
F
)
Sorted Tavg (annual)
‐20
‐10
0
10
20
1 11 21 31 41 51 61 71 81
Te
m
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a
t
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(
˚
F
)
Sorted minTavg (annual)
Station: 800 Pocatello
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 47.9 35.2 26.1 24.0 29.2 37.3 45.6 54.2 62.4 71.0 69.3 59.4 46.9 0.2
5 0.2 45.3 32.1 22.3 19.0 24.8 34.2 43.1 51.9 60.0 69.0 67.4 57.1 45.7 ‐6.5
10 0.1 44.0 30.6 20.3 16.4 22.4 32.5 41.8 50.7 58.8 68.0 66.5 55.9 45.1 ‐10.0
20 0.05 42.9 29.2 18.7 14.2 20.5 31.2 40.8 49.7 57.8 67.1 65.7 54.9 44.5 ‐12.9
50 0.02 41.6 27.8 16.9 11.8 18.3 29.7 39.6 48.5 56.7 66.2 64.8 53.8 44.0 ‐16.2
100 0.01 40.8 26.8 15.6 10.2 16.9 28.6 38.8 47.8 55.9 65.5 64.2 53.1 43.6 ‐18.4
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 48.3 35.7 26.7 24.8 30.0 37.8 46.0 54.6 62.8 71.3 69.6 59.8 47.1 1.4
5 0.2 45.8 32.7 23.0 19.9 25.6 34.8 43.6 52.3 60.5 69.4 67.8 57.6 45.9 ‐5.2
10 0.1 44.5 31.2 21.1 17.5 23.4 33.2 42.4 51.2 59.3 68.4 66.9 56.4 45.3 ‐8.6
20 0.05 43.5 30.0 19.6 15.5 21.6 31.9 41.4 50.2 58.4 67.6 66.1 55.5 44.8 ‐11.3
50 0.02 42.3 28.6 17.9 13.2 19.6 30.5 40.3 49.2 57.3 66.7 65.3 54.5 44.3 ‐14.4
100 0.01 41.5 27.7 16.8 11.7 18.2 29.6 39.5 48.5 56.6 66.1 64.7 53.8 43.9 ‐16.4
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 47.4 34.7 25.4 23.2 28.5 36.8 45.2 53.8 62.0 70.6 69.0 59.0 46.7 ‐0.9
5 0.2 44.8 31.5 21.5 18.0 23.8 33.5 42.6 51.4 59.5 68.6 67.0 56.7 45.4 ‐7.9
10 0.1 43.3 29.8 19.4 15.2 21.3 31.8 41.2 50.1 58.2 67.5 66.0 55.4 44.8 ‐11.7
20 0.05 42.1 28.4 17.6 12.8 19.3 30.3 40.1 49.0 57.1 66.6 65.2 54.3 44.2 ‐14.8
50 0.02 40.8 26.8 15.6 10.2 16.9 28.6 38.8 47.8 55.9 65.5 64.2 53.1 43.6 ‐18.4
100 0.01 39.8 25.7 14.3 8.4 15.3 27.5 37.9 46.9 55.1 64.8 63.5 52.3 43.2 ‐20.8
Tavg
NORMAL DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Lower Confidence Limit
Tavg
Station: 800 Pocatello
T Exceed.minTavg
years Prob. (P) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 47.9 35.4 26.4 24.4 29.6 37.6 45.5 54.2 62.1 71.3 69.4 59.7 46.9 0.6
5 0.2 45.3 32.2 22.4 19.2 24.9 34.3 43.1 51.9 60.0 69.2 67.5 57.2 45.7 ‐6.4
10 0.1 44.0 30.4 20.1 16.2 22.2 32.4 41.9 50.7 59.0 67.9 66.4 55.8 45.0 ‐10.2
20 0.05 42.8 28.9 18.1 13.6 19.9 30.7 40.9 49.8 58.3 66.6 65.5 54.6 44.5 ‐13.5
50 0.02 41.5 27.1 15.8 10.5 17.1 28.7 39.8 48.8 57.5 65.1 64.4 53.1 43.9 ‐17.3
100 0.01 40.7 25.9 14.1 8.4 15.2 27.2 39.1 48.1 57.1 64.0 63.7 52.0 43.5 ‐19.9
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 48.5 36.0 27.2 25.5 30.6 38.3 46.1 54.7 62.6 71.8 69.8 60.2 47.1 2.1
5 0.2 45.9 32.9 23.3 20.4 26.0 35.0 43.7 52.4 60.5 69.6 67.9 57.8 46.0 ‐4.8
10 0.1 44.7 31.3 21.2 17.6 23.5 33.2 42.5 51.4 59.6 68.4 66.9 56.5 45.4 ‐8.4
20 0.05 43.6 29.9 19.3 15.2 21.3 31.7 41.6 50.5 59.0 67.3 66.1 55.3 44.9 ‐11.4
50 0.02 42.4 28.3 17.2 12.4 18.8 29.8 40.6 49.6 58.3 65.9 65.1 53.9 44.3 ‐14.9
100 0.01 41.7 27.1 15.7 10.4 17.0 28.5 40.0 49.0 57.8 64.9 64.4 53.0 43.9 ‐17.2
T P minTavg
years prob. Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Annual Annual
2 0.5 47.3 34.7 25.6 23.3 28.7 37.0 45.0 53.7 61.6 70.9 69.0 59.2 46.6 ‐0.9
5 0.2 44.6 31.4 21.4 17.8 23.7 33.5 42.4 51.2 59.3 68.7 67.0 56.6 45.4 ‐8.2
10 0.1 43.1 29.5 18.9 14.6 20.8 31.4 41.1 50.0 58.3 67.2 65.8 55.1 44.7 ‐12.4
20 0.05 41.9 27.8 16.7 11.7 18.2 29.5 40.0 49.0 57.5 65.8 64.8 53.7 44.1 ‐16.1
50 0.02 40.4 25.7 14.0 8.2 15.1 27.2 38.8 47.8 56.6 64.1 63.6 52.0 43.4 ‐20.3
100 0.01 39.4 24.4 12.1 5.8 12.9 25.6 37.9 47.1 56.1 62.9 62.7 50.8 42.9 ‐23.3
Tavg
Lower Confidence Limit
Tavg
PIII DISTRIBUTION
Exceedance Temperatures 
Tavg
Upper Confidence Limit
Station: 800 Pocatello
42
43
44
45
46
47
48
2 5 10 20 50 100
Te
m
p
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r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
Normal Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
Normal Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
42
43
44
45
46
47
48
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Daily Average 
Exceedance Temperatures
Upper CL
Tavg
Lower CL
‐25
‐20
‐15
‐10
‐5
0
5
2 5 10 20 50 100
Te
m
p
e
r
a
t
u
r
e

(
˚
F
)
Return Period, T (years)
PIII Annual Minumum Daily Average 
Exceedance Temperatures
Upper CL
minTavg
Lower CL
11

Appendix B
Analysis Details
This appendix presents information about the methods used to analyze the data in this report.
The T-year exceedance temperatures presented in this report are statistical estimates based on
NORM and PIII probability distributions fitted using sets of sample observations. Exceedance
temperatures were calculated using the Frequency Factor method applied to the Norm and PIII
distributions (Chow et al., 1988).
At least two sources of uncertainty are involved in these T-year exceedance temperature
estimates. One source is the selection of an appropriate probability distribution to represent
the sample observations; a second source is associated with how well the random sample of
observations collected represents the underlying population. 2 (Chi-Squared) test is used
to determine if either the NORM or PIII distribution is more appropriate than the other to
represent the observations, and confidence intervals are calculated to provide a measure of
uncertainty in the estimated exceedance temperatures relative to their unknown population
values based on the fact that they are derived from a random sample of observations.
Selection of Distribution-2 (Chi-Squared) test
Assuming the sample observations adequately represent the underlying population, selection
of an unsuitable probability distribution will yield erroneous exceedance temperatures
wherever the fitted distribution deviates from the trend of the sample observations. For
example, application of the Normal distribution to observations with significant real skew will
induce errors in the estimated exceedance temperatures. One way this may be assessed is by
of the NORM and PIII distributions to each set of sample
observations using a 2 (Chi-Squared) test (Chow et al., 1988). 2-test is a hypothesis test in
which the null hypothesis, Ho, is that a proposed distribution together with its parameters fit
the observations well. The alternative hypothesis, Ha, is that the distribution and/or the
particular parameters are inadequate.
In 2 test, the range of n sample observations is divided into k intervals, and the number of
observations ni occurring in each interval is compared with the theoretical number of
observations expected within each interval based on the fitted distribution, given by np(xi).
Here, p(xi) is the theoretical probability of the random variable with cumulative distribution
function F(x) falling within the ith interval bounded between xi and xi-1. That is, p(xi) =F(xi)- F(xi-1)
It essentially compares the number of observations occurring in each bin of a histogram of the
12

data, with the number of occurrences expected within the range of each histogram bin based
on the fitted probability distribution. The squared differences of the observed minus expected
number of occurrences in each interval are normalized by the expected number of occurrences
and 2c

The sum 2c is the test statistic which is compared with a 2 distribution limiting value. The null
2c 2 distribution limiting value.
distribution is the distribution of andard normal random
variables, z. -m-1, where k is the number
of intervals, and m the number of parameters fitted for a particular distribution (m=2 for the
Normal distribution, and m=3 for PIII). The effect of m is that the limiting value for the PIII
distribution is smaller than that for the Normal distribution, so that the test is a little more
stringent for PIII to account for the fact that PIII has three parameters which allows greater
flexibility in the distribution to fit the observations. 2 - limiting value has cumulative
probability 1- . A ; it gives the likelihood
of rejecting the null hypothesis when it is true. 2 - distribution function are
available in many statistics texts (e.g., Benjamin and Cornell, 1970; Devore, 1987; Haan, 1977;
Lapin, 1983; Pearson and Hartley, 1966).
Histograms are usually set up using uniformly sized increments of the variable for each interval
so that the histogram shape is similar to the shape of the probability density function fitted to
the data. However, for the 2 test, it is desirable to select the range of values for each interval
such that each interval has the same number of expected occurrences of the random variable
within it based on the fitted distribution (e.g., 20 intervals might be selected each with 1/20th or
5% probability of occurrence), and the commonly recommended smallest number of expected
occurrences in each interval is 5 (Benjamin and Cornell, 1970). For any fitted distribution other
than a uniform distribution, this requires that the span or range of the values defining each
interval will vary. In the analysis performed here, each dataset was divided into a number of
intervals, k, sized so that the expected number of occurrences in each interval was at least 5,
. For example, with Caldwell there were n=116 years of data. The number of
23. Thus, 23 intervals were used, each having probability
p=1/k=0.0435 (4.35%).
2 test was applied to all the observations from each station, both on an annual basis for
Tavg and minTavg, and on a monthly basis for Tavg. On a WY basis, both the NORM and PIII
2 test applied to Tavg and minTavg at each station, except for one
13

failure by the NORM distribution at Station 800 (Pocatello) for minTavg. Generally, the PIII
2 test as well as or by a greater margin than did the Normal
distribution, especially when the observations contained significant skew. It is recommended
to use the PIII distribution values: When the skew is significant, as it often is for minTavg, PIII
likely provides more accurate results; when the skew is near zero, as commonly occurs with WY
Tavg, the Normal and PIII return period values are not very different, so selection of PIII to be
consistent induces no penalty and simplifies the selection process. Following this
recommendation avoids the use of the one NORM failure with minTavg.
For the Tavg monthly data, both the Normal and PIII 2 test for most
months at most stations. Across twelve months at the seven stations, there were 84 station-
months tested (ie., 7 stations x 12months) for each distribution. For the Normal distribution, 83
station-months passed 2 test, and 1 failed (December at Station 450, Boise). For the PIII
distribution, 83 passed and 1 failed (July at Station 750, Idaho Falls). From a gas demand
viewpoint, the PIII July failure is unimportant. Furthermore, since the recommendation is to
use PIII, the NORM December failure at Station 450 also does not matter. The remaining five
stations 2 test for all station-months for both distributions.
Confidence Limits
The temperature data collected at each station constitute a random sample of the underlying
populations of temperatures and these samples have been used to estimate the true frequency
curves of the corresponding populations. If a random sample consisting of the same number of
observations could be selected from a different period of time, they would probably produce a
different estimate of the population frequency curve. How well the observations represent the
underlying temperature population depends on the number of observations (sample size), its
accuracy, and whether or not the underlying distribution is known.
Confidence limits provide a measure of the uncertainty of the exceedance temperature at a
selected probability or return period. A range or confidence interval which brackets the true
exceedance temperature with a specified probability or confidence level can be calculated.
That is, for a two-sided confidence interval with an upper and lower confidence limit, and
=0.9, there is a 90% probability that the limits span or encompass the true
exceedance temperature.
-
Approximate confidence limits for the T-year exceedance temperatures for the NORM and PIII
distributions were calculated using the Interagency Advisory Committee on Water Data (1981)
method, also described in Chow, et al. (1988). Confidence limit values are reported in Figures 1
and 2 in the main body of this report, and in Appendix A.