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Air-Water Temperature Correlation 

New Mexico Environment Department 

Surface Water Quality Bureau 

August 2011 

Summary 

This document provides a tool for identifying appropriate stream classifications and attainable aquatic life 

use subcategories. The investigation described here demonstrates that, based on data for approximately 

300 New Mexico streams, air temperature is highly correlated with stream water temperature and 

subsequently with the attainable aquatic life use subcategory. 

The key results presented in this document are these, which are applicable unless there are significant 

groundwater inputs or microclimate effects: 

 (1) maximum weekly average (water) temperature is equal to July average air temperature, and 

(2) attainable aquatic life use subcategories can be related to July average air temperature, as follows: 

 high quality and coldwater uses may be attainable if July average air temperature is ≤18°C; 

 marginal coldwater and coolwater uses may be attainable if July average air temperature 

is ≤23°C; 

 uses more restrictive than warmwater are generally not attainable if July average air temperature 

is >23°C. 
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Introduction 

Temperature has been identified as a leading cause of impairment in rivers and streams in New Mexico 

(NMED/SWQB 2009). However, the Surface Water Quality Bureau (SWQB) suspects that many of these 

waters are misclassified; that is, the designated aquatic life use or associated criteria cannot be attained 

because of naturally limiting conditions. 

In the absence of significant groundwater input, stream water temperature is the result of the relationship 

of eight heat flux components: convection, conduction, fluid friction, evaporation, water back radiation, 

atmospheric (long wave) radiation, vegetative and topographic (long wave) radiation and solar (short 

wave) radiation, as illustrated in following figure from the SSTEMP water temperature model (Bartholow, 

2002). 

Figure 1 

Five of the components (evaporation, water back radiation, atmospheric radiation, solar radiation and 

vegetative-topographic radiation) generally account for more than 90% of the stream heat flux. The 

significant positive heat fluxes are atmospheric and vegetative-topographic long wave radiation, and 

short-wave solar radiation. 

 
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With the exception of solar radiation, the heat flux components cannot be measured directly, but a 

number of related factors (and solar radiation) can be. These factors include: 

Meteorological Factors Water or Streamcourse Factors 

 air temperature  inflow temperature 

 solar radiation  accretion (groundwater inflow) temperature 

 relative humidity  segment inflow (water flow at the top of the segment) 

 wind speed  segment outflow (water flow at the bottom of the segment) 

 possible sun  thermal gradient

 ground temperature 

Geographical Factors 

 latitude Insolation Factors 

 segment length  shading 

 upstream elevation  width-to-depth ratio 

 downstream elevation 

Air temperature is highly correlated with the significant positive heat flux components including solar 

radiation, and consequently with stream water temperature. The correlation is supported by the SSTEMP 

water temperature model documentation, which asserts: “Air temperature will usually be the single most 

important factor in determining mean daily water temperature.” 

The factors of relative humidity and wind speed are not directly associated with positive heat flux, 

although they have some influence on water temperature. The remaining meteorological and 

geographical factors have less influence on water temperature. None of the meteorological or 

geographical factors are amenable to human intervention. 

The water or streamcourse factors are inflow temperature, groundwater inflow, stream segment inflow 

and outflow, and thermal gradient. With few exceptions, the inflow temperature is correlated to 

meteorological factors, chiefly air temperature. Although most New Mexico streams are shallow and are 

not “gaining streams” (not fed by groundwater) for most of their length, there are specific instances where 

groundwater inflow influences water temperature. Stream flow may influence water temperature, although 

it may not be amenable to modification. The insolation factors of shading and width-to-depth ratio have 

some influence on water temperature and are amenable to human intervention through stream restoration 

activities. 
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Correlation between Air Temperature and Water Temperature

The SWQB has developed a statewide correlation between July average air temperature and MWAT 

water temperature (MWAT - maximum weekly average temperature). The MWAT is defined as the sevenday mean of consecutive daily mean temperatures, where daily means are calculated from multiple, 

equally spaced values per day (Todd et al., 2008). Water quality criteria documents such as EPA (1972) 

recommend aquatic life temperature limits for prolonged exposure based on the MWAT. Chronic water 

temperature criteria based on the MWAT have recently been developed in Colorado (Todd et al., 2008). 

The analysis provided here verifies a strong correlation between weekly and monthly averages of stream 

and air temperature. The relationship can be used to estimate the naturally attainable water temperature 

at any location in the state, absent site-specific mitigating conditions. 

Water Temperature Data 

Water temperatures were obtained from SWQB water thermograph data. Since 1999, SWQB has 

deployed long-term temperature data recorders (thermographs) at approximately 300 monitoring stations 

on New Mexico streams. During the summer season of June through August the thermographs record 

hourly temperatures, providing approximately 3,000 data points at each station. We reduced the data to 

summary statistics: the reference date (date of the first maximum temperature); the maximum 

temperature; the maximum weekly average temperature (MWAT); the 4-hour maximum temperature that 

occurs for 3 consecutive days (4T3); and the 6-hour maximum temperature that occurs for 3 consecutive 

days (6T3). 

Air Temperature Data 

Air temperatures were obtained from two sources: a publically available temperature model known as 

PRISM (Parameter-elevation Regressions on Independent Slopes Model) and SWQB air thermographs. 

PRISM, available at http://www.prism.oregonstate.edu/, provides gridded data that can be used to find 

representative July temperatures for any location in the United States. PRISM can be used to provide 

July average temperatures that can be associated with any SWQB water monitoring location. The SWQB 

co-deployed ambient air thermographs at approximately 70 water thermograph stations. Data provided by 

these thermographs was also used to calculate July average air temperatures. 

PRISM Data Evaluation

Because the PRISM data is potentially more useful than the limited number of SWQB air thermographs, 

we evaluated the suitability of PRISM data by comparing the SWQB air thermograph data to the PRISM 

data. The comparison is shown in Figure 2. 

 
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PRISM Air Temperature 

vs. 

Air Thermograph Temperature

Regression Based on 

Censored Data

y = 0.8614x + 2.0957

R2 = 0.8774

1:1 Line

10

15

20

25

30

35

10 15 20 25 30 35

July Average Air Temperature 

 Thermographs

July Average Air Temperature

PRISM

Figure 2 

The figure shows July average PRISM air temperatures plotted against July average temperatures 

measured using SWQB air thermographs. If the PRISM model correlated exactly with the air 

thermographs, the PRISM data would plot on the 1:1 line. The PRISM data may not plot precisely on the 

line for a number of reasons such as microclimate effects and imprecision of the PRISM model. To adjust 

for some of this variation, five data points where the thermograph and PRISM values were more than 

3.8°C different were not used to develop the regression line. The points that were not used are plotted as 

triangles in the figure. The cutoff of 3.8°C was chosen because it is two standard deviations from the 

mean difference between the two datasets. 

The regression indicates strong correlation and a slope of nearly 1. Based on this evaluation, we 

concluded that the PRISM dataset was suitable for use in providing July average temperatures at SWQB 

water monitoring locations. 

 
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Outlier Analysis 

Although other investigators have reported an almost 1:1 relationship between weekly average stream 

temperature and monthly average air temperature (Morrill et al. 2005), there are a number of reasons why 

the SWQB dataset may not correlate precisely with the July average air temperatures. These reasons 

include local conditions that cause the water temperature to be unusually high or low, unrepresentative 

thermograph locations, inconsistent periods of record and other causes. 

To develop a basis for removing data points not well-correlated with July air temperature, particularly 

where the water temperature is influenced by groundwater, we considered the locations where we had 

both air and water thermograph data. Based on visual examination of the thermographs, it appeared that 

at locations where the air – water difference was greater than 4°C, the temperatures were either outliers, 

influenced by microclimate effects or moderated by groundwater. 

To test this, we plotted air thermograph and water MWAT data (Figure 3). Locations identified as outliers 

in the PRISM Data Evaluation (Figure 2) are shown as triangles. Of the five points identified in the PRISM 

Data Evaluation, four also have an air-water difference greater than 4°C. One (15.00°C air, 26.62°C 

water) appears to be an outlier due to unusually low air thermograph readings, with an air – water 

difference of negative 11.6°C. The unshaded triangle, identified in the PRISM Data Evaluation, had a 

difference of 3.3°C which is less than the 4-degree cutoff. 

Figure 3 

We identified seven additional points (the larger shaded diamonds) based on a positive air – water 

difference greater than 4°C. At five of the locations, the daily water temperature variation was low (a 

reference date diel water temperature difference less than 6°C), indicating groundwater influence. Two 

had a diel difference greater than 12°C. For these, however, the thermograph temperature was about 3°C 

greater than predicted by PRISM. If the PRISM temperature had been used these points would have 

been within the 4°C cutoff and would not be shown as shaded diamonds. All seven points, as well as four 

of those identified by the PRISM Data Evaluation, plot in the lower range of the relationship. 

Based on this evaluation, we concluded that a July average air – water MWAT difference of 4°C was a 

reasonable value for use in removing data from locations significantly influenced by groundwater or 

microclimate effects. 

Water MWAT vs. 

Air Thermograph Temperature

1:1 Line

Based on censored data

y = 0.9135x + 1.0682

R2 = 0.8169

10

15

20

25

30

35

10 15 20 25 30 35

July Average Air Temperature 

Thermographs

Water MWAT
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Statewide Correlation

We compared thermograph data from 293 monitoring locations to July average air temperatures from 

PRISM and plotted the results in Figure 4. No data points were removed. The figure includes the linear 

least squares regression, the 1:1 line and percentile regression lines. 

Figure 4 

Regression Coefficients 

m b 

10th percentile 0.9033 -2.2126

25th percentile 0.9015 -0.1133

50th percentile 0.9097 1.7368

75th percentile 0.8571 4.6514

90th percentile 0.8005 6.9644

Linear regression 0.8675 2.3758

Representative results from the regressions are shown below: 

Table 1 

July Average 

Air Temp, 

°C 

Water MWAT based 

on Regression, 

°C 

Water MWAT 50th

Percentile, 

°C 

Water MWAT 25th

Percentile, 

°C 

Water MWAT 

10th Percentile, 

°C 

15 15.39 15.38 13.41 11.34 

20 19.73 19.93 17.92 15.85 

25 24.06 24.48 22.43 20.37 

Water MWAT 

vs. 

PRISM July Average Air Temperature

MWAT = 0.8675*ATEMP + 2.3758

R2

 = 0.5536

5

10

15

20

25

30

10 15 20 25 30

July Average Air Temp, °C

Water MWAT, °C

50th Percentile

75 th Percentile

90th Percentile

25th Percentile

10th Percentile

1:1 Line

Linear (Series1)
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Consistent with the Outlier Analysis, we calculated the air – water difference. There are 27 locations with 

an air – water difference greater than 4°C, and 12 with a difference less than 4°C. The distribution is 

shown in Figure 5. 

Figure 5 

Difference -6 to -8 -4 to - 6 -2 to -4 0 to -2 0 to 2 2 to 4 4 to 6 6 to 8 >8 

Frequency 2 10 57 82 69 46 16 10 1 

After removing points with a greater than 4°C difference, we plotted the remaining 254 data points as 

water MWAT vs. PRISM July average air temperature in Figure 6. 

Figure 6 

Distribution of 

Air - Water Difference

0

10

20

30

40

50

60

70

80

90

-6 to -8 -4 to - 6 -2 to -4 0 to -2 0 to 2 2 to 4 4 to 6 6 to 8 >8

Difference Range

Frequency

Water MWAT vs. PRISM July Average Air Temperature

4°C Difference Values Removed

MWAT = 0.9625*ATEMP + 0.9284

R2 = 0.7275

5

10

15

20

25

30

10 15 20 25 30

PRISM July Average Air Temp, °C

Water MWAT, °C

1:1 Line

10th Percentile

25th Percentile

50th Percentile

Linear (Regression)
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Regression Coefficients 

m b 

10th percentile 1.0353 -3.4280

25th percentile 1.0000 -1.3400

50th percentile 0.9768 0.6900

Linear regression 0.9625 0.9284

Representative results from the regressions are shown below: 

Table 2 

July Average Air 

Temp, 

°C 

Water MWAT based 

on Regression 4°C ∆

Removed, 

°C 

Water MWAT 50th

Percentile, 4°C ∆

Removed, 

°C 

Water MWAT 25th

Percentile, 4°C ∆

Removed, 

°C 

Water MWAT 

10th Percentile, 

4°C ∆ Removed, 

°C 

15 15.37 15.34 13.66 12.10

20 20.18 20.23 18.66 17.28

25 24.99 25.11 23.66 22.45

Tables 1 and 2 show that in the 15 to 25°C air temperature range, both the 4°C ∆ removed and all data 

regressions predict a temperature within 1°C of the 1:1 line (MWAT = July Average Air Temperature). 

Reference Site Evaluation 

A list of New Mexico locations considered to be reference sites has recently been developed. Sediment in 

New Mexico Streams: Existing Conditions and Potential Benchmarks (Jessup et al. 2010) includes a file, 

AppF_NM Datasets2.xlsx, that lists 45 New Mexico locations considered to be reference sites based on 

characteristics other than temperature. The 45 locations are listed in the file Bedded Sediment Reference 

Sites. SWQB has collected thermograph data at only 13 of these sites. The sites are listed in Table 3. 

At the first three sites (Rito Resumidero blw Resumidero Spring, Rio Puerco de Chama @ FR 103 and 

Bear blw Dorsey Spring), the July average air temperature (PRISM) minus the water MWAT was more 

than 4°C, and the thermographs did not exhibit the usual diel variation. As with the previous statewide 

analysis, these characteristics suggest that groundwater inflow are moderating the air temperature 

influence, so these sites were not used for this analysis. 

The Dry Cimarron River @ Jesus Mesa site had an air – water difference slightly greater than 4°C, and 

the air temperature was lower than the water temperature. Although the water temperature exhibited diel 

variation, the difference between the daily maximum and minimum was less than expected, indicating that 

factors other than air temperature may be influencing water temperature. The stream at this site is 

surrounded by exposed bedrock that may elevate the water temperature. Because of this potential 

microclimate effect, and in order to be consistent with the 4°C cutoff, the Jesus Mesa site was also not 

used for the reference site correlation. 
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Table 3

STORET ID Station 

July 

Average 

Air Temp 

(PRISM) 

°C 

MWAT 

Water 

°C 

Air-Water 

Difference 

°C 

29RResum001.9 Rito Resumidero blw Resumidero Spg 16.26 8.87 7.39 

78BearCr027.0 Bear blw Dorsey Spg 23.45 18.01 5.44 

29RPuerc037.5 Rio Puerco de Chama @ FR 103 16.97 12.54 4.43 

77Turkey001.8 Turkey Creek 23.87 21.92 1.95 

78GilaRi025.5 Gila blw Blue 26.44 25.44 0.99 

78GilaRi069.2 Gila blw Mangas 25.41 24.45 0.96 

28RGRanc013.1 RG del Rancho @ Talpa-1305269 17.68 17.82 -0.14 

77EFkGil000.2 E Fk Gila 22.40 23.14 -0.74 

28RCosti032.5 Costilla abv Comanche (blw impoundment) 13.41 14.79 -1.39 

05MPonil000.1 M Ponil abv S Ponil 17.70 19.30 -1.60 

05NPonil000.1 N Ponil abv S Ponil 18.53 20.19 -1.66 

10UteCre104.3 Ute nr Bueyeros 23.79 27.04 -3.26 

02DryCim047.2 Dry Cim @ Jesus Mesa 22.27 26.28 -4.02 

Figure 7 is a graph of the data from the remaining nine sites. 

Figure 7 

Water MWAT vs. PRISM July Average Air Temperature

for Nine Reference Sites

MWAT = 0.8322ATEMP + 4.0677

R2 = 0.8604

10

15

20

25

30

10 15 20 25 30

PRISM July Average Air Temp, °C

Water MWAT, °C

1:1 Line

Linear (MWAT Water °C)
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Representative results are shown below: 

Table 4 

July Average Air Temp, 

°C 

Water MWAT based on 

Regression using Reference 

Data 

°C 

15 16.55 

20 20.71 

25 24.87 

At 15 and 20°C, the predicted MWAT using the reference data is 0.7 to 1.6°C greater than the 1:1 line. At 

25°C, the reference data regression predicts a water temperature within 0.2°C of the 1:1 line. Despite the 

limited number of data points, it is clear that the reference sites fall along the same 1:1 air-water 

temperature relationship found for all sites. 

MWAT Prediction Equation 

Representative results from the previously discussed regressions are shown below: 

Table 5 

July Average 

Air Temp, 

°C 

Water MWAT 

based on 

Regression 4°C ∆

Removed, 

°C 

Water MWAT 

based on 

Regression using 

All Data, 

°C 

Water MWAT 

based on 

Regression 

using 

Reference 

Data 

°C 

Water MWAT 

25th

Percentile, 

All Data 

°C 

15 15.37 15.39 16.55 13.41 

20 20.18 19.73 20.71 17.92 

25 24.99 24.06 24.87 22.43 

In the15 to 25°C air temperature range, the 4°C ∆ removed and all data regressions predict a 

temperature within 1°C of the 1:1 line (MWAT = July Average Air Temperature). The reference data 

regression predicts a water MWAT slightly greater than the 1:1 line at 15 and 20°C. 

The 1:1 relationship holds for the regression based on all data and also holds when sites expected to be 

influenced by groundwater are removed. Because of this, and significantly because it also is consistent 

with the regression based on reference sites, the 1:1 relationship represents the attainable water MWAT 

for locations where water temperature is controlled by ambient air temperature. 

We conclude that for New Mexico streams not significantly influenced by groundwater, the attainable

water MWAT equals the July average air temperature from the PRISM dataset. That is, 

MWAT = ATEMP (PRISM July Average Air Temperature) 

The regressions based on all of the data, on data without locations suspected of being groundwater 

dominated, and on reference sites all follow the 1:1 line. Based on this, the 1:1 line appears to represent 

the physical relationship that exists where the attainable water temperature is correlated to air 

temperature. 

Points that plot below the 1:1 line may represent sites where the water temperature is somewhat 

influenced by groundwater, or may result from microclimate effects or data collection problems including 

unrepresentative thermograph locations or inconsistent periods of record. For these reasons, the 25th

percentile does not appear to be useful in estimating the naturally attainable water temperature unless 

there is specific local information to suggest otherwise. 
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Relationship of MWAT and Air Temperature to NM Criteria

New Mexico aquatic life temperature criteria are not based on the MWAT. As reflected in 2010 

amendments to New Mexico’s Standards for Interstate and Intrastate Waters (20.6.4 NMAC), the criteria 

are based on maximum, 4T3 and 6T3 temperatures defined as follows: maximum temperature means the 

instantaneous temperature not to be exceeded at any time; 4T3 temperature means the temperature not 

to be exceeded for four or more consecutive hours in a 24-hour period on more than three consecutive 

days; and 6T3 temperature is means the temperature not to be exceeded for six or more consecutive 

hours in a 24-hour period on more than three consecutive days. 

The air-water temperature correlation was developed to predict water MWAT values based on July 

average temperatures. Because New Mexico criteria are not based on MWAT, predicted MWATs need to 

be related to New Mexico criteria statistics. 

To do this, the dataset that includes the statistics from 293 sites was used to develop a relationship 

between maximum (TMAX), 4T3 and 6T3 temperature and MWAT. Four TMAX values that were greater 

than 38°C (100 °F) were removed before doing the correlation, because water temperatures greater than 

100°F are usually the result of the thermograph being out of the water. Correlations are in Figure 8. 

Figure 8 

TMAX, 4T3 and 6T3 

vs. MWAT

TMAX = 1.0661 * MWAT + 4.9547

R2

 = 0.7621

4T3 = 1.0573 * MWAT + 1.8166

R2

 = 0.8965

6T3 = 1.0346 * MWAT + 1.3029

R2

 = 0.9257

5

10

15

20

25

30

35

40

5 10 15 20 25 30 35

Water MWAT, C

Water Temperature, C

TMAX

4T3

6T3

Linear (TMAX)

Linear (4T3)

Linear (6T3)
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The air – water temperature correlation indicated that MWAT = ATEMP (PRISM July Average Air Temp). 

Substituting ATEMP for MWAT yields the following: 

6T3 = 1.03 * ATEMP + 1.30 

4T3 = 1.06 * ATEMP + 1.82 

TMAX = 1.07 * ATEMP + 4.95 

Based on these relationships, if the water temperature is not reduced by groundwater input or 

microclimate effects, the designated use based on water temperature is related to July average air 

temperature as follows: 

 If the air temperature is ≤18, high quality coldwater or coldwater may be attainable; 

 If the air temperature is between 18 and 23, marginal coldwater or coolwater may be attainable; 

 If the air temperature is >23, uses more restrictive than warmwater are generally not attainable. 

Table 7 

Temp, °C 

High 

Quality 

Coldwater Coldwater 

Marginal 

Coldwater Coolwater Warmwater 

Marginal 

Warmwater 

Maximum 

Criterion 23 24 29 29 32.2 32.2 

4T3 Criterion 20 - - - - - 

6T3 Criterion - 20 25 - - - 

ATEMP 

(July Average Air 

Temperature) 

≤17 ≤18 ≤23 ≤23 >23 >23 

Water Stats @ 

ATEMP 

TMAX 23.1 

4T3 19.8 

TMAX 24.2 

6T3 19.8 

TMAX 29.6 

6T3 25.0 TMAX 29.6
Page 14 

References 

Bartholow, J.M. 2002. SSTEMP for Windows: The Stream Segment Temperature Model (Version 2.0). 

U.S. Geological Survey computer model and documentation. Available at http://www.fort.usgs.gov. 

Revised August 2002. 

EPA. 1972. Water Quality Criteria 1972. EPA R373033, March 1973. Environmental Studies Board, 

National Academy of Sciences, National Academy of Engineering, Washington, D.C., 594 p. 

Jessup, B.K., D. Eib, L. Guevara, J. Hogan, F. John, S. Joseph, P. Kaufmann and A. Kosfiszer. 

2010. Sediment in New Mexico Streams: Existing Conditions and Potential Benchmarks. 

Prepared for the U.S. Environmental Protection Agency, Region 6, Dallas, TX and the New 

Mexico Environment Department, Santa Fe, NM. Prepared by Tetra Tech, Inc., Montpelier, VT. 

Morrill, J. C., R. C. Bales and M. H. Conklin. 2005. Estimating Stream Temperature from Air Temperature: 

Implications for Future Water Quality, Journal of Environmental Engineering, 131 (1): 139-146. Found at 

https://eng.ucmerced.edu/people/rbales/CV/PubsM/98, November 2, 2010. 

New Mexico Environment Department/Surface Water Quality Bureau (NMED/SWQB). 2009. 

2008-2010 State of New Mexico Integrated Clean Water Act §303(d)/§305(b) Report. 

Todd, A.S. et al. 2008. Development of New Water Temperature Criteria to Protect Colorado’s Fisheries. 

Fisheries 33(9):433-443.