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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 appropri ate 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 high ly 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 (wat er) temperature is equal to July average air temperature, and

(2) attainable aquatic life use subcategories can be rela ted 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.Page 2 

### 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 to pographic (long wave) radiation and solar (short wave) radiation, as illustrated in following figure from the SSTEMP wa ter temperature model (Bartholow, 2002).

Figure 1

Five of the components (evaporati on, water back radiation, atmosphe ric 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.Page 3 With the exception of solar radi ation, the heat flux components c annot 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 signif icant positive heat flux components including solar radiation, and consequently with stream water temperature. The correlation is supported by the SSTEMP water temperature model documentatio n, which asserts: “Air temperatur e 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 tem perature. 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 temper ature, 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 ar e specific instances where groundwater inflow influences water temperature. St ream flow may influence water temperature, although it may not be amenable to modification. The insolati on factors of shading and width-to-depth ratio have some influence on water temperature and are amenabl e to human intervention through stream restoration activities.Page 4 

### Correlation between Air Temperature and Water Temperature

The SWQB has developed a statewide correlation be tween 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, wh ere 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 prol onged 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 correl ation between weekly and mo nthly 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 (the rmographs) 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 day s (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 Ind ependent 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 therm ograph 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 comp aring the SWQB air thermograph data to the PRISM data. The comparison is shown in Figure 2.Page 5 PRISM Air Temperature

vs. Air Thermograph Temperature

Regression Based on Censored Data y = 0.8614x + 2.0957 R

2 = 0.8774 1:1 Line

10 15 20 25 30 35

10 15 20 25 30 35 July Average Air Temperature ThermographsJuly Average Air TemperaturePRISM Figure 2

The figure shows July average PRIS M air temperatures plotted again st 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 e ffects and imprecision of the PRISM model. To adjust for some of this variation, five data points wh ere 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 chos en because it is two standard deviations from the mean difference between the two datasets.

The regression indicates strong correlation and a slop e 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.Page 6 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 temper ature 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-c orrelated 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 therm ographs, it appeared that at locations where the air – water difference was great er 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 MW AT 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 great er 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 location s, 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 te mperature had been used these points would have been within the 4°C cutoff and would not be shown as sh aded 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 lo cations 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 R

2 = 0.8169

10 15 20 25 30 35

10 15 20 25 30 35 July Average Air Temperature ThermographsWater MWATPage 7 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 po ints were removed. The figure includes the linear least squares regression, the 1:1 li ne and percentile regression lines.

Figure 4

Regression Coefficients

m b 10 th percentile 0.9033 -2.2126 25 th percentile 0.9015 -0.1133 50 th percentile 0.9097 1.7368 75 th percentile 0.8571 4.6514 90 th 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 50 th Percentile, °C Water MWAT 25 th Percentile, °C Water MWAT 10 th 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 R 2 = 0.5536

5 10 15 20 25 30

10 15 20 25 30 July Average Air Temp, °CWater MWAT, °C

50th Percentile
75 th Percentile
90th Percentile
25th Percentile
10th Percentile
1:1 Line Linear (Series1)Page 8 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 RangeFrequency

Water MWAT vs. PRISM July Average Air Temperature 4°C Difference Values Removed

MWAT = 0.9625*ATEMP + 0.9284 R 2 = 0.7275

5 10 15 20 25 30

10 15 20 25 30 PRISM July Average Air Temp, °CWater MWAT, °C

1:1 Line
10th Percentile
25th Percentile
50th Percentile Linear (Regression)Page 9 Regression Coefficients

m b 10 th percentile 1.0353 -3.4280 25 th percentile 1.0000 -1.3400 50 th 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 50 th Percentile, 4°C ∆ Removed, °C Water MWAT 25 th Percentile, 4°C ∆ Removed, °C Water MWAT 10 th 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 t he 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 loca tions considered to be reference sites based on characteristics other than te mperature. 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 Re sumidero Spring, Rio Puerco de Chama @ FR 103 and Bear blw Dorsey Spring), the Ju ly 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 groundw ater 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 temperat ure. 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.Page 10 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 im poundment) 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 R

2 = 0.8604

10 15 20 25 30

10 15 20 25 30 PRISM July Average Air Temp, °CWater MWAT, °C

1:1 Line Linear (MWAT Water °C)Page 11 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 te mperature within 0.2°C of the 1:1 line. Despite the limited number of data points, it is clear that t he 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 25 th 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 th is, 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 temper ature 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 lin e. Based on this, the 1:1 line appears to represent the physical relationship that exists where the a ttainable water temperature is correlated to air temperature.

Points that plot below the 1:1 line may represen t sites where the water temperature is somewhat influenced by groundwater, or may result from micr oclimate effects or data collection problems including unrepresentative thermograph locations or inconsiste nt periods of record. For these reasons, the 25 th percentile does not appear to be useful in estimati ng the naturally attainable water temperature unless there is specific local information to suggest otherwise.Page 12 

### Relationship of MWAT and Air Temperature to NM Criteria

New Mexico aquatic life temperature criteria ar e 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 an y 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 excee ded 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 statisti cs 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 correl ation, 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
R 2

= 0.7621

4T3 = 1.0573 * MWAT + 1.8166
R 2

= 0.8965

6T3 = 1.0346 * MWAT + 1.3029
R 2

= 0.9257

5 10 15 20 25 30 35 40

5 10 15 20 25 30 35 Water MWAT, CWater Temperature, C

TMAX
4T3
6T3 Linear (TMAX) Linear (4T3) Linear (6T3)Page 13 The air – water temperature correlation indicated t hat 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 temp erature is not reduced by groundwater input or microclimate effects, the designated use based on wate r 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 restrict ive 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 29.6Page 14 

### References

Bartholow, J.M. 2002. SSTEMP for Windows: The Stream Segment Temperature Model (Version 2.0). U.S. Geological Survey computer mo del 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. Pr epared 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.