# Some of the documents we have considered during this project:

## Alexander H. MacKay

### Biographies and background:

• this source for \$10 (per month, but it should only take us a month to get all the copies!:). We can also figure out when MacKay published, and just get those issues...

## Air and Soil Temperature Articles

Objectives

• Develop a general methodology for estimation of daily soil temperature at continental scales using daily air temperature and precipitation data for bare ground.
• Demonstrate how the predictions of soil temperature would effect annual soil respiration assuming different ${\displaystyle Q_{10}}$ values.
• Simulate temperature under vegetation based on leaf area index (LAI)

Background

• Air temperature correlates well with soil temperature
• A depth of 10cm was used for soil temperatures because most soil ecosystem processes occur within the top layers of soil.
• Weather stations normally measure in places with no vegetation therefore the model was created to estimate soil temperature for bare ground.
• Lag time exists between air and soil temperatures. (4h for minimum temperatures and 6h for maximum temperatures)
• If snow is present the relationship between air and soil temperatures will be different from those without snow. (This is due to snow insulation)

Model Description

• The model calculates 1-dimensional snowpack according to air temperature and precipitation data. The snowpack increases when the daily mean air temperature is below or equal to ${\displaystyle {0}^{\circ }C}$ and decreases or disappears whenever the mean air temperature is below ${\displaystyle {0}^{\circ }C}$
• The rate of change in soil temperature will be less do to snow's low thermal diffusivity and high albedo.

Equation 1: ${\displaystyle F(J)=[A(J)-A(J-1)]M_{1}+E(J-1)}$, where ${\displaystyle M_{1}=0.1}$(used when snowpack is present) Equation 2: ${\displaystyle F(J)=[A(J)-A(J-1)]M_{2}+E(J)}$, where ${\displaystyle M_{2}=0.25}$( (used when no snowpack is present)

• The rate scalers ${\displaystyle M_{1}}$ and ${\displaystyle M_{2}}$, were selected initially from regressions of the running average of air temperature and the observed soil temperature for each site. (except Alaska)

Prediction of soil temperature under vegetation

• Experimental studies have shown that vegetation canopies can lower soil temperature during growing season significantly and reduce mean annual soil temperature.
• According to Beer-Lambert law, the fraction of radiation transmitted through a canopy is equal to ${\displaystyle e^{-K(LAI)}}$ where K is the extinction coefficient and LAI is the 1-sided leaf area index.

Equation 3 is used for simulating soil temperatures under vegetation cover when ${\displaystyle A(J)>T(J-1)}$: ${\displaystyle T(J)=T(J-1)+[A(J)-T(J-1)](M_{2})(exp^{-K(LAI)})}$ where T(J) and T(J-1) are the mean soil temperatures under vegetation for current and previous day respectively.

When ${\displaystyle A(J)\leq T(J-1)}$ equation 4: ${\displaystyle T(J)=T(J-1)+[A(J)-T(J-1)](M_{2})}$

Sites used for model development

• Milton, Florida: humid, warm-summer climate
• Corvallis, Oregon: maritime, cool-summer site with little to no snow
• Chatham Experimental Farm. Michigan: a humid-continental, cool-summer site with a long period of snow cover
• Jackson Experimental Station, Tennessee: humid, warm-summer site
• Branch Station, Montana: a cold and dry site
• Old Edgerton, Alaska: a subarctic site
• Safford, Arizona: a subtropical desert site

Estimation of annual soil respiration

• It has long been recognized that soil respiration rate increases exponentially with temperatures respiration increases exponentially with temperature; respiration increases about 2.4 times for a 10 degree C increase in temperature (${\displaystyle Q_{10}=2.4}$)
• If the specific rate does not change over the year, then predicted relative annual soil respiration is calculated from the temperature function alone: ${\displaystyle Y_{m}=\sum exp[X(F(J))]}$ where F(J) is the predicted soil temperature on Julian day J and X is 0.07, 0.09, 0.11 for ${\displaystyle Q_{10}}$'s of 2.0, 2.4, or 3.0. ${\displaystyle Y_{m}}$ (unitless) is calculated by

${\displaystyle Y_{m}=\sum exp[X(G(j))]}$ where G(J) is daily measured soil temperature for each of the 7 model development sites.

• ${\displaystyle \%_{error}=(Y_{p}-Y_{m})/Y_{m}(100\%)}$

Results and Discussion

• With the exception of Oregon (due to its maritime climate), the absolute value of the regression intercepts increased with the increase in latitude, perhaps because the sites located in higher latitude usually have greater variability of air and soil temperatures.
• Values of ${\displaystyle R^{2}}$ ranged from 0.85 to 0.96 and the standard error of estimates ranged from 1.5 to 2.9 degrees C.
• Daily soil temperatures at 10cm depth for various sites and years may be predicted from daily air temperature, once equations have been established for different climatic regions.

Koster, R, & Walker, G 2015, 'Interactive Vegetation Phenology, Soil Moisture, and Monthly Temperature Forecasts', Journal Of Hydrometeorology, 16, 4, pp. 1456-1465, Academic Search Complete, EBSCOhost, viewed 8 June 2016.