Microclimate modelling at macro scales: a test of a general microclimate model integrated with gridded continental-scale soil and weather data

Authors


Summary

  1. The microclimate experienced by organisms is determined by local weather conditions. Yet the environmental data available for predicting the effect of climate on the distribution and abundance of organisms are typically in the form of long-term average monthly climate measured at standardized heights above the ground.
  2. Here, we demonstrate how hourly microclimates can be modelled mechanistically over decades at the continental scale with biologically suitable accuracy.
  3. We extend the microclimate model of the software package niche mapper to capture spatial and temporal variation in soil thermal properties and integrate it with gridded soil and weather data for Australia at 0·05° resolution.
  4. When tested against historical observations of soil temperature, the microclimate model predicted 85% of the variation in hourly soil temperature across 10 years from the surface to 1 m deep with an accuracy of 2–3·3 °C (c. 10% of the temperature range at a given depth) across an extremely climatically diverse range of sites.
  5. This capacity to accurately and mechanistically predict hourly local microclimates across continental scales creates new opportunities for understanding how organisms respond to changes in climate.

Introduction

In the last two decades, studies of climate–organism interactions have made use of long-term-average gridded climatic data that is now readily available on a global scale (e.g. the ‘worldclim’ data base, Hijmans et al. 2005). The vast majority of these studies involve the statistical correlation of species' occurrences with the climatic data and have proven to be powerful interpolative tools (Guisan & Zimmermann 2000; Elith & Leathwick 2009). However, such correlative species distribution models are not well suited for obtaining a detailed understanding of climatic constraints limiting species distributions, since processes are only captured implicitly (Dormann et al. 2012). Moreover, correlative models may not extrapolate to novel climatic conditions, such as those encountered through climate change or invasions (Davis et al. 1998; but see Buckley et al. 2010; Kearney, Wintle & Porter 2010). Consequently, there is increasing interest in the development of mechanistic models of the climatic responses of organisms (e.g. Porter et al. 2000, 2002; Kearney & Porter 2004, 2009; Helmuth, Kingsolver & Carrington 2005; Buckley 2008; Helmuth 2009; Buckley et al. 2010; Helmuth et al. 2010; Kearney et al. 2010, 2013; Suggitt et al. 2011). For terrestrial organisms, this is an especially challenging problem because the most basic elements of such predictions, that is, the thermodynamic processes of heat and water exchange, require knowledge of microclimates at fine spatial and temporal scales, and these are not available through gridded climate data.

The study of microclimates, that is, ‘the climate near the ground’, and the development of methods to predict them has a long history (Geiger 1950; Campbell & Norman 1998; Geiger, Aron & Todhunter 2003), largely driven from an agricultural perspective. However, such mechanistic microclimatic modeling approaches are rarely applied at the continental or global spatial scales used in correlative species distribution modelling. One microclimate model which has been used in landscape-scale calculations of the physiological impacts of climate (e.g. Porter et al. 2002; Kearney & Porter 2004; Natori & Porter 2007; Kearney et al. 2008; Mitchell et al. 2008, 2013; Kearney, Shine & Porter 2009; Kearney, Wintle & Porter 2010; Kearney 2012; Fuentes & Porter 2013) is part of the software package ‘niche mapper’ and was developed by Porter et al. in the 1970s (Beckman, Mitchell & Porter 1973; Porter et al. 1973; Mitchell et al. 1975; Porter & James 1979; Porter & Mitchell 2006). This microclimate model was tested under limited conditions during its initial development (Porter et al. 1973; Porter & James 1979). Here, we present a comprehensive assessment of its capabilities by integrating it with historical, daily, continent-wide grids of weather conditions for Australia and then testing it against three-hourly soil and surface temperature observations made by the Australian Bureau of Meteorology (BoM) across a wide range of sites throughout Australia (Fig. 1).

Figure 1.

Weather stations from which soil and surface temperatures were extracted to test the microclimate model predictions. The size of the symbols is proportional to the number of days of observations, with the maximum being 99·9% of days over the 10-year study period (2000–2009). Further details about the weather stations are in Table 1.

We describe modifications of the microclimate model to enable soil properties to vary with both depth and time, and demonstrate the utility of these modifications by integrating the model with soil properties from the Digital Atlas of Australian Soils (McKenzie et al. 2000) and with monthly historical soil moisture estimates provided by the Australian Water Availability Project (Raupach et al. 2009). We also compare the model's performance against a recently developed statistical model of soil temperature that was fitted to the BoM soil temperature records (Horton & Corkrey 2011; Horton 2012). Our analysis shows that the model can make usefully accurate, mechanistic, continent-wide calculations of microclimate on hourly time-scales. Capturing environmental variation on this time-scale is critical for predicting many biological responses because of nonlinearity and threshold effects in physiological and behavioural responses of organisms to temperature and moisture (e.g. Tracy 1976; Huey 1982; Heinrich 1993; Helmuth, Kingsolver & Carrington 2005; Woods & Bonnecaze 2006; Kearney, Shine & Porter 2009). Accurate microclimatic calculations therefore provide a powerful basis for inferring the responses of species to changes in climate.

Materials and Methods

Model Description

The niche mapper microclimate model was first described in Porter et al. (1973) and Beckman, Mitchell and Porter (1973), with further descriptions in Porter and Mitchell (2006) and Fuentes and Porter (2013). It is a fortran program that includes routines for hourly calculations of solar and infrared radiation intensities, above-ground profiles of air temperature, wind velocity and relative humidity, and soil temperature profiles at 10 nodes from the surface down to a user-specified maximum depth (typically around 2 m). These calculations are made for two user-provided extremes of shading by vegetation.

The model requires as input the maximum and minimum daily values of air temperature, wind speed, relative humidity and cloud cover, the timing of the maxima and minima relative to dawn or solar noon, soil properties (conductivity, specific heat, density, solar reflectivity, emissivity, surface wetness) as well as the roughness height, slope and aspect. Clear sky solar radiation is computed based on latitude and longitude using the algorithm described in McCullough and Porter (1971). In the present version, aerosol attenuation is computed based on the Global Aerosol Data Set (GADS) (Koepke et al. 1997), instead of the original profile from Elterman (1968, 1970) (otherwise Australian solar radiation was underestimated by up to 15%). We modified the original GADS Fortran program to give output for the full spectral profile for a single location, and took the average of the summer and winter values.

We added a new subroutine to version 2011b of niche mapper to account for variation in soil properties. The original version of the microclimate model did not permit soil properties to vary with depth or time. In the present version, we have allowed up to 10 different soil properties with depth (i.e. unique properties for each node) and allowed these to change on an hourly basis according to the soil temperature and moisture levels. We used node intervals of 0, 2·5, 5, 10, 15, 20, 30, 50, 100 and 200 cm. The user specifies the conductivity, specific heat capacity, density and water-holding capacity of the mineral components of the different soil layers together with the bulk density and a time vector for each layer of relative soil moisture values. The overall soil conductivity, specific heat and density values are then adjusted for bulk density and soil moisture, as well as for soil temperature, using the methods described in Campbell et al. (1994, equations 8, 9) and Campbell and Norman (Campbell & Norman 1998, equations 8.13, 8.17, 8.20 and data in Tables 8.2 and 9.1). This new version has been set up to run in the R environment (nichemapr) and will be made publicly available.

Soil temperatures are computed based on a one-dimensional partial differential equation that uses above- and below-ground boundary conditions (Porter et al. 1973). The soil surface temperature is computed via a heat balance equation, accounting for heat exchange via radiation, convection, conduction and evaporation. To calculate evaporative heat loss in the present study, we set the fractional surface area wet to 0·9 during rainfall events but otherwise assumed no evaporation from the surface. The deep soil temperature was assumed to be the (running) mean annual air temperature, based on the previous 365 daily maximum and minimum air temperatures.

Weather Inputs

For the majority of calculations, daily weather data were extracted for each site from historical continent-wide 0·05° grids (c. 5 km) of interpolated weather station data, compiled via the Australian Water Availability Project (AWAP, Jones, Wang & Fawcett 2009; Raupach et al. 2009). Temperature data were provided as daily maxima and minima and were corrected with an adiabatic lapse rate of 0·0055 °C m−1 from the original 0·05° values to a resolution of 0·0025° (c. 250 m), based on Digital Elevation Models (DEMs) of corresponding resolution (Hutchinson & Dowling 1991; Hutchinson et al. 2008) (we note that lapse rates may vary from the value we used according to the amount of moisture in the air). Vapour pressure was provided for 9·00 and 15·00 h, which we averaged and converted to relative humidity corresponding to the air temperature maxima and minima. Daily cloud cover was derived as the ratio of daily integrated clear sky solar radiation (pre-computed with the microclimate model) compared to the observed daily integrated solar radiation grids obtained from the AWAP. To derive an approximate daily cycle from these estimates of mean daily cloud cover, we made the minima half the value of the daily mean and the maxima twice the value of the daily mean.

Daily historical gridded wind speed data were not available, so we used daily interpolations [‘spline’ function of the statistical package ‘r’ v. 2.15.2, (R Development Core Team 2012)] of monthly grids of long-term average 9·00 and 15·00 h 10 m wind speed surfaces for Australia derived from the package ANUCLIM (Hutchinson 2000). The maximum wind speed was taken to be whichever was higher of the 9·00 and 15·00 h values, and the minimum was assumed to be 10% of the maximum (based on comparisons with hourly data from Bureau of Meteorology stations). For one analysis scenario, we used the raw weather station observations of rainfall, air temperature, wind speed, relative humidity and cloud cover. For the latter three variables, we extracted the maximum and minimum values from hourly observations. Missing data were approximated using the ‘na.approx’ function of the package ‘zoo’ for ‘r’ (default settings were used) (Zeileis & Grothendieck 2005).

Wind speed values were adjusted from a 10 m reference height to a 1·2 m reference height (i.e. to the same reference heights for air temperature and humidity observations) using the relationship

display math

where v is the velocity at the new height h (m s−1), vo and ho are the corresponding values at the reference height, and a is the wind shear exponent, which we assumed to be 0·143 (the 1/7th power law). Air temperature and wind speed maxima were assumed to occur 1 h after local solar noon, as were minima for relative humidity and cloud cover. Air temperature and wind speed minima were assumed to occur at local sunrise, as were maxima for relative humidity and cloud cover.

Soil Property Inputs

Soil parameters were based on a generalized soil, the mineral fraction of which had a thermal conductivity of 2·5 W mC−1, a density of 2560 kg m−3 and a specific heat of 870 J kg−1-K (Table 8.2 in Campbell & Norman 1998), assuming a bulk density of 1400 kg m−3. Additional, spatially explicit soil properties were obtained from the Digital Atlas of Australian Soils (DAAS) (McKenzie et al. 2000), specifically 50th percentile estimates of soil depth (two horizons) and horizon-specific bulk density and volumetric water content (0·1 bar matric potential) (Table 1). For these spatially explicit analyses, the soil profile was broken up into four sections with potentially varying thermal properties, with depth and time as a function of DAAS properties, soil moisture estimates for each day and estimated soil temperature of the previous hour: (i) a 0–5 cm ‘O-horizon’ layer, (ii) a variable depth ‘A-horizon’ based on the value of the closest soil node to the first horizon depth from the DAAS, (iii) a variable depth ‘B-horizon’ based on the value of the closest soil node to the second horizon depth from the DAAS and (iv) a final layer extending from the latter depth to the 200 cm boundary condition. The first two layers were assigned the site-specific bulk density and volumetric water content of the DAAS A-horizon, and the second two layers were assigned the corresponding DAAS values for the B-horizon. Where only data for one horizon were provided in the DAAS, we used that value for the whole profile. Relative soil moisture was obtained from daily interpolations of monthly historical 0·05°-resolution grids from the AWAP, for each soil horizon.

Table 1. Australian Bureau of Meteorology weather stations from which soil observations were used to test the model and elevation and soil properties for these locations based on the Digital Atlas of Australian Soils (McKenzie et al. 2000)
No.LatLongStation nameNo. obsElevThickAThickBBDensABDensBWaterAWaterB
  1. No. obs, the number of days for which three-hourly records were available from 2000 to 2009; Elev, elevation extracted from a 0·0025° digital elevation model; ThickA and ThickB, thicknesses of soil horizons A and B (m); BDensA and BDensB, bulk density of soil horizons A and B (Mg m−3); WaterA and WaterB, volumetric water content of soil horizons A and B (m3 m−3); AWS, automatic weather station; AMO, approved maintenance organization.

2012−18·25127·65Halls Creek Airport32854190·10·41·51·60·260·25
2056−15·8128·7Kununurra Aero596220·151·50·2
3003−17·9122·25Broome Airport331560·30·81·291·50·210·2
4032−20·35118·65Port Hedland Airport310240·30·81·291·50·210·2
5007−22·25114·05Learmonth Airport3594260·21·290·28
6011−24·9113·7Carnarvon Airport3143130·150·891·51·60·260·37
7045−26·6118·55Meekatharra Airport30655130·20·311·20·320·32
8051−28·8114·7Geraldton Airport Comparison3158310·21·390·2
9021−31·95116Perth Airport3346260·690·51·291·70·210·19
9741−34·95117·8Albany Airport3309650·690·51·291·50·210·2
9789−33·8121·9Esperance3316120·51·390·2
10092−31·5118·3Merredin30343410·150·891·51·60·260·37
11003−31·65128·9Eucla26211000·10·31·51·60·30·27
11045−31·1125·65Balgair33601600·10·31·51·60·30·27
14015−12·4130·9Darwin Airport3591200·41·390·32
14508−12·25136·8Gove Airport2757230·41·50·2
14612−15·55133·2Larrimah28141900·151·291·21·390·450·41
14938−13·75130·7Mango Farm269350·30·61·61·70·220·33
15135−19·65134·2Tennant Creek Airport33293800·41·50·23
15590−23·8133·9Alice Springs Airport33195420·30·81·291·50·210·2
15594−23·45134·7Arltunga31626640·151·50·2
15666−18·6129·5Rabbit Flat24334210·30·81·291·50·210·2
23090−34·9138·6Adelaide (Kent Town)3638410·20·61·61·70·250·33
24024−34·45140·6Loxton Research Centre1607410·250·21·391·50·320·31
32037−17·6146South Johnstone Exp Stn401100·21·50·891·20·450·41
33002−19·6147·4Ayr Dpi Research Stn16560·30·690·891·20·340·32
35264−23·55148·2Emerald Airport1911810·21·21·21·390·450·41
36031−23·45144·3Longreach Aero10501880·151·291·21·390·450·41
40082−27·55152·35University of Queensland, Gatton215890·10·891·291·50·430·4
41522−27·15151·25Dalby Airport12863440·21·21·21·390·450·41
41525−28·2152·1Warwick34675330·10·691·21·20·450·45
43091−26·55148·8Roma Airport8832990·10·891·291·50·430·4
48245−30·05145·95Bourke Airport AWS5861000·21·21·21·390·450·41
51049−32147·95Trangie Research Station AWS17972150·150·891·51·60·260·37
52088−30·05148·1Walgett Airport AWS3571300·21·21·21·390·450·41
61087−33·4151·35Gosford AWS1960180·40·891·51·60·20·27
67105−33·6150·8Richmond RAAF20690·40·51·391·790·20·3
72150−35·15147·45Wagga Wagga AMO36492020·20·691·391·390·270·29
75041−34·25146·05Griffith Airport AWS4271290·20·691·391·390·270·29
80091−36·35145·05Kyabram DPI22091060·150·891·51·60·260·37
81049−36·45145·25Tatura Inst Sustainable Ag35171160·150·891·51·60·260·37
91219−41·15147·5Scottsdale36501440·30·61·61·70·220·33
95003−42·7146·9Bushy Park (Bushy Park Estates)2226250·30·51·61·790·220·3

Preliminary model simulations using soil properties from the DAAS resulted in good fits to deep soil temperatures but resulted in excessively high fluctuations at 5, 10 and 20 cm (see 'Results'). We found that this discrepancy was resolved by assuming that the top 5 cm of the soil layer, that is, the ‘O-horizon’, had the properties of an ‘organic’ soil, that is, substantially lower thermal conductivity (0·2 W m−1 °C−1) and a higher heat capacity (1920 J kg−1 °C−1) (Table 8.2 in Campbell & Norman 1998). An example of the resultant bulk soil properties of the O-, A- and B-horizons resulting from variable properties with depth, and temporal adjustments for moisture content and temperature, as described above, are provided in Fig. 2 for Perth over the years 2007–2009. Site-specific values for these soil properties, averaged over the 10 years, are shown in Figure S1.

Figure 2.

Estimated bulk soil thermal properties through time for Perth for three levels in the soil, the O-horizon (top 5 cm, black dashed line), the A-horizon (variable depth, 5–50 cm in this case, grey line) and the B-horizon (variable depth, 50–200 cm in this case, black line). Also indicated are the (constant) bulk soil properties for the A- and B-horizons (identical values for each) under the scenarios where site-specific soil properties and soil moisture values were not used (dotted line).

Soil solar reflectivity was assumed to be fixed at 0·2, based on the mean (1994–1999) of the continent-wide soil albedo layer (I. Grant 2004 Bureau of Meteorology, after Schaaf et al. 2002; Dilley et al. 2000) used in the AWAP calculations (Briggs 2011), and we assumed no shading of the soil surface, as weather stations are typically located in very open areas. For analyses using spatially explicit soil properties, the monthly emissivity for long-wave radiation exchange was extracted from a 0·05° global emissivity data base (Seemann et al. 2008) and interpolated with the ‘spline’ function of the statistical package ‘r’ to daily values (mean 0·95, range 0·91–0·98, across all 43 sites).

Soil Temperature Observations

The microclimate model predictions were tested against soil temperature observations from weather stations administered by the Australian Bureau of Meteorology (BoM). The BoM records the terrestrial minimum surface temperature (0·5 cm above the ground) as well as soil temperatures at depths of 5, 10, 20, 50 and 100 cm at selected weather stations across Australia. Soil temperatures are measured at up to three-hourly intervals at some stations but, for many stations, are only measured twice per day at 9·00 and 15·00 h. Moreover, not all stations have observations at 5 cm. We used data from 43 stations selected based on the criteria that they included at least 100 quality-controlled observations at 12·00 h at the 10 cm depth over the period 2000–2009 (Table 1, Fig. 1). This criterion ensured that stations had some periods with three-hourly observations. The total number of days with observations available under this criterion ranged from 3650 (99·9% complete) for Scottsdale to 165 (4·5% complete) at Ayr DPI Research Station (Table 1, Fig. 1). All selected stations had observations for all depths from 10 cm and lower, while 24 stations also had observations at 5 cm. Predictions were made for all hours of all days across the 10-year study period. These predictions were compared directly to all available observations for the corresponding hours, as well as for the terrestrial minimum air temperature. Time in the model predictions was relative to local solar noon, while time in the observations was based on the local time zone, potentially introducing small errors for near-surface predictions.

Comparison with an Empirical Model

We also compared our model predictions with those from a recently developed empirical model of soil temperature (Horton & Corkrey 2011). This weighted-coefficient model predicts daily minimum and maximum soil temperature at fixed depths (5, 10, 20, 50 and 100 cm) from daily rainfall, daily minimum and maximum air temperature, and latitude, using lag factors of up to 28 days (Horton & Corkrey 2011). We developed an r script to implement the model and drove it with weather data obtained from the same data sets as we used for the microclimate model.

Results

We present comparisons between the microclimate model predictions and the soil temperature and ‘terrestrial minimum’ surface temperature observations under five scenarios with increasingly detailed input data: (i) ‘uniform’ – using typical soil properties (see methods), assuming no variation in soil moisture, (ii) ‘cap’ – as in scenario 1 but with the 5 cm organic cap (see methods) added, (iii) ‘soilprop’ – as in scenario 2 but with site-specific soil properties, from the Digital Atlas of Australian Soils, (iv) ‘moist’ – as in scenario 3 but with AWAP soil moisture estimates incorporated and (v) ‘BoM’ – as in scenario 4 but using the direct Bureau of Meteorology weather station observations of air temperature, wind speed, cloud cover and relative humidity, rather than interpolated grids.

The coefficient of determination r2, the root mean squared deviation ‘RMSD’ and the normalized root mean squared deviation ‘RMSD%’ were used to summarize comparisons of predictions made across all sites by each of the five scenarios against the observed soil temperatures, for each depth and hour of observation (Fig. 3). We also used these statistics to compare daily minimum and maximum soil temperatures across all sites (Fig. 4), following Horton and Corkrey (2011). The r2 values for terrestrial minimum surface temperature were 0·90 for all scenarios, and the respective RMSDs for this variable for scenarios one to five were 2·0, 2·0, 2·1, 2·0 and 1·8, respectively. Site-specific values of r2 and RMSD for terrestrial minima and hourly soil temperatures are presented in Figures S2 and S3, respectively, for scenario 4 (‘moist’), which is the most fully parameterized model based on gridded data.

Figure 3.

Coefficients of determination (r2), root mean squared deviations (RMSD) and normalized root mean squared deviations (RMSD%) for predictions of soil temperature compared against three-hourly observations, averaged across all 43 sites, for each depth at which observations were available. Results are presented for five scenarios, explained in the main text.

Figure 4.

Coefficients of determination (r2), root mean squared deviations (RMSD) and normalized root mean squared deviations (RMSD%) for predictions of minimum and maximum soil temperature compared against minima and maxima of three-hourly observations, averaged across all 43 sites, for each depth at which observations were available. Results are presented for five scenarios simulated with the microclimate model and two scenarios simulated with the statistical model of Horton and Corkrey (2011), explained in the main text.

Examples of observed and predicted temperature traces for four climatically distinct locations for a 3-year slice of the study period (2007–2009) and for a 1 month slice (December 2008) are shown in Figs 5–9 for scenario 4 (‘moist’). These include a coastal warm-temperate site (Perth, Figs 5–6), a tropical coastal site that experiences monsoonal wet–dry seasons (Darwin, Fig. 7), a coastal cool temperate site (Bushy Parks, near Hobart, Fig. 8) and an inland warm-temperate site (Wagga Wagga, Fig. 9). The 3-year time slices for all 43 locations for this scenario are provided in Figures S4–S46.

Figure 5.

Three years (2007–2009) of hourly predictions and observations of surface and soil temperatures for Perth, a warm-temperate location, either (a) without an organic soil cap or (b) with an organic soil cap. The top panels show the simulated air temperature 0·5 cm above the ground (black lines), the observed air temperature 0·5 cm above the ground (red circles – ‘terrestrial minimum’ observations) and the soil surface temperature (grey lines). In all other panels, the black lines are predictions and the red lines are observations.

Figure 6.

One month (December 2008) of hourly predictions and observations of surface and soil temperatures for Perth, a warm-temperate coastal location, either (a) without an organic soil cap or (b) with an organic soil cap. The top panels show the simulated air temperature 0·5 cm above the ground (black lines), the observed air temperature 0·5 cm above the ground (red circles – ‘terrestrial minimum’ observations) and the soil surface temperature (grey lines). In all other panels, the black lines are predictions and the red lines are observations.

Figure 7.

Three years (2007–2009, a) or 1 month (December 2008, b) of hourly predictions and observations of surface and soil temperatures for Darwin, a monsoonal tropical coastal location. The top panels show the simulated air temperature 0·5 cm above the ground (black lines), the observed air temperature 0·5 cm above the ground (red circles – ‘terrestrial minimum’ observations) and the soil surface temperature (grey lines). In all other panels, the black lines are predictions and the red lines are observations.

Figure 8.

Three years (2007–2009, a) or 1 month (December 2008, b) of hourly predictions and observations of surface and soil temperatures for Bushy Parks near Hobart, a cool temperate coastal location. The top panels show the simulated air temperature 0·5 cm above the ground (black lines), the observed air temperature 0·5 cm above the ground (red circles – ‘terrestrial minimum’ observations) and the soil surface temperature (grey lines). In all other panels, the black lines are predictions and the red lines are observations.

Figure 9.

Three years (2007–2009, a) or 1 month (December 2008, b) of hourly predictions and observations of surface and soil temperatures for Wagga Wagga, an inland temperate location. The top panels show the simulated air temperature 0·5 cm above the ground (black lines), the observed air temperature 0·5 cm above the ground (red circles – ‘terrestrial minimum’ observations) and the soil surface temperature (grey lines). In all other panels, the black lines are predictions and the red lines are observations.

Modelling the presence of the organic cap provided the greatest improvement in model performance (scenario 2) when compared with the simplest assumption of a uniform soil profile (scenario 1), particularly for depths between 5 and 20 cm (Figs 3–4). An example of the nature of the improvement of adding this cap can be seen in Figs 5–6, which show the 3-year and 1-month slices with and without the cap. Specifically, predicted amplitudes of fluctuations at 5, 10 and 20 cm depths were substantially overestimated without modeling the presence of the cap.

The predictive capacity was only subtly affected through the inclusion of site-specific soil properties (scenario 3) or through the additional consideration of soil moisture (scenario 4) (Figs 3–4), with slight gains in accuracy for shallow depths (5, 10 and 20 cm) and losses in accuracy for deeper depths (50 and 100 cm). Model predictions of the terrestrial minimum surface temperature improved slightly under scenario 5, using the direct BoM weather station observations, as already indicated above. However, this same scenario reduced the predictive accuracy for shallow soil temperatures (Figs 3–4).

Predictions of minimum and maximum soil temperature were slightly more accurate under the statistical Horton and Corkrey model than under the mechanistic microclimate model (Fig. 4). Moreover, and in contrast to the mechanistic model, the Horton and Corkrey model performed slightly better when driven by the BoM weather station data (scenario 5) than when driven by the interpolated AWAP data (Fig. 4).

Discussion

The aim of this study was to test the capacity of a mechanistic microclimate model to accurately predict microclimate conditions using coarse gridded data on soil and weather. No site-specific calibrations of model parameters were undertaken, as the aim was to assess the predictive capacity of a generic data set applied at the continental scale. Overall, the predictive capacity of the model was high, typically explaining over 85% of the variation in hourly soil temperature and surface minimum temperature observations with an accuracy (at the hourly scale) of around 2–3 °C over a 10-year period across an extremely climatically diverse range of sites (Figs 3–9, S2–S46, Tables S1 and S2). This substantially expands on previous tests of the model, which showed a similar accuracy and precision over a 52-h period at an arid North American site (Porter et al. 1973) and over a 4-day period in tropical Africa (Porter & James 1979).

Discrepancies between the microclimate model predictions and meteorological observations have four different sources: (i) errors in the soil observation data, (ii) model misspecification (including assumptions made and missing model inputs), (iii) inaccurate weather input data and (iv) inaccurate soil property data. Regarding the observation data, at some sites, there do appear to be short periods of noise from damaged thermistors (e.g. Figures S11, S20, S32, S33 and S41). However, we only used observations ranked as ‘high quality’ in the data base (as judged by the Bureau of Meteorology), thus any such errors should be minimal.

Regarding model misspecification, the present version of the microclimate model has added realism over the original version (Beckman, Mitchell & Porter 1973; Porter et al. 1973) through the implementation of time- and depth-varying soil properties, as well as the inclusion of algorithms for how soil properties vary as a function of soil moisture and temperature. One major limitation is that it does not explicitly model the soil water budget but, rather, uses input from a second model for soil moisture, in this case the Australian Water Availability Project simulation output (Raupach et al. 2009, 2011). The advantage of this strategy is that it reduces model complexity, computational intensity and parameter requirements, and in this particular application, it capitalizes on an ongoing, well-resourced initiative producing outputs of soil moisture suitable for continent-scale analyses. A disadvantage is that it is subject to any inadequacies in the soil moisture model used, and it does not easily capture local-scale interactions between soil and moisture, such as porosity, run-on–run-off and microtopographic effects. In the present study, the inclusion of soil moisture did little to improve the predictions of the model. However, including AWAP soil moisture estimates in many future, continental-scale modelling applications will be critical given the importance of soil moisture for animals such as burrowing frogs and for processes such as plant growth.

A key aim of the present study was to assess the efficacy of gridded weather data for predicting microclimates. For Australia, we were able to obtain gridded daily maximum and minimum temperature and rainfall data as well as estimates of daily humidity (albeit from 9·00 to 15·00 h data) and cloud cover (indirectly from integrated solar radiation). Historical, daily wind speed grids were unavailable, and instead we used long-term average monthly interpolations of 9·00 and 15·00 h weather station observations. This approach to the weather input data appears unlikely to be a major source of error since there was little difference (in fact a slight overall decrease) in model performance when the actual weather station observations were used rather than interpolated values. This was despite the fact that weather station observations included daily maximum and minimum wind speed, relative humidity and cloud cover. It is possible that the slightly better performance of the simulations based on the AWAP data was due to more accurate estimates of cloud cover derived from the solar grids in comparison with the observer estimates at the weather stations. For both the interpolated grids and the weather station data, we assumed that the times of the minima and maxima for temperature, humidity, wind speed and cloud cover occurred at fixed times each day relative to sunrise or solar noon. This assumption may have reduced the accuracy of surface temperature predictions, but we were nonetheless able to predict minimum surface temperatures to within 2 °C on average. Unfortunately, maximum surface temperatures were unavailable for comparison with model predictions.

In regard to soil properties, we found that it was necessary to model a 5-cm cap of ‘organic’ material to obtain realistic diel temperature amplitudes. Without this cap, the fluctuations were too high at 5, 10 and 20 cm, despite temperatures at the surface (0·5 cm above ground) and at depth (50 and 100 cm) being of the right magnitude (e.g. Figs 5–6). Other attempted changes to the soil surface properties (including solar reflectance and evaporative cooling, results not shown) failed to provide correct amplitudes in the shallow depths without also underestimating deep soil temperatures and surface temperatures. This implies that biological material and activity in the top 5 cm of the soils strongly alters thermal conditions at the sites considered (reduced thermal conductivity, higher heat capacity), with the effect of damping fluctuations in the top 20 cm compared to the scenario of a uniform soil profile. This may plausibly include burrowing activity in this surface layer by invertebrates such as earthworms, which can double soil porosity and increase organic material (Lee 1985), as well as the presence of cropped grass and root systems, as is typically the case at meteorological stations. Consistent with this notion, applications of the same modelling system to in situ beach sands produced accurate soil temperature estimates throughout the sand profile without the need for an organic cap (M. R. Kearney et al. in prep.).

After including the soil cap, a surprising aspect of our analyses was how little improvement was gained in the predictions when location-specific soil properties, including soil moisture, were used, compared to simulations with a uniform, dry soil profile across the entire continent (i.e. scenario 2, ‘cap’, compared with scenarios 3 ‘soilprop’ and 4 ‘moist’, Figs 3–4). Nonetheless, this is consistent with the fact that Horton and Corkrey (2011) were able to obtain similarly accurate predictions of minimum and maximum daily soil temperature (see also Fig. 4) without any location-specific predictors besides latitude. Site-specific calibrations or in situ parameter measurements, especially of surface conditions such as solar reflectance and also roughness heights, will undoubtedly improve model accuracy for site-specific applications.

Compared to the statistical model of Horton and Corkrey (2011), the performance of the mechanistic microclimate model was slightly poorer, with correlation coefficients around 1–2% lower on average and root mean squared deviations around half a degree less accurate. However, there are a number of important advantages of a mechanistic approach over a correlative one. First, in addition to soil temperature, the mechanistic model predicts the microclimates above ground that are required to understand the energy and mass budgets of organisms living on the surface, which are critical inputs for biophysical models of species' distributions. The emphasis on the capacity of the model to predict soil temperatures in this study is in part because they provide an integrated assessment of how accurately the microclimatic conditions above ground are being predicted by niche mapper when driven by these environmental inputs. These microclimatic conditions include short- and long-wave radiation environments, wind speed, air temperature and relative humidity profiles with height above the ground, all of which are necessary for calculating heat and mass balances of organisms on the surface (Kearney et al. 2013). Of course, soil temperature itself is also critical for many biological and physical processes such as decomposition, egg development and frost.

Secondly, the physics-based and process-explicit nature of a mechanistic microclimate model permits use in a wider range of applications. A disadvantage of statistical models is that they can only be applied to the conditions under which they are fitted, in the present case the soil environments found at weather stations. Such environments typically involve unshaded, open, flat ground with a turf vegetation cover. In contrast, the mechanistic microclimate model can explicitly account for variation in soil and topographic properties, including rock vs. soil, shade, slope, aspect, mulch, roughness, solar reflectance, etc. This not only provides greater applicability but also permits tests of the efficacy of manipulative interventions, for example, improvement of nesting sites via manipulative shading (Mitchell et al. 2008). It is also possible to simulate a range of potential microhabitats available to bound possibilities, if exact properties are not known. Application of the model to future climate change scenarios could make use of techniques for characterizing patterns of stochasticity based on present conditions, such as weather generators (Furrer & Katz 2007) or environmental bootstraps (Denny & Dowd 2012).

We are yet to make detailed tests of the model's capacity to capture microtopographic effects of surface soil properties (e.g. reflectance), slope and aspect and shade from vegetation and hills. In some cases, mesoscale processes such as cold-air drainage, mist and wind dynamics would be crucial to accurate predictions of microclimates. However, our study shows that it is possible to model microclimatic conditions at fine temporal (hourly) and spatial (5 km) scales across a wide range of open environments across an entire continent. Moreover, the AWAP weather input data we used extend back in time at daily resolution to 1990 for the full data set of rainfall, temperature, vapour pressure and radiation. This provides a powerful foundation for process-explicit inferences of how past, present and future climates constrain the distribution and abundance of terrestrial organisms.

Acknowledgements

We thank Gaylon Campbell, Keith Bristow and Brian Horton for discussion. This work was supported by a University of Melbourne Science Faculty Seed Grant to M.R.K., A.A.H. and D.J.K., an Australian Research Council (ARC) Fellowship to M.R.K., an ARC Laureate Fellowship to A.A.H., and an ARC Federation Fellowship to D.K., while R.T. was supported by the ARC Centre of Excellence for Environmental Decisions.

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