Abstract
?
?In this study, an empirical model for predicting urban evapotranspiration (ET) is examined for the Phoenix metropolitan area that is in a subtropical desert climate using in situ ET measurements from a local flux tower and remotely sensed moderate-resolution imaging spectroradiometer land products. Annual ET maps of Phoenix are then created for the period from 2001 to 2015 using the empirical model developed. A time-series trend analysis is finally performed using predicted ET maps to discover the spatio-temporal patterns of ET changes during the study period. Results suggest that blue-sky albedo and land surface temperature are two statistically significant variables explanatory to model urban ET for Phoenix. Areas that have experienced significant increases of ET are highly spatially clustered, and are mainly found on the outskirts of the city, while areas of decreasing ET are generally associated with highly developed areas, such as downtown Phoenix.
1. Introduction
Conversion from natural terrain and agricultural land to built-up environment has taken place ubiquitously worldwide at an increasing rate to meet the ever-increasing demand of rapid growth of urban population (Seto et al. Citation2011). Associated with the use of construction and building materials, such as asphalt, concrete, bricks, etc., urbanization modifies surface energy balance and hydrological cycle, leading to significant impacts on local and regional hydroclimate (Owen, Carlson, and Gillies Citation1998; Kondoh and Nishiyama Citation2000; Zhang et al. Citation2009; Georgescu, Mahalov, and Moustaoui Citation2012; Wang, Bou-Zeid, and Smith Citation2013). Evapotranspiration (ET) is one of the major components of the hydrologic cycle, but the impacts of urbanization on ET vary largely with local climatic conditions. Liu et al. (Citation2010) studied the relationship between different land use land cover (LULC) types and urban ET for a semi-arid city in Oklahoma, USA, and found that different LULC types have different ET rates in the urban area with the lowest ET found in highly developed areas. They also argued that the conversion from natural vegetated landscape and waterbody to built-up environment could significantly lower ET (Liu et al. Citation2010). On the other hand, Balling and Brazel (Citation1987a) studied ET rates using Phoenix, Arizona, USA as the study area, and found that rapid urbanization had caused a significant increase of ET level under a subtropical desert climate.
In many circumstances, urban ET exceeds precipitation and is mainly sustained by the use of external water (Grimmond and Oke Citation1999), and urban vegetation receives a substantial amount of water from anthropogenic irrigation, especially in arid and semi-arid areas (Gober et al. Citation2009; Johnson and Belitz Citation2012). A previous study reported that irrigation of private gardens consumes about 16–34% of the total urban water supplied, let alone the water used for irrigating large open space such as public parks and golf courses (Mitchell, Mein, and McMahon Citation2001). Field experiments also found that potential ET rate of irrigated urban lawn was about 1.3 times greater than that from a rural pasture (Oke Citation1979). This phenomenon is especially significant to desert cities because irrigated urban vegetation patches can help the city stay cooler than the surrounding dry desert region, which is known as the urban oasis effect (Oke Citation1979; Yang et al. Citation2015).
Although the impacts of LULC change on urban ET rate have long been a focal research area, most studies made use of temporally discrete ET data collected from local weather stations or flux towers, which only provide information for a limited spatial coverage surrounding the station. Predicting and mapping ET for the spatial continuum of the entire urban area remain challenging. A number of numerical methods have been developed for estimating urban ET during the past decade, which can be broadly categorized into two groups. The first group uses urban land surface models where ET is calculated using a bulk transfer formula (Best et al. Citation2011; Niu et al. Citation2011). This group of models is able to solve ET physically with a reasonable accuracy. However, it requires accurate estimates of input parameters related to urban geometry and thermal properties, which are not readily available from field collections and are very difficult to acquire. The second group is the empirical models that are developed from regression analysis using in situ ET measurements (Granger and Hedstrom Citation2011; Morton Citation1983). Compared to the urban land surface models, empirical models are more site-specific, which may not be applicable to areas with different geographical and meteorological conditions. On the other hand, empirical models require significantly less input data and are usually more accurate at the local scale, as information of physical processes is implicitly contained in the measurements.
Remote-sensing techniques offer great opportunities to acquire continuous Earth’s surface observations without having direct physical contact with the surface. Many remote-sensing based models have been developed and widely used to model and map ET at both regional and global scales, such as SEBAL (Bastiaanssen et al. Citation1998, Citation2005), METRIC (Allen et al. Citation2007), ReSET (Elhaddad and Garcia Citation2008), and ALARM (Suleiman and Crago Citation2002) to name a few. All these models quantify the surface energy balance using remotely sensed thermal data as an input that are associated with evaporation and transpiration processes to provide predicted ET maps. However, all these models also require the input of meteorological data to some degree, such as wind speed, humidity, solar radiation, and air temperature, which are very difficult to collect simultaneously with the acquisition of satellite images. Furthermore, meteorological data are usually collected from a limited number of local weather stations. An extrapolation technique is, therefore, required to predict and map ET for a larger geographic area which is sometimes not accurate for locations that are far away from weather stations. Some other studies developed models to estimate urban ET using remotely sensed data through vegetation indices, such as the normalized difference vegetation index (NDVI) (Nouri et al. Citation2013; Johnson and Belitz Citation2012). These models may be effectively applicable to a city with relatively high vegetation cover, but is not applicable to the Phoenix metropolitan area due to its unique desert environment.
One of the most widely used satellite remotely sensed dataset is the moderate-resolution imaging spectroradiometer (MODIS) data that provides daily observations for the entire surface of the Earth. Many MODIS land products have been produced at various spatial and temporal resolutions to meet different scientific demands. One of the most popular products is the MODIS global terrestrial ET product (MOD16) that provides regional and global observations for surface water and energy balances and soil moisture status (Mu et al. Citation2007; Mu, Zhao, and Running Citation2013). The predicted ET data from this product, however, are not available for urban areas because the model was not specifically developed for the urban land cover type. In addition, this dataset only covers the time period from 2000 to 2010 at 1 km spatial resolution. The short temporal coverage and relatively coarse spatial resolution make it unsatisfactory for urban ET studies. Therefore, a specific model is needed to predict urban ET using remotely sensed data at a finer spatial resolution for a longer temporal coverage in order to study spatial and temporal changes of urban ET.
To fill the gap in literature, two objectives of this study are posed. The first objective is to establish an empirical model specifically for the Phoenix metropolis to predict urban ET using in situ ET measurements and remotely sensed data. The second objective is to discover specific areas that have experienced significant ET changes and the spatio-temporal patterns of urban ET change for the entire Phoenix metropolitan area from 2001 to 2015.
2. Study area
The Phoenix metropolitan area is located in the northeast part of the Sonoran Desert in the central Arizona, USA, and is the sixth largest U.S. city encompassing a total area of approximately 2800 km2 (Figure 1) with an estimated population of 4.4 million (U.S. Census Bureau Citation2013). It lies within an arid subtropical desert climate region with extremely hot summers but mild winters. Phoenix receives an average annual precipitation of 204 mm (8.04 in.) over the last 30 years (U.S. Climate Data Citation2014). Late spring and early summer are particularly dry periods, while the summer monsoon season normally occurs between early July and early September that can bring more than 30% of the total annual precipitation through intense thunderstorms (Balling and Brazel Citation1987b; Adams and Comrie Citation1997; Vivoni et al. Citation2008). The daily high temperature exceeds 37.8°C (100°F) for an average of 110 days every year that normally occurs from late May until early September. The highest temperature can reach more than 43.3°C (110°F) for an annual average of 18 days. The study area has diverse LULC types, including commercial, industrial, and residential areas, undisturbed desert, agriculture, grassland, and waterbodies.
Published online:
17 October 2016Figure 1. Map of study area. For full color versions of the figures in this paper, please see the online version.
Figure 1. Map of study area. For full color versions of the figures in this paper, please see the online version.
3. Data and methods
3.1. Remotely sensed data
This study uses three sets of readily available standard MODIS land products that are processed and distributed by NASA and USGS. These products have demonstrated high scientific quality and are being used to answer science questions in a variety of disciplines. The first MODIS land product contains the bidirectional reflectance distribution function and albedo (MCD43A3) that provides both directional hemispherical reflectance (black-sky albedo) and bihemispherical reflectance (white-sky albedo) images with a 500-m spatial resolution. The data accuracy is well less than 5% albedo at the majority of the validation sites (Wang et al. Citation2014). The production function of black-sky albedo is based on the assumption that the entire light source is directional, while the white-sky albedo is based on the assumption that the light source is diffuse. The actual albedo (blue-sky albedo) is an interpolation of these two as a function of the fraction of diffuse skylight using: 
(1)
where αblue, αws, and αbs are the blue-sky, white-sky, and black-sky albedo, respectively, and fdiff is the diffuse skylight ratio. This MODIS product is produced every 8 days with an acquisition duration of 16 days. For example, the first production period (Period 001) includes acquisition days from day 1 to day 16, and the second production period (Period 009) includes acquisition days from day 9 to day 24, and so on. It can be found that there is an 8-day overlap between every two consecutive production periods. Therefore, the last production period is Period 345 that includes acquisition days from day 345 to day 360. A total of 44 blue-sky albedo images are therefore acquired for every year.
The second MODIS product used is the temperature and emissivity (MOD11A1) product. This product provides daily land surface temperature (LST) with a spatial resolution of 1 km for both daytime and nighttime. The data validation study reported that the LST products were validated within 1 K in the range of 263–322 K and the atmospheric column water vapor range of 0.4–3.0 cm (Wan et al. Citation2002). A mean daily LST dataset for Phoenix is generated by averaging daytime and nighttime LST images.
Another potentially relevant parameter is vegetation index for estimation urban ET. However, the MODIS vegetation indices do not include data for urban areas. It is, therefore, necessary to generate vegetation index datasets for the Phoenix metropolitan area on our own. The MODIS global surface reflectance (MOD09GA) product is collected daily at 500 m spatial resolution. It has been reported that 86.5% of the observation points for the red band (Terra Band 1) and 93.99% of the observation points for the near-infrared (NIR) band (Terra Band 2) were within a relative error of ±(0.005 + 5%) (Vermote and Kotchenova Citation2008). The NIR and red band reflectance images are used to calculate the NDVI using the following formula: 
(2)
where ρNIR is the reflectance of the near-infrared band, and ρred is the reflectance of the red band.
Using the same phased production method as the MODIS albedo datasets, 16-day mean LST and NDVI images are produced every 8 days with 16 days of acquisition from 2001 to 2015 for the entire Phoenix metropolitan area. This procedure generates 44 images for blue-sky albedo, mean LST, and NDVI for every year.
3.2. In situ ET measurements
In situ ET measurements were obtained from a flux tower deployed in a residential area located in western Phoenix (33.483847° N, 112.142609° W) through the Central Arizona-Phoenix Long-Term Ecological Research (CAP LTER) program funded by the National Science Foundation (NSF). This flux tower uses eddy-covariance methods to measure the exchanges (fluxes) of carbon dioxide (CO2), water vapor, and energy between the terrestrial ecosystems and the overlying atmosphere within a footprint area of about 500 m in radius. The land cover/land use type around the flux tower mainly consists of low-rise, single-family residences of relatively small lot size (Chow and Brazel Citation2012). Garden hose for ad hoc is mainly used for lawn watering, instead of automated watering systems (Chow et al. Citation2014). Swimming pools only cover less than 1% of the surface area, and most of them are left empty throughout the year (Chow et al. Citation2014).
Local scale urban surface energy balance data for the entire calendar year of 2012 and 2014 are available. The raw 10 Hz flux data were collected and processed using the EDiRe software platform. The detailed data collection and processing procedures can be found in Chow et al. (Citation2014). ET measurements were acquired, quality-controlled, and converted from W/m2 to mm/day. The same phased production strategy used for MODIS data has also been applied to the ET measurements to calculate 16-day mean ET values. The 2012 data are going to be used for establishing the empirical model, and the 2014 data are used for model verification.
3.3. Multiple regression analysis
A 500-m-radius circle is created using the flux tower as the center in ArcGIS software. The circle feature is used to mask 2012 blue-sky albedo, LST, and NDVI images and to extract pixel values for the corresponding dates when ET data are available. The correlation matrix among these three variables is shown in . The low and insignificant correlation values indicate a small likelihood of multicollinearity problem.
Table 1. Correlation matrix among blue-sky albedo, LST, and NDVI.
An ordinary least squares (OLS) regression analysis is then performed using ET as the dependent variable, and albedo, LST, and NDVI as independent variables to establish a multiple regression model of the best fit. The model is formulated as 
(3)
where β1, β2, and β3 are the coefficients for albedo, LST, and NDVI respectively. β0 is the intercept, and ε is the error term that assumes to be normally distributed with mean 0.
3.4. Urban ET mapping and time-series trend analysis
The multiple regression model established above is then applied to all the image pixels to make ET predictions for the entire Phoenix metropolitan area. The annual ET map is then created by adding all 44 predicted ET images for every year from 2001 to 2015. The 15-year mean annual ET values of every single pixel stack are treated as the dependent variable and analyzed against the year sequence (2001–2015) by OLS regression. The regression model is written as 
(4)
where a is the intercept, b is the slope coefficient that carries a practical meaning of the mean annual ET change from 2001 to 2015, and ε is the error term. Only pixels that have statistically significant changes (p ≤ 0.05) of ET over the study period are retained.
4. Results
4.1. Multiple regression model
The blue-sky albedo, LST, and NDVI values extracted from the MODIS images are used to perform an OLS regression against the 2012 ET data to establish an empirical model for ET predictions. It was initially anticipated that NDVI could potentially be correlated to urban ET. However, it turned out that NDVI was not statistically significant at the 0.05 level. Adding NDVI does not help improve the goodness-of-fit of the model, it is therefore dropped. The detailed regression analysis results are reported in , and the estimated regression equation is written as 
(5)
Table 2. Multiple regression analysis results.
The model adjusted R2 value is 0.887, which means 88.7% of the total variance of measured ET can be explained by the estimated regression equation, indicating that the model has a good fit of the data. The p-value of the F-statistic is smaller than 0.05, suggesting that the model is highly statistically significant. The p-values of the t-statistics for albedo and LST variables indicate that the coefficients are significantly different from zero, and both variables have statistically significant linear relationships with ET. The small variance inflation factor (VIF) value indicates no multicollinearity issue.
4.2. Model verification
Using Formula (5) as the estimated regression equation and MODIS blue-sky albedo and LST image pixel values as variable inputs, 44 time-series predicted ET maps are then created for 2014. The predicted ET values are extracted from the image pixel where the flux tower is deployed, and then analyzed against the measured ET data for model verification using OLS regression. Figure 2 shows that the relationship between predicted and measured ET data is strong (R2 = 0.9071) and statistically significant (p < 0.05), implying that the empirical model established is valid and can be used to predict urban ET for the Phoenix metropolitan area for other years.
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17 October 2016
Figure 2. The relationship between modeled and measured urban ET for 2014.
4.3. Predicted annual ET maps and time-series trend analysis results
Figure 3 shows annual urban ET maps of Phoenix from 2001 to 2015. The red pixels indicate areas of low annual ET, while blue pixels denote high ET areas. It can be found that low ET values have been consistently observed over the study period in suburban areas on the city outskirts, such as the southeast, northwest, and west parts of the metropolis. In contrast, high ET values are found in highly urbanized areas, such as the downtown and some high-density residential areas in northern Phoenix.
Published online:
17 October 2016Figure 3. Predicted annual ET maps for the Phoenix metropolitan area from 2001 and 2015. For full color versions of the figures in this paper, please see the online version.
Figure 3. Predicted annual ET maps for the Phoenix metropolitan area from 2001 and 2015. For full color versions of the figures in this paper, please see the online version.
The results of time-series trend analysis are shown in Figure 4. Figure 4(a) and (b) are the slope coefficient and the coefficient of determination (R2) maps, respectively, that show areas in the Phoenix metropolitan area where have experienced statistically significant (p ≤ 0.05) changes of ET during the study period. The slope coefficient represents the mean annual ET change from 2001 to 2015. The blue pixels in Figure 4(a) represent areas of increasing ET with positive slope coefficient values, while the red pixels denote areas of decreasing ET with negative slope coefficients. The total area of increasing ET is approximately 2050 km2, which occupies more than 70% of the entire metropolitan area, while the total area of decreasing ET is only 19.5 km2. The largest positive slope coefficient value is 5.35, representing the highest mean annual ET increase of 5.35 mm, while the largest negative slope coefficient is −5.10, representing a mean annual ET decrease of 5.1 mm. It can be found that the increasing magnitude of urban ET is overall much higher than the decreasing magnitude.
Published online:
17 October 2016Figure 4. The time-series trend analysis results of predicted urban ET data for the Phoenix metropolitan area. (a) The slope coefficient map that shows the slope coefficient values derived from the OLS regression analysis, with blue pixels representing areas of increasingly higher ET and red pixels representing decreasing ET areas. The slope coefficient carries a practical meaning of mean annual ET change from 2001 to 2015. (b) The coefficient of determination (R2) map that shows the goodness-of-fit of the OLS regression model for each pixel that has statistically significant changes of ET during the study period. For full color versions of the figures in this paper, please see the online version.
Figure 4. The time-series trend analysis results of predicted urban ET data for the Phoenix metropolitan area. (a) The slope coefficient map that shows the slope coefficient values derived from the OLS regression analysis, with blue pixels representing areas of increasingly higher ET and red pixels representing decreasing ET areas. The slope coefficient carries a practical meaning of mean annual ET change from 2001 to 2015. (b) The coefficient of determination (R2) map that shows the goodness-of-fit of the OLS regression model for each pixel that has statistically significant changes of ET during the study period. For full color versions of the figures in this paper, please see the online version.
Areas of increasing ET overspread the entire city, but the highest increments are mainly found on the city outskirts such as the southeast (i.e. south of Chandler and Gilbert) and northwest (i.e. northwest of Sun City) parts of the metropolis. These areas also have relatively higher R2 values [blue pixels in Figure 4(b)], indicating a much stronger increasing trend during the study period. The areas of decreasing ET can be mainly found in three regions that are downtown Phoenix, the residential areas to the west of Phoenix downtown, and southwestern Chandler. The ET decreasing trend is relatively low in these regions because of low R2 values [red pixels in Figure 4(b)], although all the pixels are statistically significant at the 0.05 level.
The global Moran’s I-technique was used to assess the spatial autocorrelation and to discover if there is a statistically significant spatial pattern for those areas of increasing and decreasing ET. shows that both increasing and decreasing ET areas exhibit a spatially clustered pattern, and the low p-values tell that there is a very small likelihood that this clustered pattern could be the result of random chance.
Table 3. Spatial autocorrelation analysis results for the areas of statistically significant ET changes from 2001 to 2015.
5. Discussion
In Formula (5), the parameter estimate for albedo is negative, while the estimated coefficient for LST is positive. It indicates that urban ET is negatively correlated with albedo but positively correlated to LST. It is because as the albedo of surface material increases, more incoming solar radiation would be reflected rather than absorbed. Less absorbed energy leads to the reduction in the energy available for vaporizing soil water content, therefore decreased ET. This finding is consistent with Jackson (Citation1967), in which albedo was found to be negatively related to ET. Higher surface temperature in the urban area, on the contrary, enhances the surface vaporization process and therefore increases surface ET. Carlson and Buffum (Citation1989) also found a strong positive relationship between remotely sensed surface temperature and ET, and used this relationship, together with other meteorological variables, to calculate daily ET from the surface energy budget.
The insignificance of NDVI proves that vegetation cover is unnecessarily the major contribution to urban ET for a desert city, but it mainly comes from evaporation of soil water and outdoor water use, rather than transpiration from vegetation. It is not only because the vegetation cover rate is low in Phoenix, but also NDVI values lack a temporal variation throughout the year as the major vegetation type in this area is evergreen trees and shrubs. Although there are some small patches of grass and lawn, they are well maintained by outdoor irrigation system, so the moisture availability and biological functions are at a relatively constant level. NDVI of this area therefore does not have a large temporal variation.
Areas of increasing ET have been mainly found on the outskirts of the metropolitan area that are newly urbanized during the study period. Conversion from undisturbed desert and open soil to built-up area was the major LULC change type in these areas (Wang et al. Citation2016). Urbanization has introduced more outdoor water availability for a desert city through anthropogenic irrigation and pool construction, which would not only lead to the remarkable increase in ET over the outskirt areas but also create an urban oasis effect to cool down surface temperature (Oke Citation1979; Yang et al. Citation2015). This phenomenon is unique for a desert city and is contradictory to the existing research findings that ET would be significantly reduced due to urbanization and the rapid conversion from naturally vegetated landscape to built-up environment (Liu et al. Citation2010).
The areas that have experienced significant decreases of urban ET have been mainly found in the center of the metropolitan area, such as downtown Phoenix [red pixels in Figure 4(a)]. It is because downtown Phoenix had been highly urbanized before 2001, and the surface had been completely covered by impervious and other anthropogenic materials. Increased urbanization during the study period has resulted in more constructions and more use of anthropogenic materials, which would therefore result in decreased ET. In addition, downtown Phoenix is mainly composed of compact high-rise buildings with little vegetation cover. It is unlike residential and recreational land uses that have higher percent vegetation cover and more outdoor water use. Urbanization would therefore cause decreased ET in central Phoenix metropolitan area. The highly significant cluster pattern of ET changes () demonstrates that urbanization activities in Phoenix are also spatially clustered.
The time-series urban ET changes show similar spatial distribution patterns as LST changes for Phoenix described in Wang et al. (Citation2016). It has been found that the most significant changes of the urban heat island (UHI) intensity took place on the city outskirts for both daytime and nighttime, and the highest UHI intensity was found at the southeast corner of the Phoenix metropolitan area due to rapid urban expansion. Our results show that the southeast Phoenix areas also experienced the highest increase of ET. The coexistence and coevolution of ET and UHI intensity in this area are intriguing, but this seems contradictory to the generally accepted perception that reduced evaporative cooling contributes considerably to the formation of the UHI effect. In fact, the positive relationship between the ET increase and UHI intensity is reasonable and unique for desert cities. Self-supporting native vegetation in the desert has a small evapotranspiration capacity to prevent moisture lost to intensive temperatures. On the other hand, urban vegetation can have a much larger evapotranspiration capacity, as moisture supply is secured by anthropogenic irrigations. Under this circumstance, although vegetative fraction is reduced in the process of urbanization, ET arise from the same area actually increases. Furthermore, higher temperature associated with urbanized areas enhances potential ET of sparse urban vegetation through the oasis effect. Therefore, urbanization activities under an arid desert environment can actually lead to increases in regional ET.
6. Conclusions
This study explores the statistical relationship between urban ET measurements and MODIS data, and examines the spatial-temporal patterns of urban ET change from 2001 to 2015 for the Phoenix metropolitan area. An empirical model was first established to predict urban ET using blue-sky albedo and LST datasets as explanatory variables that were derived from MODIS products. The model was then applied to the entire Phoenix metropolitan area to create predicted annual ET maps. A time-series trend analysis was also performed to discover urban areas that have experienced statistically significant changes of ET during the study period.
Unexpectedly, NDVI is not statistically significant to model urban ET for Phoenix. Phoenix is a city with an arid subtropical desert climate, where vegetation cover rate is low and NDVI lacks a large temporal variation. The urban surface moisture availability is mainly controlled by anthropogenic irrigation, especially in residential areas. Both surface albedo and LST, rather than the vegetation cover, play significant roles in determining the magnitude of urban ET.
Rapid urbanization in Phoenix has caused extensive LULC changes from agriculture, naturally vegetated landscape, and desert to built-up environment, such as high-density residential areas and impervious surfaces. Urban expansion has been mainly found on the outskirts of the metropolis during the study period. The time-series trend analysis indicates that urban ET has increased substantially in southeast and northwest parts of the metropolis, which correspond to newly urbanized areas during the study period.
Although changes in urban ET have been well studied for the Phoenix metropolitan area, this research has its own limitation. The ET prediction model developed in this study was based on ET measurements from a local residential area. Thus the model may not be fully applicable to all the other LULC types, such as industries, and croplands. More in situ ET measurements over various LULC types in the built-up areas are required to more accurately model urban ET.
| Variable | Albedo | LST | NDVI |
|---|---|---|---|
| Albedo | 1.0000 | ||
| LST | −0.0983 | 1.0000 | |
| (0.5742) | |||
| NDVI | −0.3046 | −0.4110 | 1.0000 |
| (0.0852) | (0.0642) |
Note: Values in parentheses are p-values.
| F-statistic | 134.64 |
| Prob. > F | 0.000 |
| R2 | 0.894 |
| Adjusted R2 | 0.887 |
| RMSEa | 0.114 |
| Variable | Coefficient | Standard error | t-Statistic | p-Value | 95% Confidence interval | VIFb | 1/VIF | |
|---|---|---|---|---|---|---|---|---|
| Albedo | −2.258 | 0.937 | −2.41 | 0.022 | −4.167 | −0.350 | 1.01 | 0.99 |
| LST | 0.033 | 0.002 | 15.92 | 0.000 | 0.029 | 0.037 | 1.01 | 0.99 |
| Constant | 0.171 | 0.163 | 1.05 | 0.303 | −0.162 | 0.504 | – | – |
aRoot mean square error.
bVariance inflation factor.
| Areas of increasing ET (positive slope coefficients) | Areas of decreasing ET (negative slope coefficients) | |
|---|---|---|
| Moran’s I index | 0.7560 | 0.5865 |
| Expected index | −0.0001 | −0.0130 |
| Variance | 0.0000 | 0.0016 |
| z-Score | 198.0650 | 15.0639 |
| p-Value | 0.0000 | 0.0000 |
| Spatial autocorrelation | Clustered | Clustered |
Both increasing and decreasing ET areas show a significant clustered spatial pattern.
Acknowledgements
This research is based upon work supported by the National Science Foundation under grant Number BCS-1026865, Central Arizona Phoenix Long-Term Ecological Research (CAP LTER).
Disclosure statement
No potential conflict of interest was reported by the authors.