Temporal analysis of productivity in the Desert - Mediterranean Transition Zone ecological unit using satellite images from the years 1984-2020

Productivity for a given season is the maximum NDVI for that season (spring months). The response variable examined is the relative rate of change in productivity, computed by calculating the absolute rate of change in productivity and dividing by the average productivity over the entire time series.

Diagnostic plots - cleveland dotplots

Remove suspected outlier points with the following indices:

261: outlier in Slope_NDVI (high). Checked visually and seems near agriculture.

235, 264: outliers in Slope_Precipitation (high and low, respectively)

27: outlier in Slope_Temp (high)

Examining multicollinearity (correlations between variables)

Slope_Precipitation Slope_Temp Slope_Eva Precipitation_mean Elevation_m Slope Temp_37y_mean Temp_37y_min Temp_37y_max Aspect
Slope_Precipitation 1.0000000 0.2802844 -0.5166776 -0.0910252 0.5044167 0.2519849 -0.5413453 -0.5856998 0.1249766 0.0269166
Slope_Temp 0.2802844 1.0000000 -0.2655564 -0.6798054 0.5567680 0.0969163 -0.2191680 -0.6004540 0.2514410 -0.0482744
Slope_Eva -0.5166776 -0.2655564 1.0000000 0.0213142 -0.8197881 -0.3169874 0.4894140 0.7622645 -0.4857086 -0.0277280
Precipitation_mean -0.0910252 -0.6798054 0.0213142 1.0000000 -0.1732199 0.1620561 -0.1575463 0.1489525 -0.2949044 0.0649390
Elevation_m 0.5044167 0.5567680 -0.8197881 -0.1732199 1.0000000 0.4594485 -0.6361908 -0.9217956 0.3230689 -0.0213605
Slope 0.2519849 0.0969163 -0.3169874 0.1620561 0.4594485 1.0000000 -0.4150908 -0.3990316 -0.0244714 0.1048988
Temp_37y_mean -0.5413453 -0.2191680 0.4894140 -0.1575463 -0.6361908 -0.4150908 1.0000000 0.8079016 0.4015010 -0.0327612
Temp_37y_min -0.5856998 -0.6004540 0.7622645 0.1489525 -0.9217956 -0.3990316 0.8079016 1.0000000 -0.1344201 -0.0069754
Temp_37y_max 0.1249766 0.2514410 -0.4857086 -0.2949044 0.3230689 -0.0244714 0.4015010 -0.1344201 1.0000000 -0.0144317
Aspect 0.0269166 -0.0482744 -0.0277280 0.0649390 -0.0213605 0.1048988 -0.0327612 -0.0069754 -0.0144317 1.0000000

The above Cleveland plots show that all the temperature plots and Slope_Eva are quite discretized.This is due to the low spatial resolution of the raw data (11Km). The above correlation matrix and pairs plot show that Elevation is highly correlated with Slope_Eva and Temp_37y_min, and is moderately correlated with Slope_Temp and Slope_Precipitation. In addition, Slope_Temp is correlated with Precipitation_mean and with Temp_37y_min. Temp_37y_min is highly correlated with Temp_37y_mean and other variables.

As all three temperature variables mean, min and max are correlated with each other, leave only mean.

Test the variance inflation factor of each term:

##  Precipitation_mean Slope_Precipitation          Slope_Temp               Slope 
##            2.380009            1.699846            3.468693            1.475207 
##              Aspect           Slope_Eva         Elevation_m       Temp_37y_mean 
##            1.030647            4.387314            7.990013            2.364290

drop Elevation_m because it is greater than 5 and highest overall.

##  Precipitation_mean Slope_Precipitation          Slope_Temp               Slope 
##            2.376826            1.661582            2.418741            1.280058 
##              Aspect           Slope_Eva       Temp_37y_mean 
##            1.015218            1.550235            1.919301

Full model

This is the model with all the remaining predictors:

## 
## Call:
## lm(formula = Y ~ Precipitation_mean * Slope_Precipitation + Slope_Temp + 
##     Slope_Temp:Precipitation_mean + Slope + Aspect + Temp_37y_mean * 
##     Slope_Temp + Temp_37y_mean:Precipitation_mean, data = P)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.37911 -0.34075 -0.00517  0.29354  1.72096 
## 
## Coefficients:
##                                          Estimate Std. Error t value Pr(>|t|)
## (Intercept)                            -1.982e+02  6.695e+01  -2.961  0.00335
## Precipitation_mean                      7.058e-02  4.250e-02   1.661  0.09795
## Slope_Precipitation                    -4.955e-01  3.270e-01  -1.515  0.13088
## Slope_Temp                              3.863e+03  1.398e+03   2.764  0.00611
## Slope                                  -1.226e-02  8.890e-03  -1.379  0.16919
## Aspect                                 -2.023e-04  3.086e-04  -0.656  0.51267
## Temp_37y_mean                           1.048e+01  3.352e+00   3.126  0.00197
## Precipitation_mean:Slope_Precipitation  2.244e-03  1.317e-03   1.704  0.08962
## Precipitation_mean:Slope_Temp           4.959e-01  3.023e-01   1.640  0.10211
## Slope_Temp:Temp_37y_mean               -2.053e+02  6.981e+01  -2.941  0.00357
## Precipitation_mean:Temp_37y_mean       -4.572e-03  1.848e-03  -2.474  0.01399
##                                          
## (Intercept)                            **
## Precipitation_mean                     . 
## Slope_Precipitation                      
## Slope_Temp                             **
## Slope                                    
## Aspect                                   
## Temp_37y_mean                          **
## Precipitation_mean:Slope_Precipitation . 
## Precipitation_mean:Slope_Temp            
## Slope_Temp:Temp_37y_mean               **
## Precipitation_mean:Temp_37y_mean       * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5221 on 261 degrees of freedom
## Multiple R-squared:  0.271,  Adjusted R-squared:  0.243 
## F-statistic: 9.701 on 10 and 261 DF,  p-value: 9.361e-14

Model selection using stepwise selection

## Start:  AIC=-342.82
## Y ~ Precipitation_mean * Slope_Precipitation + Slope_Temp + Slope_Temp:Precipitation_mean + 
##     Slope + Aspect + Temp_37y_mean * Slope_Temp + Temp_37y_mean:Precipitation_mean
## 
##                                          Df Sum of Sq    RSS     AIC
## - Aspect                                  1   0.11714 71.250 -344.37
## - Slope                                   1   0.51800 71.651 -342.85
## <none>                                                71.133 -342.82
## - Precipitation_mean:Slope_Temp           1   0.73347 71.867 -342.03
## - Precipitation_mean:Slope_Precipitation  1   0.79110 71.924 -341.81
## - Precipitation_mean:Temp_37y_mean        1   1.66835 72.802 -338.51
## - Slope_Temp:Temp_37y_mean                1   2.35683 73.490 -335.95
## 
## Step:  AIC=-344.37
## Y ~ Precipitation_mean + Slope_Precipitation + Slope_Temp + Slope + 
##     Temp_37y_mean + Precipitation_mean:Slope_Precipitation + 
##     Precipitation_mean:Slope_Temp + Slope_Temp:Temp_37y_mean + 
##     Precipitation_mean:Temp_37y_mean
## 
##                                          Df Sum of Sq    RSS     AIC
## <none>                                                71.250 -344.37
## - Slope                                   1   0.56978 71.820 -344.21
## - Precipitation_mean:Slope_Temp           1   0.74051 71.991 -343.56
## - Precipitation_mean:Slope_Precipitation  1   0.78396 72.034 -343.40
## + Aspect                                  1   0.11714 71.133 -342.82
## - Precipitation_mean:Temp_37y_mean        1   1.67311 72.924 -340.06
## - Slope_Temp:Temp_37y_mean                1   2.31943 73.570 -337.66

Resulting model:

## 
## Call:
## lm(formula = Y ~ Precipitation_mean + Slope_Precipitation + Slope_Temp + 
##     Slope + Temp_37y_mean + Precipitation_mean:Slope_Precipitation + 
##     Precipitation_mean:Slope_Temp + Slope_Temp:Temp_37y_mean + 
##     Precipitation_mean:Temp_37y_mean, data = P)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.39778 -0.34538 -0.01044  0.29717  1.74651 
## 
## Coefficients:
##                                          Estimate Std. Error t value Pr(>|t|)
## (Intercept)                            -1.967e+02  6.684e+01  -2.943  0.00354
## Precipitation_mean                      7.059e-02  4.245e-02   1.663  0.09755
## Slope_Precipitation                    -4.944e-01  3.266e-01  -1.514  0.13132
## Slope_Temp                              3.827e+03  1.395e+03   2.744  0.00650
## Slope                                  -1.280e-02  8.842e-03  -1.447  0.14896
## Temp_37y_mean                           1.040e+01  3.346e+00   3.108  0.00209
## Precipitation_mean:Slope_Precipitation  2.234e-03  1.316e-03   1.698  0.09072
## Precipitation_mean:Slope_Temp           4.983e-01  3.020e-01   1.650  0.10011
## Slope_Temp:Temp_37y_mean               -2.035e+02  6.968e+01  -2.920  0.00380
## Precipitation_mean:Temp_37y_mean       -4.578e-03  1.846e-03  -2.480  0.01375
##                                          
## (Intercept)                            **
## Precipitation_mean                     . 
## Slope_Precipitation                      
## Slope_Temp                             **
## Slope                                    
## Temp_37y_mean                          **
## Precipitation_mean:Slope_Precipitation . 
## Precipitation_mean:Slope_Temp            
## Slope_Temp:Temp_37y_mean               **
## Precipitation_mean:Temp_37y_mean       * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5215 on 262 degrees of freedom
## Multiple R-squared:  0.2698, Adjusted R-squared:  0.2447 
## F-statistic: 10.75 on 9 and 262 DF,  p-value: 3.342e-14

Model validation

Visualize effects

only effects significant on the level of \(\alpha = 0.1\) are displayed.

Re-fit the model using standardized IVs (independent variables) to identify the variables with highest contribution to the rate of change of productivity

Observations 272
Dependent variable Y
Type OLS linear regression
F(9,262) 10.755
R² 0.270
Adj. R² 0.245
Est. S.E. t val. p
(Intercept) 0.001 0.090 0.014 0.989
Precipitation_mean 0.406 0.089 4.551 0.000
Slope_Precipitation 0.025 0.067 0.373 0.710
Slope_Temp -0.012 0.117 -0.103 0.918
Slope -0.086 0.059 -1.447 0.149
Temp_37y_mean 0.220 0.080 2.764 0.006
Precipitation_mean:Slope_Precipitation 0.116 0.068 1.698 0.091
Precipitation_mean:Slope_Temp 0.135 0.082 1.650 0.100
Slope_Temp:Temp_37y_mean -0.258 0.088 -2.920 0.004
Precipitation_mean:Temp_37y_mean -0.281 0.113 -2.480 0.014
Standard errors: OLS

Summary

On average, there is an increase in productivity, with a slope of 0.5587442 NDVI units per year, which is on average 225.63 percent per year. The only IVs with a positive effect on the rate of change of productivity are mean precipitation and maximum temperature, but only under mutual interaction. For mean precipitation there is a positive effect only under low maximum temperatures (i.e. the wetter it gets, productivity increases more - but the opposite effect occurs under high maximum temperatures). Similarly, max temperature has a positive effect only in areas with LOW mean precipitation; under high mean precipitation it shows a negative effect.

The rate of change of precipitation has a significant negative effect.

The rate of change of temperature has a negative effect (i.e., the higher the rate of temp increase, the lower the rate of increase of productivity). This variable is interacting with mean precipitation, and it’s effect is higher in dryer areas.

Topographic slope has a marginally significant negative effect (i.e. the steeper it gets, the lower is the rate of increase in productivity).

Using standardized IVs we see that the most important IVs (with the highest influence on the DV (dependent variable) per change of 1 SD in the IV) are the rate of change of temperature, precipitation mean, and max temperature. Probably of these precipitation mean is the most important because it is interacting with the other two. The least important is the rate of change in precipitation, which is also the least significant (yet still statistically significant on a level of \(\alpha = 0.05\))