Environmental and Anthropogenic Degradation of Vegetation in the Sahel from 1982 to 2006

There is a great deal of debate on the extent, causes, and even the reality of land degradation in the Sahel. Investigations carried out before approximately 2000 using remote sensing data suggest widespread reductions in biological productivity, while studies extending beyond 2000 consistently reveal a net increase in vegetation production, strongly related to the recovery of rainfall following the extreme droughts of the 1970s and 1980s, and thus challenging the notion of widespread, long-term, subcontinental-scale degradation. Yet, the spatial variations in the rates of vegetation recovery are not fully explained by rainfall trends. It is hypothesized that, in addition to rainfall, other meteorological variables and human land use have contributed to vegetation dynamics. Throughout most of the Sahel, the interannual variability in growing season ΣNDVIgs (measured from satellites, used as a proxy of vegetation productivity) was strongly related to rainfall, humidity, and temperature (mean r2 = 0.67), but with rainfall alone was weaker (mean r2 = 0.41). The mean and upper 95th quantile (UQ) rates of change in ΣNDVIgs in response to climate were used to predict potential ΣNDVIgs—that is, the ΣNDVIgs expected in response to climate variability alone, excluding any anthropogenic effects. The differences between predicted and observed ΣNDVIgs were regressed against time to detect any long-term (positive or negative) trends in vegetation productivity. Over most of the Sahel, the trends did not significantly depart from what is expected from the trends in meteorological variables. However, substantial and spatially contiguous areas (~8% of the total area of the Sahel) were characterized by negative, and, in some areas, positive trends. To explore whether the negative trends were human-induced, they were compared with the available data of population density, land use, and land biophysical properties that are known to affect the susceptibility of land to degradation. The spatial variations in the trends of the residuals were partly related to soils and tree cover, but also to several anthropogenic pressures.


Introduction
Since the 1990s, the human population in the Sahelian and Sudanian ecoclimatic zones (collectively referred to here as the "Sahel") increased from approximately 120 million to over 280 million [1].Population growth has been accompanied with cropland expansion and agricultural intensification [2][3][4], and with an increase in livestock numbers, from approximately 200 to over 430 million [5,6].These changes coincided with two sequences of extremely dry years in 1972-1973 and again in 1983-1984 that were part of a longer drought that lasted from the end of the 1960s to the mid-1990s [7,8].
Coincident with intensification in land use and with the 1970s-1980s droughts, were noticeable reductions in vegetation productivity [9] and numerous studies, albeit local in scale, have reported cases of land degradation (e.g., [10][11][12]).These, plus anecdotal accounts of a progressive southwards march of the Sahara Desert [13,14], led to the popular view that population growth in the predominantly agrarian economies of the Sahelian countries was causing an extension of cultivation into marginal lands, shortened fallow periods, increased grazing intensity, and increased fuel-wood extraction, and that these population pressures coupled with the prolonged drought had caused widespread land degradation [15].
The existence of such widespread degradation has been challenged in a growing number of case studies that have found significant local variations in the relation between the increasing food demands, changes in land use patterns, and land degradation (e.g., [16][17][18][19]).It has been demonstrated that, under certain conditions, the standard degradation scenario has not occurred, owing to agricultural intensification and the emergence of mixed crop-livestock farming systems [20], and, furthermore, different measurement techniques have often resulted in different conclusions [21].To date, the existence, causes, extent, and severity of land degradation throughout the Sahel remain controversial [22][23][24][25].
In contrast to the widespread belief in dryland degradation ("desertification") of the Sahel, analysis of multitemporal satellite data from the 1990s onwards has revealed a consistent trend of vegetation recovery from the extreme droughts of the 1970s and early 1980s [26][27][28][29][30][31], suggesting that the perceived widespread degradation in the Sahel can largely be attributed to climate variability and not to irreversible changes in land productivity [28,30,32].Currently, there is little if any evidence that the Sahelian drought alone (i.e., independent from human utilization of the land) has caused any land degradation [15].Thus, it seems logical to distinguish between the effects of drought, which are temporary, and human-induced land degradation, which may have a trend of increasing severity, and can reach an end point of degradation that is usually long-term and even irreversible.The management implications for even extreme drought are very different to a system that will never return to its former state once climatological norms return [33].
The term land degradation is taken here to refer to the process by which less-productive biophysical conditions emerge owing to the excessive utilization of land with respect to its resilience [33].Since net primary production (NPP) provides the energy that drives most biotic processes on Earth, persistent reductions in NPP from its potential-that is, the NPP expected in response to climate variability alone, excluding any human-induced changes in productivity-provides a useful indicator for land degradation monitoring [32][33][34].This definition also serves to distinguish drought, in which vegetation and edaphic factors fully recover from a temporary reduction in rainfall, and land degradation, in which, over time, there is incomplete recovery [35] .It is important to note, however, that negative or positive trends in vegetation production relative to its potential are not necessarily the result of land degradation or land improvement as they can be caused by other factors including changes in land use, agricultural intensification, and CO 2 fertilization, among others.Therefore, negative trends only highlight potentially degrading areas where further examination is necessary to confirm the diagnosis [30,33,36].However, in drylands, interannual variation in NPP is dominated by meteorological conditions, particularly by erratic rainfall [37], which mask more subtle and gradual changes such as degradation [36].Thus, it is difficult to interpret trends in NPP without first accounting for the effects of meteorological variability on productivity [38].
A key requirement for detection of degradation is the availability of a reference-often the potential or non-degraded condition [39][40][41].However, such sites are rarely known a priori, hence detection techniques are needed.Process-based, prognostic vegetation models (e.g., BIOME-BGC [42], LPJ-DVGM [43]) can estimate potential NPP for entire regions, however, the scarcity and coarse resolution of the necessary input data [44] and the requirement for many parameters, some complex (e.g., quantitative measures of the outcome of competition between plant functional types), largely exclude this type of model except for spatially uniform vegetation-an unusual occurrence.Furthermore, no existing process models can simulate human disturbance of the sort associated with degradation.
The method employed here uses NPP estimated using a light use efficiency approach in which satellite measurements of spectral reflectance are used to calculate the normalized difference vegetation index (NDVI), which is then summed over each growing season (ΣNDVI gs ).The potential, or non-degraded NPP is inferred from the observed relationship of ΣNDVI gs and rainfall by regression-that is the rain-use efficiency (RUE, [32]).This method is an example of diagnostic, data-oriented, sometimes called "top-down" modeling.An important strength is that comparisons with the reference are made for each individual site, so differences between sites in unaccounted factors (such as soil differences) are normalized, allowing direct inter-site comparison.It can also be used at scales from local to global.However, the use of RUE in its simple form is subject to some important preconditions (Table 1) which are often not met; ideally, each of these must either be addressed in a more elaborate normalization than is used in RUE or at least acknowledged to be unknown, hence qualifying the findings.

Precondition Number Precondition
i NPP must be primarily and linearly related to rainfall [32,45] ii NPP responds to rainfall within the current year with no carry-over from earlier years iii There are no supplements to current season rainfall, for example run-on from neighboring areas iv Within-season temporal patterns of rainfall do not affect NPP v The rainfall-NPP relationship does not vary between wet and dry years vi Potential NPP can be detected amongst data for sites both at their potential and degraded when mixed, and the status of each site is unknown vii Interannual trends in deviations between degraded and reference NPP are linear viii Deviation of ΣNDVI gs from the potential is a result of land degradation, not recognizing any other processes The most important of these preconditions is that a reference, potential, or maximum NPP can be determined from the observed NPP of all sites, degraded or not (vi).Given that it is not known which sites are degraded, a regression of NPP on rainfall is inevitably affected by sites that are degraded, usually reducing the slope and the estimation of reference NPP.Quantile regression techniques [46][47][48], in particular, upper quantile (UQ) regression, on the other hand, use the probability distribution of NPP to select the higher NPP values for each amount of rainfall, and therefore can reduce (but not eliminate) the bias caused by degraded sites.More generally UQ regression has the distinct advantage of predicting the ΣNDVI gs -rainfall relationship in any part of the conditional distribution of ΣNDVI gs response to rainfall.Here, a number of different conditional UQ regression models were tested to predict potential ΣNDVI gs using the mean and upper 95th quantile distributions of observed ΣNDVI gs responses to rainfall.
In a study of vegetation responses to climate variability in the Sahel [37], it has been shown that variations in ΣNDVI gs were overall better explained by precipitation, specific humidity (ratio of mass of water vapor to the mass of air in which it is mixed-dimensionless-used here to remove the temperature effect on humidity), atmospheric pressure, and incident solar radiation [49] and temperature than by precipitation alone (thus not satisfying precondition (i) for RUE, Table 1).Therefore, these additional variables were included here in conditional UQ regressions to develop upper boundary functions of ΣNDVI gs response to: (a) rainfall; (b) its seasonal variance; (c) seasonal skewness; (d) specific humidity; and (e) temperature.
The objectives of this study were to detect degradation in vegetation productivity by comparison with the undegraded potential by regressing the deviations in ΣNDVI gs each year from the UQ regression line on time, and testing for significance of any trends in the time-series (a technique called RESTREND analysis [50]).RUE is the relationship between rainfall and NPP, typically calculated with data for multiple years, while RESTREND is a temporal derivative of RUE in which the RUEs for individual sites are rearranged into a temporal sequence in order to detect interannual trends.In so far as significant negative trends indicate an ongoing process of land degradation, we tested the hypothesis that high population density and land use intensity lead to land degradation [19,36,[51][52][53] against the alternative that site biophysical properties determine the susceptibility of land to degradative processes [54].The results of this study are relevant to the ongoing debate on the location, extent, and causes of land degradation in the Sahel [25].

Remote Sensing Data
The AVHRR daily reflectance data in the Land Long Term Data Record (LTDR) version 2 [55] were used to reconstruct daily NDVI values from 1982 to 2006 at a spatial resolution of 0.05 • .The study was limited to 1982-2006 since the LTDR record using AVHRR terminated in 2006.While it could have been continued with MODIS data, the consistency of the LTDR data source was judged to be more important than the added 3 years.Details of the data and it post-processing are given in [37,56].It should be noted that, in comparison with the various 15-day GIMMS data sets, LTDR data are daily, which allows better within-season resolution, especially necessary in areas with short growing seasons.ΣNDVI gs was calculated as the sum of daily values between the onset of leaf development and leaf senescence [37].Annual and growing season sums of daily NDVI, precipitation, average temperature, and humidity were calculated for each year .(For details of the meteorological data, see Section 2.2 below) The data were aggregated to 3 × 3 AVHRR pixels to reduce spatial and random error [57].

Meteorological Data
The Princeton Hydrology Group (PHG), bias-corrected, hybrid, meteorological datasets of daily precipitation, surface air temperature, and specific humidity [49] were used in this study.The datasets were constructed from the National Center for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis data and corrected for biases using station observation datasets of precipitation and air temperature.The daily data for the period 1982-2006 were downscaled spatially from 1 • to the 0.05 • resolution of the AVHRR dataset using bilinear interpolation.In addition to growing season precipitation totals, any effects of within-season distribution of precipitation were assessed to test precondition (iv) (Table 1) by calculating two higher-order moments of growing season precipitation, namely variance and skewness.High variance indicates higher than normal deviation from mean seasonal precipitation and can result from extended periods of drought or from intense precipitation events, or a combination of both, while skewness is a measure of the dominant frequency of either high intensity precipitation events (negative skewness) or low intensity precipitation events (positive skewness).

Demography, Land Use, and Livestock
Sahelian population data were obtained from the Gridded Population of the World (GPW) population density data (ver.3) for the year 2000 [58].These data are constructed from national and sub-national census data, but data deficiencies in large areas of Chad, Sudan, and Guinea reduce the resolution there.
Global agricultural, gridded landcover data for the year 2000 was obtained from SEDAC [59].
A gridded dataset of livestock density for the entire Sahel was obtained from the Food and Agriculture Organization (FAO) GeoNetwork database [60] for the year 2000.The dataset includes information on cattle, sheep, and goats (animals per km 2 ).In this study, the data were transformed to total livestock unit (LSU) density using the FAO species coefficients for sub-Saharan Africa [61].Because the impact on soil erosion of shrub or tree cover, reduction is usually considered to be more severe than that associated with reductions in grass cover [15].Browser and grazer LSU densities were also calculated using livestock species food preferences: studies of goats and sheep food preferences estimate the diet of goats to be made up of approximately 80% shrub and tree browse and 20% grasses and forbs, whereas sheep eat, on average, 20% browse and 80% herb (e.g., [62][63][64]).Cattle, on the other hand, were considered to depend mainly on grasses and forbs [65].
Human land use pressures are not limited to grazing and agricultural production, but also include, among others, waste disposal, urbanization, construction, and fuel-wood collection.These factors have been aggregated in the index of Human Appropriation of NPP (HANPP) at a spatial resolution of 0.25 • [66].
All coarse resolution, mapped data were resampled to the 0.05 • resolution of the AVHRR dataset using bilinear interpolation before aggregation to the same 3 × 3 pixel cells used for ΣNDVI gs .

Soil and Land Cover
Soil physical and hydrological data were obtained from the Harmonized World Soil Database (HWSD [67]).In the Sahel region, the database merges the soil map units (SMU) from the FAO Soil Map of the World at a scale of 1:5 million with Soil and Terrain (SOTER) regional studies in Sudan, Ethiopia, Senegal, and Gambia, at scales ranging between 1:1 million and 1:5 million.Thus, the spatial detail and quality of the data varied across the Sahel.In the HWSD database, estimates of topsoil and subsoil variables within each SMU are derived using soil profiles (contained in the second version of the WISE database [68]) and soil taxonomy-based pedotransfer functions.In addition to the variables contained in the HWSD, the Soil Erodibility Factor was estimated using a mathematical representation [69] of a nomograph method [70].
The proportional estimates of bare ground and woody and herbaceous vegetation cover for the year 2000, provided by MODIS MOD44B Vegetation Continuous Fields product [71], were used.These data provide an improved depiction of spatially complex landscapes, compared with discrete classifications [71].
As with human population and land use, the soil mapping units were rasterized to a spatial resolution of 0.05 • to match that of the ΣNDVI gs data.

Potential ΣNDVI gs
Potential growing season ΣNDVI gs values were estimated using OLS and UQ linear regression techniques from the observed ΣNDVI gs response to: (i) precipitation; (ii) precipitation, specific humidity, and air temperature; and (iii) precipitation, growing season precipitation variance, and its skewness-giving six regression models in all.The models were applied to every grid cell (3 × 3 AVHRR pixels) within the study area.To reduce the risk of model overfitting, either the full set or a subset of the explanatory variables was selected to predict potential ΣNDVI gs [72].The selection criteria included a test for multicollinearity between the explanatory variables [73] and a search for the subset that resulted in the highest r 2 value adjusted for degrees of freedom [74].Further details on the selection criteria can be found in [37].
Inferences of standard errors for the UQ regressions were obtained using the "wild bootstrap" method [75], and the standard errors for the OLS regressions were calculated from the regression goodness of fit (r 2 ) and the standard deviation of observed ΣNDVI gs values.Potential ΣNDVI gs prediction errors were then calculated from the standard errors of the intercept and slopes at the 95% confidence level.An important qualification is that the standard errors were estimated with the assumption that the regression covariates were measured with no error (see discussion below).

Residual Trends (RESTREND)
The residuals, calculated by the difference of the observed ΣNDVI gs and potential ΣNDVI gs , were regressed against time by the linear OLS or UQ regressions.Negative or positive slopes (trends in time), if significant, indicated persistent, multi-year changes in ΣNDVI gs relative to the potential, as calculated from one or more of the meteorological variables.To estimate the errors associated with the calculation of residuals, the errors of the AVHRR NDVI measurements [37] were combined with the errors of the regression used to estimate potential ΣNDVI gs .The standard errors of the ΣNDVI gs values were estimated to range between ±1.47 ΣNDVI gs units in grasslands (~3.3% of the ΣNDVI gs signal) and ±3.3 ΣNDVI gs units in forests (~4.1% of the ΣNDVI gs signal) [37].Both sources of error were combined using the sum rule for the propagation of error.The errors of the residuals were then propagated to the time-series linear regression used to estimate the RESTREND (see Equation ( 1)) [76].Significant RESTREND values were identified as the ones statistically different from zero (probability of the F value <0.05) and having absolute values greater than their respective uncertainties at the 95% confidence level.
where σ β is the 1 standard deviation uncertainty of the slope value β, σ i is the standard error associated with each residual value y i , x i is the time variable, and N is the number of observations.The capability of temporal trend models to detect significant trends in degradation has been simulated for an example data set [77]; the findings were a specific case of well-known issues that arise when analyzing short time series (e.g., [78]).Rather than using simulation to determine the boundary conditions of significance, here we propagated the errors from the OLS and UQ linear regressions of observed ΣNDVI gs on the sets of meteorological variables to the RESTREND analysis.As in [77], many apparent negative trends were rejected following this test of significance.A different limitation arises if there were changes in slope within the time series, however, splitting a time series of 24 years will decrease the degrees of freedom and reduce the capability of the method to detect trend, particularly since such a break is unlikely to happen in the middle of the time series, so one segment must have <11 points.Thus, it is a choice: risk missing changes in slope or risk reducing the significance of the regression.Here we chose to risk missing changes in slope.

Relating RESTREND to Population, Land Cover, and Soil Variables
The relationships of RESTREND with land use and environmental factors were explored using statistical summaries, multivariate linear regression, and regression tree analysis (RTA, [79]).RESTREND values were ranked by each anthropogenic metric (e.g., population density) and placed in 25 equal-sized groups.The mean and standard deviation of the RESTREND values within each group were plotted against the corresponding mean of the anthropogenic metric.In addition to these univariate statistical summaries, multivariate linear regression models were used to detect additive effects of population metrics.
Environmental factors may attenuate or accelerate the effects of population on land productivity [33,80] and RTA has been found to be effective in uncovering such hierarchical relations [79], both additive and multiplicative [81].Two RTA techniques were used: (i) Classification and Regression Trees (CART; [82]), which provided hierarchical maps of the relations between the explanatory variables and RESTREND value; and (ii) Random Forests (RF; [83,84]), which evaluated the ability of the explanatory variables to account for the variability in RESTREND values, based on reductions in percentage variance explained when the explanatory variable was omitted.
Several RF models were developed, each using a subset of uncorrelated explanatory variables-for example, soil erodibility and soil texture were not used in the same model.Five hundred trees were grown for each RF model, each using a randomly selected training sample of 67% of the entire population of significant RESTREND values and their covariates.The remaining 33% of the data produced 500 "out-of-bag" samples [84], each corresponding to one RF model.Each tree was then used to predict the RESTREND value for each data point in its out-of-bag sample.The predictions were averaged and compared with their corresponding observed values to calculate the mean square error (MSE) and the strength (r 2 ) of the model [79,84].To test the accuracy of the out-of-bag method, 10 set-aside test sets were selected randomly, each about one-third the total population size.The remaining data (i.e., training sets) were used to develop ten RF models, which were used to predict the RESTREND values of the test sets.The predicted and original RESTREND values were compared to estimate the errors and strengths of the RF models.The MSE and r 2 values obtained by cross-validation were almost equal and even sometimes slightly better than the corresponding values obtained from the out-of-bag method.

Potential ΣNDVI gs
As expected, overall, UQ estimates of potential ΣNDVI gs were higher than those of OLS regression models (Table 2).Furthermore, the UQ precipitation regression coefficients were consistently higher than their OLS counterparts.The differences between the predicted values (UQ-OLS) were higher in wet years than in dry years (Figure 1a).Model A is the RUE, in which only precipitation was used and OLS regression.It had the highest mean error of all the models tested (Table 2).Adding specific humidity and temperature or seasonal precipitation distribution variance and skewness as co-independent variates in the OLS regression models (Table 2, models B & C) increased the ability of these models to account for the observed variability in ΣNDVI gs (Figure 2d), the consequences of which were more constrained predictions of potential ΣNDVI gs values.However, UQ regressions using precipitation alone, on average, had the lowest prediction errors (Table 2).The geographical distribution of prediction errors was characterized by a pronounced latitudinal gradient with larger errors at lower latitudes (e.g., Figure 2a).Adding specific humidity, air temperature, seasonal precipitation variance, and skewness to precipitation as predictor variables in OLS regression models decreased potential ΣNDVI gs prediction errors, particularly at middle and higher latitudes (Figure 2b,c).obtained by cross-validation were almost equal and even sometimes slightly better than the corresponding values obtained from the out-of-bag method.

Potential ΣNDVIgs
As expected, overall, UQ estimates of potential ΣNDVIgs were higher than those of OLS regression models (Table 2).Furthermore, the UQ precipitation regression coefficients were consistently higher than their OLS counterparts.The differences between the predicted values (UQ-OLS) were higher in wet years than in dry years (Figure 1a).Model A is the RUE, in which only precipitation was used and OLS regression.It had the highest mean error of all the models tested (Table 2).Adding specific humidity and temperature or seasonal precipitation distribution variance and skewness as co-independent variates in the OLS regression models (Table 2, models B & C) increased the ability of these models to account for the observed variability in ΣNDVIgs (Figure 2d), the consequences of which were more constrained predictions of potential ΣNDVIgs values.However, UQ regressions using precipitation alone, on average, had the lowest prediction errors (Table 2).The geographical distribution of prediction errors was characterized by a pronounced latitudinal gradient with larger errors at lower latitudes (e.g., Figure 2a).Adding specific humidity, air temperature, seasonal precipitation variance, and skewness to precipitation as predictor variables in OLS regression models decreased potential ΣNDVIgs prediction errors, particularly at middle and higher latitudes (Figure 2b,c).

Residual Trends
The total errors of the residuals calculated from potential ΣNDVI gs and observed ΣNDVI gs error components were larger at lower (wetter) than at higher (drier) latitudes, thus preconditions (v) and (vii) for a simple RUE (Table 1)) were not met.At higher latitudes, the two error components were similar in magnitude and contributed equally to the residual errors.At lower latitudes, however, residual errors were dominated by the uncertainties of potential ΣNDVI gs values.
A comparison of the combined errors (Equation ( 1)) and F tests for four example sites (Figure 3) showed that the test for uncertainty was sufficient: the probability of the F value test was <0.05 for all slope values greater than their uncertainty, while the reverse was not always true (Figure 3c,d).Note, however, some indication of a change in slope after 1998 for the site shown in (c), in contravention of precondition (vii) of the RUE (Table 1).

Residual Trends
The total errors of the residuals calculated from potential ΣNDVIgs and observed ΣNDVIgs error components were larger at lower (wetter) than at higher (drier) latitudes, thus preconditions (v) and (vii) for a simple RUE (Table 1)) were not met.At higher latitudes, the two error components were similar in magnitude and contributed equally to the residual errors.At lower latitudes, however, residual errors were dominated by the uncertainties of potential ΣNDVIgs values.
A comparison of the combined errors (Equation ( 1)) and F tests for four example sites (Figure 3) showed that the test for uncertainty was sufficient: the probability of the F value test was <0.05 for all slope values greater than their uncertainty, while the reverse was not always true (Figure 3c,d).Note, however, some indication of a change in slope after 1998 for the site shown in (c), in contravention of precondition (vii) of the RUE (Table 1).The geographical patterns of the residuals and their significance for the six models (Figure 4) were similar.There were relatively large areas with significant negative trends: in western Sudan, centered on Nyala; in southern Niger around the cities of Zinder, Maradi, Dosso, and Niamey; in Nigeria, extending between Kano in the north and Abuja in the south; and throughout Burkina Faso.However, there were areas of disagreement between the models, including in western Senegal and in Ethiopia, to the east of Lake Tana.Large areas with positive trends (i.e., increases in productivity beyond what can be explained by meteorological conditions) were recorded in Chad, Benin, Togo, Ghana, and elsewhere (Figure 4a-f).The six RESTREND models (Table 2) showed that, compared to the OLS (Figure 4a-c), the maps of the UQ regression models (Figure 4d-f) had more area with significant negative trends and less with significant positive trends.Expressing HANPP [66] as a percentage of NPP (%HANNP) revealed considerable heterogeneity in the spatial patterns of consumption and production throughout the Sahel (Figure 4g).The geographical patterns of the residuals and their significance for the six models (Figure 4) were similar.There were relatively large areas with significant negative trends: in western Sudan, centered on Nyala; in southern Niger around the cities of Zinder, Maradi, Dosso, and Niamey; in Nigeria, extending between Kano in the north and Abuja in the south; and throughout Burkina Faso.However, there were areas of disagreement between the models, including in western Senegal and in Ethiopia, to the east of Lake Tana.Large areas with positive trends (i.e., increases in productivity beyond what can be explained by meteorological conditions) were recorded in Chad, Benin, Togo, Ghana, and elsewhere (Figure 4a-f).The six RESTREND models (Table 2) showed that, compared to the OLS (Figure 4a-c), the maps of the UQ regression models (Figure 4d-f) had more area with significant negative trends and less with significant positive trends.Expressing HANPP [66] as a percentage of NPP (%HANNP) revealed considerable heterogeneity in the spatial patterns of consumption and production throughout the Sahel (Figure 4g).2); (g) % Human Appropriation of Net Primary Production (%HANPP); and (h) proportion of cropland datasets used to explore the relationship between RESTREND value and land use [5,59].The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.2); (g) % Human Appropriation of Net Primary Production (%HANPP); and (h) proportion of cropland datasets used to explore the relationship between RESTREND value and land use [5,59].The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.

Relating RESTREND to Population, Land Use, and Soil Variables
The geographic patterns of the trends of the residuals and population and land use show close visual correspondence between negative trends and high %HANPP, livestock unit density, and percentage of land area used for agriculture (Figure 4g,h).
Significant trends were compared with population and land use.Plots of the mean and standard deviation of 25 equally sized groupings of RESTREND values ranked by each population and land use variable (Figure 5) showed a poor relationship between population density and the magnitude of the trends of residuals, although, overall, a negative trend is clear (Figure 5a).However, there was a significant inverse relationship between RESTREND and %HANPP values (Figure 5b), possibly because %HANPP accounts for the effects of population density and the geographical variation in per capita consumption levels.The plots also suggest a near-linear inverse relationship between RESTREND and livestock unit density and a similar relation with livestock unit density divided by productivity (LSU/NPP) (Figure 5c,d).However, Figure 5e shows a weak inverse logarithmic relationship between RESTREND value and %crop cover.This relationship was further investigated using an index (% crop cover/mean annual precipitation-MAP) to assign higher values to the same % crop cover in drier, compared with wetter, areas.Residual trends were found to be inversely related to this index (Figure 5f).This suggests that agricultural extensification affects land productivity disproportionately more in dry areas.
The multivariate linear regression analysis of RESTREND and the additive effects of multiple land uses within a grid cell (Table 3) were better related than the univariate correlations.The highest goodness of fit (r 2 = 0.49) was between model E RESTREND and the three variables (%HANPP, LSU/NPP, %crop cover/MAP), while the lowest (r 2 = 0.34) was for the trends calculated using model D.
The RF regression analysis indicated that, in addition to population and land use, land cover and soil properties were significant (model E) (Table 4).The addition of fraction tree cover, soil bulk density, and soil erodibility increased r 2 values (Tables 4 and 5).For example, the percentage variance in RESTREND values accounted for by the variables LSU/NPP, crop density, and population density was approximately 60%.Adding soil bulk density or fraction tree cover increased the percentage variance explained (r 2 ) by more than 14% (Table 4).Similarly, %HANPP alone explained 25% of the variability in RESTREND values, but adding soil bulk density and fraction tree cover increased the percentage variance accounted for to approximately 80% (Table 5).The r 2 and the RMSE values of the RF models estimated using the "out-of-bag" method were similar to those obtained using the cross-validation approach, which indicates that, while RF trees were grown to a maximum without pruning, there was no evidence of model overfitting.Cross validation results for two RF models with relatively high r 2 values are shown in Figures 6c and 7c.The most important variables in relation to the spatial distribution of RESTREND values listed in descending order were: fraction tree cover; soil bulk density; soil erodibility; livestock unit density divided by local NPP (LSU/NPP); the index of cropping density divided by mean annual precipitation (% crop/MAP); and, finally, population density (Figures 6b and 7b).The component loadings obtained from principal component analysis suggest that, except for fraction tree cover, all other variables were inversely related to RESTREND values (Figures 6a and 7a).The same analytical procedure was repeated, but by utilizing RESTREND values calculated from the other models (i.e., models A, B, C, D, & F; Table 2).While the nature of the relationships with land use, land cover, and the geographical positions of soil properties were similar to these described for model E, the strength of the relationships (r 2 values) were persistently lower when RESTREND values for models A & D were used in RF regression analysis, whereas the r 2 values for model B approached the corresponding model E values.CART single tree models did not capture the spatial variability in model E RESTREND values so well as RF models, nonetheless they provided a graphical demonstration of the nature of the relation of RESTREND values to the explanatory variables (Figures 8 and 9).Negative RESTREND values were associated with areas characterized by high soil erodibility (>0.41) and population densities above 6.5 persons per km 2 , whereas areas with very high soil erodibility and population density below 6.5 persons per km 2   8).The areas with low fraction tree cover (<8.5%), high soil bulk density (>140.5),and high %HANPP (>24.5%) were generally associated with negative RESTREND values, whereas areas with high fraction tree cover (>18.5%) and low soil bulk density (<136.5)were associated with positive trend values.CART single tree models did not capture the spatial variability in model E RESTREND values so well as RF models, nonetheless they provided a graphical demonstration of the nature of the relation of RESTREND values to the explanatory variables (Figures 8 and 9).Negative RESTREND values were associated with areas characterized by high soil erodibility (>0.41) and population densities above 6.5 persons per km 2 , whereas areas with very high soil erodibility and population density below 6.5 persons per km 2   8).The areas with low fraction tree cover (<8.5%), high soil bulk density (>140.5),and high %HANPP (>24.5%) were generally associated with negative RESTREND values, whereas areas with high fraction tree cover (>18.5%) and low soil bulk density (<136.5)were associated with positive trend values.CART single tree models did not capture the spatial variability in model E RESTREND values so well as RF models, nonetheless they provided a graphical demonstration of the nature of the relation of RESTREND values to the explanatory variables (Figures 8 and 9).Negative RESTREND values were associated with areas characterized by high soil erodibility (>0.41) and population densities above 6.5 persons per km 2 , whereas areas with very high soil erodibility and population density below 6.5 persons per km 2   8).The areas with low fraction tree cover (<8.5%), high soil bulk density (>140.5),and high %HANPP (>24.5%) were generally associated with negative RESTREND values, whereas areas with high fraction tree cover (>18.5%) and low soil bulk density (<136.5)were associated with positive trend values.

Discussion
The analyses clearly indicated that variance in ΣNDVI gs (the surrogate for NPP) was better explained by combined growing season precipitation, specific humidity, and temperature, and by seasonal variance and skewness of precipitation, rather than by RUE (precipitation alone-Model A) (Figure 2d).This was expected because of the roles these meteorological variables play in growth and rates of development of vegetation throughout the Sahel [37,[85][86][87].However, it should be recognized that herbaceous and woody components of the vegetation, which may vary independently [88], were not distinguished here.
The proportion of significant relationships between precipitation and ΣNDVI gs found here was similar to other reports [89]-the differences probably related to the different preprocessing of data used and inclusion or exclusion of precipitation outside the main growing season, although there is another study [28] that reported a very low percentage of the region with significant relationships.
Despite significant increases in r 2 values, the strength of the relationship between ΣNDVI gs and the meteorological variables was not uniformly high.For example, it was relatively weak south of the 900mm isohyet (Figure 3), presumably because the environmental variables studied do not limit NPP there to the same degree as in the drier areas [37,88].In drier areas, low correlations may arise near perennial lakes, rivers, and irrigated agriculture where the vegetation can utilize water from rainfall gathered elsewhere (in which case precondition (iii) for RUE would not be met (Table 1).Similarly, for trees which may access water deep in the soil profile [90] (also not satisfying precondition (iii).Table 1), or, in some cases, the rainfall-soil moisture relationship can become increasingly non-linear (not satisfying precondition (i)) owing to reduced infiltration and surface evaporation.
Potential ΣNDVI gs prediction errors were calculated with the assumption that the meteorological datasets were error-free.This is clearly not the case and could reduce the extent of the areas with significant trends.Unfortunately, modeled meteorological data sets are rarely accompanied by measures of error, and tests with meteorological stations data are not valid since those data are used in calibration [49].Moreover, the systematic error component of the AVHRR data has not been evaluated, since data from other sensors were not available for the full study period .However, the corrections applied to the meteorological and to the AVHRR data [49,57] have been applied to the processing stream and are reported to significantly reduce the systematic error components and therefore are not expected to have influenced greatly the findings of this study.
Potential ΣNDVI gs values estimated from OLS regressions were generally lower than their counterparts obtained from the 95 th upper quantile (UQ) distribution (Figure 1).This was expected, since OLS regressions can underestimate vegetation production potential because, in years when vegetation production was not only limited by precipitation, other factors, including humidity and temperature, in addition to degradation, can reduce the estimate of potential production [32].Furthermore, a number of slow processes, such as depletion of seed and bud banks [91], nutrient limitations, excessive run-off, grazing, and fuel-wood collection [92] among other causes, may also contribute, and result in an under estimation of potential vegetation production [32].Sites affected by these are indistinguishable from those at their potential (so precondition (vi) for use of RUE is not met (Table 1)) and the mean rates of change in ΣNDVI gs would underestimate the production expected in response to climate variability (i.e., potential ΣNDVI gs values), reducing the "degradation" signal and overestimating the "greening" signal.This is not to suggest that estimating potential ΣNDVI gs using UQ regression functions is without its own problems; it is still subject to the same errors as OLS because it is also affected by the degraded sites, albeit using a more appropriate statistical model.
The OLS RESTREND models (models A, B, and C) resulted in larger areas with significant positive trends than the UQ based RESTREND models (models D, E, and F) (Table 6), however, in all cases the largest areas had no significant trends (mean of all models 70%), in agreement with other studies (e.g., [28,101]).Despite the differences between the models in the significance of these trends, they all indicate large and spatially coherent areas that "greened" faster than can be accounted for by changes in meteorological conditions (Figure 4) [88,102].Similarly, after removing the effects of rainfall on NDVI, positive trends have been found, for example, over parts of the Senegal, Southern Mali, and Chad and the entire Sahel [28,30,88,[103][104][105]. Explanations of the greening trends in the literature include agricultural intensification, improvements in soil and water conservation techniques, supplementary irrigation, and fertilization, all as a result of increased investment [88], CO 2 fertilization, increased carry-over effects of soil moisture from previous wet years, and increases in seed and bud banks associated with high vegetation productivity in previous years [32,90,102,[105][106][107][108].The present results also detected large parts of Burkina Faso, northern Nigeria, southern Niger, and western Sudan with significant negative trends (Figure 4).Surprisingly, similar analyses (e.g., [105]) have not found this pattern, possibly because different data sets were used.In addition to the frequently quoted effects of excessive cultivation, increases in grazing, etc., suggestions for the negative trends include land abandonment associated with economic migration and civil strife, and transitions to new quasi-stable vegetation composition following the extreme droughts of the 1970s and 1980s [20,27,32,33,43].Even though some disagreement can be expected due to differences between the climate datasets used here and in other studies, and because of differences in the AVHRR data used [105], the lack of agreement over such large areas is surprising.The RESTREND results were compared qualitatively with published case studies of land degradation and rehabilitation in the Sahel ( [12,30,97,98,[100][101][102][103][104][105][106][107][108][109][110]) and by comparison with field observations by experts (e.g., Gray Tappan, 2008 pers.com.).While these comparisons showed favorable agreement (Table 7), they should not be construed as validation results.Validation sensu stricto requires direct measurements of vegetation at appropriate scales over a distributed set of sites.Until such datasets become available, validation of satellite-derived degradation indices at the scales studied here will not be easy.
Analysis of the relation between RESTREND values and population density did not support the notion that higher population density in the Sahel invariably causes reductions in land productivity (Tables 4 and 5).%HANPP, on the other hand, was related to reductions in land productivity (r = −0.55).
It should be noted that the calculation of %HANPP [66] does not account for lateral flows (imports or exports) of NPP-based products.Including these effects may provide a better accounting of the pressures people impose on their local environment.Nevertheless, the relationship between %HANPP and RESTREND was strong enough to suggest that higher demands for NPP-based goods in relation to local NPP production are likely to impoverish local ecosystems [111].
Further examination of the relation of land uses such as livestock production and area of land used in cultivation with the RESTREND values found moderate-weak correlations (Table 4).However, stronger relationships were found between RESTREND and the ratios of both LSU to livestock carrying capacity (LSU/NPP; r = −0.51)and %crop area to mean annual precipitation (%crop/MAP; r = −0.55).While the inverse relationship between RESTREND values and LSU/NPP was expected, the relation with %crop/MAP suggests that the extension of cultivation into marginal lands, not suitable for agriculture, may result in long-term reductions in productivity or degradation [15,80].
A meta-analysis of case studies of land degradation [80] found that, contrary to the theory of single-factor causation [53,112], land degradation in Africa can more often be attributed to multiple factors, and even to remote influences, including changes in agricultural policies such as intensification of livestock production, production of cash crops, and irrigation.Also, the spatial variations in RESTREND values were not only better explained by a multiplicity of land uses but also by local variations in natural resource endowments (Figures 6 and 7).Of the biophysical variables explored, soil bulk density, soil erodibility, and the fraction land area covered by trees were strongly related to degradation of NPP.These variables also enhanced the adverse effects of population and land use pressures (Figures 8 and 9).One possible mechanism is that fuel wood collection, agriculture, and grazing reduce perennial plant cover and simplify the vegetation structure exposing the soil to wind and water erosion [15]; also soil erosion and dispersion rates are higher in landscapes with higher soil bulk density and soil erodibility [113][114][115][116].

Conclusions
Many studies have demonstrated that the return of more favorable climate conditions in the Sahel following the extreme droughts of the 1970s and early 1980s has been accompanied by a net increase in vegetation greenness (e.g., [26,102,103,117]).Yet, the spatial variations in the rates of vegetation recovery can only partially be explained by climate trends [27, 88,118], thus reinvigorating the debate about the influence of anthropogenic land degradation and restoration on vegetation productivity [22,23].The focus of this study was therefore twofold: first, to investigate where the land surface in the Sahel has been greening "faster" (i.e., positive RESTREND), or "slower" (i.e., negative RESTREND) than what would be expected from the trends in climate; and, second, to relate the spatial variations in RESTREND values to land use and human population density.
The results suggest that, over large areas of the Sahel, the average area of insignificant trends was 70%, similar or larger than reported in other studies (e.g., [88]).Overall, in >87% of the area, NPP (vegetation greenness) either exceeded (i.e., positive RESTREND) or did not significantly depart from what is expected from the trends in climate (i.e., insignificant RESTREND).The areas with positive RESTREND were frequently associated with relatively low population and land use pressures.Undoubtedly, there are places where land rehabilitation efforts have increased land productivity-perhaps irrigation, shortened fallow period, erosion control, fertilizer use, CO 2 fertilization (e.g., [20])-but, at the scale of observation used here, there was little evidence to suggest that land rehabilitation or agricultural intensification were adequate explanations of the long-term increases in NPP.The scales of the phenomena and the explanations must match; explanations that do include an increase in water use efficiency caused by CO 2 fertilization, higher nitrogen deposition, higher atmospheric aerosol loadings, or transitions to new quasi-stable vegetation compositions following the extreme droughts of the 1970s and 1980s [43,[119][120][121][122] and, perhaps, non-linear, accelerating responses of vegetation to the changing climate, do fit the scale of the satellite observations.Contrary to findings in similar studies [28,30], we found large (7%-13% of the study area), spatially coherent areas with significant negative trends in production.These areas were found to have high livestock densities relative to their carrying capacity, intensive cultivation, overworked marginal lands, or combinations of these.The results suggest that population and land use pressures have had a measurable impact on vegetation dynamics in some parts of the Sahel during the period 1982-2006.

Figure 1 .
Figure 1.Properties of the models used to estimate potential ΣNDVIgs from the relationship between observed ΣNDVIgs and climate variables.(a) The OLS and UQ regression lines of ΣNDVIgs on precipitation and their prediction intervals (Pred.Int) at the 95% confidence level for a cropland site (3.725°W, 11.525°N);(b) The difference between the OLS and UQ precipitation coefficient values for all sites throughout the Sahel study region; (c) The ability of precipitation (model A), precipitation and its intra-seasonal distribution (model B) and precipitation, specific humidity and temperature (model C) to account for the variations in ΣNDVIgs.SHUM-specific humidity.

Figure 1 .
Figure 1.Properties of the models used to estimate potential ΣNDVI gs from the relationship between observed ΣNDVI gs and climate variables.(a) The OLS and UQ regression lines of ΣNDVI gs on precipitation and their prediction intervals (Pred.Int) at the 95% confidence level for a cropland site (3.725 • W, 11.525 • N); (b) The difference between the OLS and UQ precipitation coefficient values for all sites throughout the Sahel study region; (c) The ability of precipitation (model A), precipitation and its intra-seasonal distribution (model B) and precipitation, specific humidity and temperature (model C) to account for the variations in ΣNDVI gs .SHUM-specific humidity.

Figure 2 .
Figure 2. Potential ΣNDVIgs prediction errors: (a) errors of the OLS regression between ΣNDVIgs and precipitation (model A); Compared with model A are: (b) percentage reduction in potential ΣNDVIgs prediction errors of the OLS regression between ΣNDVIgs and precipitation, specific humidity, and temperature (model B); and (c) percentage reduction in potential ΣNDVIgs prediction errors of the OLS regression between ΣNDVIgs and precipitation, its seasonal distribution variance, and skewness (model C); (d) Frequency distribution of prediction errors for the three models normalized by the range of ΣNDVIgs values (prediction error/maximum ΣNDVIgs-minimum ΣNDVIgs); and (e) frequency distribution of the values in (b,c).The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.

Figure 2 .
Figure 2. Potential ΣNDVI gs prediction errors: (a) errors of the OLS regression between ΣNDVI gs and precipitation (model A); Compared with model A are: (b) percentage reduction in potential ΣNDVI gs prediction errors of the OLS regression between ΣNDVI gs and precipitation, specific humidity, and temperature (model B); and (c) percentage reduction in potential ΣNDVI gs prediction errors of the OLS regression between ΣNDVI gs and precipitation, its seasonal distribution variance, and skewness (model C); (d) Frequency distribution of prediction errors for the three models normalized by the range of ΣNDVI gs values (prediction error/maximum ΣNDVI gs -minimum ΣNDVI gs ); and (e) frequency distribution of the values in (b,c).The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.

Figure 3 .
Figure 3. Temporal trends (slopes) of ΣNDVIgs residuals (observed-potential) regressed over time at four locations in the Sahel.The trends in sites (a,b) are significantly different from zero (p value of the F test <0.05 and their absolute values are greater than their respective uncertainty), whereas the trends for the sites shown in (c,d) have a p values of the F test <0.05, but the slope values are less than their respective uncertainty.

Figure 3 .
Figure 3. Temporal trends (slopes) of ΣNDVI gs residuals (observed-potential) regressed over time at four locations in the Sahel.The trends in sites (a,b) are significantly different from zero (p value of the F test <0.05 and their absolute values are greater than their respective uncertainty), whereas the trends for the sites shown in (c,d) have a p values of the F test <0.05, but the slope values are less than their respective uncertainty.

Figure 4 .
Figure 4. Residual trends and two maps of human land use.(a-f) Trends (slopes) of NDVIgs residuals (observed-potential) over time as obtained from the six RESTREND models (A) through (F); see Table2); (g) % Human Appropriation of Net Primary Production (%HANPP); and (h) proportion of cropland datasets used to explore the relationship between RESTREND value and land use[5,59].The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.

Figure 4 .
Figure 4. Residual trends and two maps of human land use.(a-f) Trends (slopes) of NDVI gs residuals (observed-potential) over time as obtained from the six RESTREND models (A) through (F); see Table2); (g) % Human Appropriation of Net Primary Production (%HANPP); and (h) proportion of cropland datasets used to explore the relationship between RESTREND value and land use[5,59].The red lines from north to south are the 300 mm, 700 mm and 1100 mm rainfall isohyets.

Figure 5 .
Figure 5. Mean RESTREND values (observed-potential) within groupings of: (a) population density (persons/ha); (b) percentage human appropriation of NPP (HANPP%); (c) livestock unit density (units/ha); (d) livestock unit density normalized by site productivity; (e) fraction land area used for crops; and (f) fraction land area used for crops normalized by mean annual precipitation.Filled circles are trends of the residuals where potential NDVI was obtained from OLS multivariate regression between NDVI and precipitation, specific humidity, and temperature.Open circles are trends of the residuals where potential NDVI was obtained from OLS multivariate regression between NDVI and precipitation, its seasonal variance, and skewness.Error bars are ±1 standard deviation around the mean.Dashed lines mark the zero RESTREND values.

Figure 5 .
Figure 5. Mean RESTREND values (observed-potential) within groupings of: (a) population density (persons/ha); (b) percentage human appropriation of NPP (HANPP%); (c) livestock unit density (units/ha); (d) livestock unit density normalized by site productivity; (e) fraction land area used for crops; and (f) fraction land area used for crops normalized by mean annual precipitation.Filled circles are trends of the residuals where potential NDVI was obtained from OLS multivariate regression between NDVI and precipitation, specific humidity, and temperature.Open circles are trends of the residuals where potential NDVI was obtained from OLS multivariate regression between NDVI and precipitation, its seasonal variance, and skewness.Error bars are ±1 standard deviation around the mean.Dashed lines mark the zero RESTREND values.

Figure 6 .
Figure 6.The relationship between significant RESTREND values and four explanatory variables, soil erodibility factor, livestock unit density normalized by site productivity (LSU/NPP), fraction land used for agriculture (cropping density), and population density.(a) biplot of the first and second principal component loadings of a principal component analysis; (b) variable importance values calculated by the Random Forest (RF) regression tree model; (c) comparison between RESTREND values modeled from the NDVIgs time series (x-axis) and RESTREND values predicted by RF analysis (y-axis); and (d) histogram of the differences between the plotted values in (c).Residual trends insignificantly different from zero were excluded.

Figure 6 .
Figure 6.The relationship between significant RESTREND values and four explanatory variables, soil erodibility factor, livestock unit density normalized by site productivity (LSU/NPP), fraction land used for agriculture (cropping density), and population density.(a) biplot of the first and second principal component loadings of a principal component analysis; (b) variable importance values calculated by the Random Forest (RF) regression tree model; (c) comparison between RESTREND values modeled from the NDVI gs time series (x-axis) and RESTREND values predicted by RF analysis (y-axis); and (d) histogram of the differences between the plotted values in (c).Residual trends insignificantly different from zero were excluded.

Figure 7 .
Figure 7.The relationship between significant RESTREND and the three explanatory variables, fraction tree cover (fTree), percentage human appropriation of NPP (%HANPP), and soil bulk density.(a) biplot of the first and second principal component loadings of a principal component analysis; (b) variable importance values calculated by the regression tree model Random Forest (RF); (c) comparison between RESTREND values modeled from the NDVIgs data time series (x-axis) and RESTREND values predicted by RF analysis (y-axis); and (d) histogram of the differences between the plotted values in (c).Residual trends insignificantly different from zero were excluded.

Figure 7 .
Figure 7.The relationship between significant RESTREND and the three explanatory variables, fraction tree cover (fTree), percentage human appropriation of NPP (%HANPP), and soil bulk density.(a) biplot of the first and second principal component loadings of a principal component analysis; (b) variable importance values calculated by the regression tree model Random Forest (RF); (c) comparison between RESTREND values modeled from the NDVI gs data time series (x-axis) and RESTREND values predicted by RF analysis (y-axis); and (d) histogram of the differences between the plotted values in (c).Residual trends insignificantly different from zero were excluded.

Figure 8 .
Figure 8. Pruned regression tree showing the hierarchical relations of RESTREND to land use, population, and soil erodibility.Regression tree r 2 = 0.6 and RMSE = 0.23; LSU/NPP (livestock unit density normalized by site net primary productivity); Cropping density (fraction land area used for crops); S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Figure 9 .
Figure 9. Pruned regression tree showing the hierarchical relations of RESTREND to %HANPP and to soil and land cover properties.Regression tree r 2 = 0.65 and RMSE = 0.21; f Tree-fraction tree cover; %HANPP-percentage human appropriation of NPP; S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Figure 8 .
Figure 8. Pruned regression tree showing the hierarchical relations of RESTREND to land use, population, and soil erodibility.Regression tree r 2 = 0.6 and RMSE = 0.23; LSU/NPP (livestock unit density normalized by site net primary productivity); Cropping density (fraction land area used for crops); S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Figure 8 .
Figure 8. Pruned regression tree showing the hierarchical relations of RESTREND to land use, population, and soil erodibility.Regression tree r 2 = 0.6 and RMSE = 0.23; LSU/NPP (livestock unit density normalized by site net primary productivity); Cropping density (fraction land area used for crops); S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Figure 9 .
Figure 9. Pruned regression tree showing the hierarchical relations of RESTREND to %HANPP and to soil and land cover properties.Regression tree r 2 = 0.65 and RMSE = 0.21; f Tree-fraction tree cover; %HANPP-percentage human appropriation of NPP; S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Figure 9 .
Figure 9. Pruned regression tree showing the hierarchical relations of RESTREND to %HANPP and to soil and land cover properties.Regression tree r 2 = 0.65 and RMSE = 0.21; f Tree-fraction tree cover; %HANPP-percentage human appropriation of NPP; S.V.-node split value; S.D.-standard deviation of values at the node; V.-value at terminal node; N-number of observations at terminal node.

Table 1 .
Preconditions for valid application of Rain Use Efficiency (RUE) for detection of dryland degradation.

Table 2 .
Independent variables used in OLS and UQ regression models to estimate potential ΣNDVIgs values.The mean regression coefficient values and potential ΣNDVIgs prediction errors at the 95% confidence level are the averages of all regression equations estimated for each 3 × 3-pixel grid cell.SHUM-specific humidity; OLS-ordinary least squares; UQ-upper quartile regression; SKEW-skewness of intra-annual, daily precipitation frequency; ppt-precipitation; T-air temperature.

Table 2 .
Independent variables used in OLS and UQ regression models to estimate potential ΣNDVI gs values.The mean regression coefficient values and potential ΣNDVI gs prediction errors at the 95% confidence level are the averages of all regression equations estimated for each 3 × 3-pixel grid cell.SHUM-specific humidity; OLS-ordinary least squares; UQ-upper quartile regression; SKEW-skewness of intra-annual, daily precipitation frequency; ppt-precipitation; T-air temperature.

Table 3 .
Correlation values (r) between RESTREND, population, and land use.The multi-correlation value was estimated from the relation of RESTREND values to Human Appropriation of Net Primary Production (%HANPP), livestock unit density normalized by site net primary productivity (LSU/NPP), and %crop cover/mean annual precipitation (%crop/MAP).Stronger relations are shown in bold.SHUM-specific humidity; OLS-ordinary least squares; UQ-upper quartile regression.

Table 4 .
Spatial variation in RESTREND values correlated with land use (livestock unit density-LSU and cropping density-CD), land use and soil properties, and land use and land cover, using RF regression tree models.LSU/NPP-livestock unit density normalized by site primary productivity; CD/MAP-cropping density normalized by mean annual precipitation.

Table 4 .
Spatial variation in RESTREND values correlated with land use (livestock unit density-LSU and cropping density-CD), land use and soil properties, and land use and land cover, using RF regression tree models.LSU/NPP-livestock unit density normalized by site primary productivity; CD/MAP-cropping density normalized by mean annual precipitation.

Table 5 .
Spatial variation in RESTREND values correlated with %HANPP and soil properties, and %HANPP and land cover, using RF regression tree models.

Table 5 .
Spatial variation in RESTREND values correlated with %HANPP and soil properties, and %HANPP and land cover, using RF regression tree models.

Table 6 .
Percentage land area with significant negative and positive trends.OLS-ordinary least squares; UQ-upper quartile regression.