One Ecosystem :
Research Article
|
Corresponding author: Solen Le Clec'h (solenle@ethz.ch)
Academic editor: Benjamin Burkhard
Received: 30 Jul 2018 | Accepted: 03 Jan 2019 | Published: 31 Jan 2019
© 2019 Solen Le Clec'h, Simon Dufour, Janic Bucheli, Michel Grimaldi, Robert Huber, Izildinha Miranda, Danielle Mitja, Luiz Silva Costa, Johan Oszwald
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Le Clec'h S, Dufour S, Bucheli J, Grimaldi M, Huber R, Miranda I, Mitja D, Silva Costa L, Oszwald J (2019) Uncertainty in ecosystem services maps: the case of carbon stocks in the Brazilian Amazon forest using regression analysis. One Ecosystem 4: e28720. https://doi.org/10.3897/oneeco.4.e28720
|
|
Ecosystem Service (ES) mapping has become a key tool in scientific assessments of human-nature interactions and is being increasingly used in environmental planning and policy-making. However, the associated epistemic uncertainty underlying these maps often is not systematically considered. This paper proposes a basic procedure to present areas with lower statistical reliability in a map of an ES indicator, the vegetation carbon stock, when extrapolating field data to larger case study regions. To illustrate our approach, we use regression analyses to model the spatial distribution of vegetation carbon stock in the Brazilian Amazon forest in the State of Pará. In our analysis, we used field data measurements for the carbon stock in three study sites as the response variable and various land characteristics derived from remote sensing as explanatory variables for the ES indicator. We performed regression methods to map the carbon stocks and calculated three indicators of reliability: RMSE-Root-mean-square-error, R2-coefficient of determination - from an out-of-sample validation and prediction intervals. We obtained a map of carbon stocks and made explicit its associated uncertainty using a general indicator of reliability and a map presenting the areas where our prediction is the most uncertain. Finally, we highlighted the role of environmental factors on the range of uncertainty. The results have two implications. (1) Mapping prediction interval indicates areas where the map's reliability is the highest. This information increases the usefulness of ES maps in environmental planning and governance. (2) In the case of the studied indicator, the reliability of our prediction is very dependent on land cover type, on the site location and its biophysical, socioeconomic and political characteristics. A better understanding of the relationship between carbon stock and land-use classes would increase the reliability of the maps. Results of our analysis help to direct future research and fieldwork and to prevent decision-making based on unreliable maps.
Deforestation; ecosystem services; prediction intervals; reliability; statistical modelling; variability
Ecosystem services (ES) have progressively become an important concept in environmental planning and policy-making to bridge the science – policy interface in the management of ecosystems (
The importance of uncertainty in the use and analysis of spatial data has long been recognised in land-use and landcover change mapping (e.g.
Uncertainty is complex and there are many definitions or typologies of uncertainty in ES analyses (
The objective of this research is to describe a simple approach to assess and spatially represent uncertainties associated with the extrapolation of measured field data using regression analysis to map an ES indicator (vegetation carbon stock). Our results express the degree of certainty that we have about our ES map and the confidence that policy-makers can have in the map. To this end, we firstly used field data measurements for vegetation carbon stock in the Brazilian Amazon forest as a response variable and various land characteristics derived from remote sensing as potential explanatory factors of the ES indicator. We implemented the mapping techniques from earlier works (
Site description
We estimated and mapped uncertainty related to ES maps using the case of the Brazilian Amazon forest, a global hotspot of ES provision (
Within Pará, we conducted field measures of ES within three local study sites that are representative of the regional variability in socio-economics, deforestation temporalities and ES change (Fig.
In a deforestation front context, because of the lack of law, public policies and environmental management, the study of ES is highly relevant. It allows us a better understanding of the impacts of deforestation and cultivation on the environment, in other words to evaluate the impacts of the past and current public policies (or their absence) on the ecosystems.
Data
We used two different datasets to apply predictive statistical methodologies for the ES indicator: field data related to the ES indicator (response variable) and remote sensing data (explanatory variables – Table
Description of the data used in this study.The data constitutes the input of the statistical model.
Variable name |
Source |
Description |
Unit/range |
|
Response variable (ES indicator) |
Vegetation carbon stock |
Field measurement |
Aboveground dry biomass of trees, bushes and herbaceous plants |
Mg/ha |
Explanatory variables (ES potential drivers) |
Land cover |
Landsat TM (30x30m) |
Supervised maximum-likelihood classifications of six land-cover classes |
6 modalities |
Historical trajectory of land cover |
Classes of land-use trajectories (Oszwald et al. 2012), from a homogeneous forest structure (class 1) to an agricultural dynamic of extensive breeding (class 5) |
5 modalities |
||
NDVI |
Vegetation density (index) |
-1;1 |
||
NDWI |
Water content into plants (index) |
-1;1 |
||
Elevation |
DEM Aster (30mx30m) |
Elevation at every point |
m |
|
Slope |
Altitude difference between two adjacent pixels |
% |
||
Synthesis of topography |
Characterisation of the topographic context |
4 modalities |
||
Distance to water |
Buffers around the rivers |
5 modalities |
||
Site |
General location |
3 modalities |
Field data: carbon stocks
According to the definition of ES proposed by
The carbon stock was estimated using a factor of 0.5 (
Remote sensing data
We built and applied linear regression to extrapolate and map the ES indicator, using the plot-level measures and local high-resolution satellite imagery (Table
We used remote-sensing data to characterise the land-cover of the three study sites for 2007. A Landsat TM image from the dry season (30 m spatial resolution) was used to build a supervised classification by maximum likelihood, to calculate two vegetation indexes (NDVI and NDWI) and to determine a historical trajectory of land-cover (
Data also provided information about the elevation (in metres) at every point. Slopes synthesised the altitude difference between two adjacent pixels and are provided as a percentage. These two variables (elevation and slope) are quantitative and are treated as continuous raw data. The "topography" variable corresponds to a synthetic characterisation of the topographic context comprising four modalities: bottom of valleys, hilltops, zones of steep slopes and zones of low slopes. Finally, we deduced the hydrographic network from the DEM which was used to determine a distance to the rivers (0 to 100 m, 100 to 200 m, 200 to 300 m, 300 to 500 m and more than 500 m).
We also used a variable, named “Site” that corresponds to the identity of the study site to which each pixel belongs. This variable aims to (1) estimate the spatial auto-correlation of the sampling points and (2) take into account the inter-sites variability, due to homogeneous biophysical conditions and socioeconomic characteristics within each location.
Statistical approach
We aimed to evaluate and map the confidence we have in our prediction, as a way to represent the uncertainty related to the ES map. We based our approach on the implementation of statistical methodologies that link field (ES indicator) and remote sensing (explanatory) data. These statistical methodologies are used to (1) extrapolate field data using remote sensing to the three study sites. They also (2) give us information about the reliability of the resulting maps, through a general and a spatialised indicator (Fig.
Regression methods represent one of the possible statistical approaches to map ES indicators from field and remote sensing data (
We computed a linear model on the 135 sampling points. The model linked the ES indicator (carbon stocks - field data) and remote sensing data (related to the site, land cover and topography – Fig.
Outputs of the final linear model. Acronyms: SitePR: Palmares II and Land Covern: class n of Land Cover (F: Forest; BF: Burned Forest; JC: Jucuira-Capoeira-Fallow lands; PL: Pasture with tree; CP: Clean Pasture and BS: Bare Soil).
Linear model: lm(formula = VCSt ~ SitePR + LC) Residuals: |
||||
Min |
1Q |
Median |
3Q |
Max |
-103.41 |
-27.34 |
-10.23 |
19.96 |
143.19 |
Coefficients: | ||||
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
Intercept |
161.57 |
13.474 |
11.99 |
< 2e-16 *** |
SitePR |
-37.77 |
9.82 |
-3.85 |
0.000202 *** |
Land CoverBF |
60.64 |
16.51 |
3.67 |
0.000375 *** |
Land CoverJC |
-89.37 |
15.33 |
-5.83 |
5.86e-08 *** |
Land CoverPT |
-143.46 |
16.78 |
-8.55 |
9.07e-14 *** |
Land CoverCP |
-143.06 |
16.65 |
-8.592 |
7.20e-14 *** |
Land CoverBS |
-131.70 |
17.58 |
-7.49 |
1.99e-11 *** |
Significativity codes: 0 ‘***’ Residual standard error: 47.99 on 108 degrees of freedom Multiple R2: 0.75, Adjusted R2: 0.73 F-statistic: 52.62 on 6 and 108 DF, p-value: < 2.2e-16 |
We used the final model to extrapolate the vegetation carbon stocks to the whole study sites. To do so, the final model, trained on the 135 sampling points, was then applied to all the study sites to predict new carbon stocks, based on the land-cover data and the typology of the study sites (for more information, see
In the second step, we used the same final model to estimate a simple indicator that gives information on the confidence we have in our prediction. In linear regression, one way to associate confidence/uncertainty to the prediction is the calculation of the prediction intervals on predictions (
We proposed an index based on width of 95% prediction intervals. To do so, we calculated the difference between the upper and lower bounds of prediction confidence intervals. A high index characterised areas with high uncertainty around the prediction (up to 90 MgC/ha around the prediction). For each predicted value (pixel), we thus applied the final linear model to get (1) an estimated carbon stock and (2) the prediction interval around the predicted value. As we predicted an ES value for each pixel of the study sites, we also obtained an uncertainty index for each pixel. Thus, we can propose a spatial representation of the uncertainty. Finally, we represented the variations of the index within the two explanatory variables of the final model: the land cover and the site classifications.
Maps of carbon stocks and their global reliability
The linear model based on the land-cover classification and the site classification was used to map vegetation carbon stock. The maps of vegetation carbon stock show the influence of land-cover changes on ES supply (Fig.
Mapping uncertainty associated with the ES map
We mapped the uncertainty index related to the application of a statistical method to predict values of an ES indicator for the vegetation carbon stock. The resulting map gives an overview of the areas where the map is and is not reliable. High prediction intervals express low confidence and can be associated with our inability to reliably predict carbon stocks, whereas high prediction intervals express our ability to estimate the vegetation carbon stocks with much greater certainty.
The index of uncertainty takes high values in highly anthropised areas (grazed landscapes and bare soils). Grazed grasslands have very heterogeneous profiles because they can be declined from bare soil to pasture with trees. Moreover, forest areas are associated with high carbon stock and quite high variability. Forests of the three study sites are at different stages of degradation and carbon stock is therefore relatively heterogeneous within these forests. Variability in transition areas can be explained by the nature of the class itself. Transition areas consist of secondary vegetation and fallow lands. This class is relatively homogeneous in Maçaranduba (Fig.
Role of land cover and location
We analysed how the uncertainty index varies with the two explanatory variables of the final linear model: the land cover and the site classifications. This analysis helped us to better understand the level of uncertainty related to our assessments. To do so, we plotted the prediction intervals (1) within the six land-cover classes and (2) within the three study sites. Such analyses highlight the uncertainty related to the explanatory data that our knowledge of the study sites (socioeconomic, political and/or biophysical contexts and conditions) can explain. The range of the prediction intervals modelled, based on the final model (Table
A map is a generalisation or a schematisation of reality (
We proposed an exploratory approach to assess and communicate epistemic uncertainties related to ES mapping and valuation and thus specifically addressed a lack in the representation of errors inherent to the extrapolation of point-based measurements to produce empirical based ES maps. It is only one of the uncertainties produced in an ES assessment (
Overall, the regression model provided a reliable map of carbon stocks that allowed us to highlight carbon hotspots and, at the same time, to identify areas where this prediction of carbon stocks is highly uncertain. The results showed that prediction intervals for bare soils and clean pastures had higher mean values but also a wider range of values and thus emerged as highly variable classes. The map’s trustworthiness is thus partially a consequence of the uncertainty related to the explanatory data underlying these classes. From a scientific perspective, these findings have three implications. First, a better understanding of the drivers of ES provision could help to reduce the uncertainty stemming from the variability of the provision of ES per land-cover class. This aspect is very critical in the Amazon rainforest where the slowdown of deforestation rates leads to an increase in forest degradation. The consequences of forest degradation on ES provision in these areas are still largely unknown. Secondly, the land-cover classification should account for as many different classes as possible to reduce intra-class variability. This underlines the importance of studies on local scales with detailed information on land use/land cover to complement large scale maps with less accuracy in land-use classes (
The use of prediction intervals to assess epistemic uncertainties in ES maps has also certain drawbacks. Not all methodologies allow a feedback between data and ES maps. The indicator proposed here, can only be applied in the case of certain statistical procedures. Even for some statistics, such as regression trees (CART algorithm -
Uncertainty can become particularly important when maps aim to support policy development, for example, when they are used to analyse trade-offs and synergies (
Uncertainties are inherent and unavoidable in the assessment of environmental management in general and in particular in ES mapping. They exist in different stages of the assessments and some cannot integrally be reduced. We used here a linear model to describe the method because prediction intervals can be directly calculated. This approach could be extended to other methods, especially by the use of bootstrapping. However, their identification, acknowledgement and explanation should, at least, be systematic, to raise awareness and to determine the optimal use(s) of the maps, especially in the context of environmental policy-making and governance (
This research was funded by the Institut des Amériques and by the French Agence Nationale de la Recherche through two grants: ANR AMAZ, coordinated by P. Lavelle and ANR AGES, coordinated by X. Arnauld de Sartre and by the Brazilian Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), also through two Grants: Processes 484990/2007-1 and 490649/2006-8.