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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

Changing trends in ecosystem productivity can be quantified using satellite observations of Normalized Difference Vegetation Index (NDVI). However, the estimation of trends from NDVI time series differs substantially depending on analyzed satellite dataset, the corresponding spatiotemporal resolution, and the applied statistical method. Here we compare the performance of a wide range of trend estimation methods and demonstrate that performance decreases with increasing inter-annual variability in the NDVI time series. Trend slope estimates based on annual aggregated time series or based on a seasonal-trend model show better performances than methods that remove the seasonal cycle of the time series. A breakpoint detection analysis reveals that an overestimation of breakpoints in NDVI trends can result in wrong or even opposite trend estimates. Based on our results, we give practical recommendations for the application of trend methods on long-term NDVI time series. Particularly, we apply and compare different methods on NDVI time series in Alaska, where both greening and browning trends have been previously observed. Here, the multi-method uncertainty of NDVI trends is quantified through the application of the different trend estimation methods. Our results indicate that greening NDVI trends in Alaska are more spatially and temporally prevalent than browning trends. We also show that detected breakpoints in NDVI trends tend to coincide with large fires. Overall, our analyses demonstrate that seasonal trend methods need to be improved against inter-annual variability to quantify changing trends in ecosystem productivity with higher accuracy.

Climate change will likely change biome distributions, ecosystem productivity and forest carbon stocks [

Indeed, positive NDVI trends (“greening”) occur in the high latitudes [

The estimation of trends depends on the length, temporal and spatial resolution of the time series, the quality of the measured data [

NDVI trends are not always monotonic but can change. A positive trend can change for example into a negative one and

Breakpoints in NDVI time series are related to different effects caused by inter-annual variability. Inter-annual variability of NDVI time series can be caused by (1) artefacts of a harmonized dataset from different sensors, (2) meteorological distortions like clouds or snow cover and (3) environmental processes like effects of year-to-year variations in weather conditions on plant activity or ecosystem disturbances. Inter-annual variability affects the annual mean (e.g., reduction of NDVI because of a disturbance), seasonality (e.g., longer growing season because of prolonged warmer temperatures) as well as short-term patterns (e.g., unusual snowfall in a summer month) of NDVI time series. The aggregation of NDVI time series to mean annual values integrates these different effects which, despite the loss in temporal detail, allow us to define and quantify inter-annual variability as the standard-deviation of mean annual NDVI values.

The purpose of this study is to evaluate the performance of different methods for detecting trends and trend breakpoints in long-term NDVI time series. Previous studies have used different trend and breakpoint analysis methods on NDVI time series without or with limited demonstration of its methodological robustness [

The GIMMS NDVI3g dataset (third generation GIMMS NDVI) is a newly available long-term NDVI dataset and was derived from NOAA AVHRR data (National Oceanic and Atmospheric Administration, Advanced Very High Resolution Radiometer) [

We further pre-processed the GIMMS NDVI3g dataset for the specific requirements of our study. The year 1981 was excluded from our analysis in order to analyse only years with full data coverage. Especially in high-latitude regions NDVI observations are often affected from snow or cloud cover. Such NDVI values are flagged as “snow” or “interpolated” in the GIMMS NDVI3g dataset [

The breakpoint detection algorithm as described by Bai and Perron [

The breakpoint detection algorithm was used based on recommendations of Bai and Perron [

Method AAT estimates trends and trend changes on annual aggregated time series. The seasonal NDVI time series is first aggregated to annual values. The annual mean, growing season mean or annual peak NDVI can be calculated to aggregate the seasonal NDVI time series to annual values. Mean annual NDVI was used for the factorial experiment based on surrogate time series. Breakpoints are estimated on the annual time series using the method of Bai and Perron [

The trend and breakpoint estimation in method STM (season-trend model) is based on the classical additive decomposition model and we followed the formulation used in BFAST [_{1} is the intercept and _{2} the slope of the trend, _{1}, _{2} are estimated using ordinary least squares (OLS) regression whereby the derived time series segments are considered as categorical interaction term with the trend slope _{2}. The significance of the trend in each segment is estimated from a t-test on the interaction parameter of the regression between time series segment and _{2}.

Methods MAC (mean annual cycle) and SSA (annual cycle based on singular spectrum analysis) estimate trends on seasonal-adjusted time series, which is the full-resolution time series with removed seasonality. The seasonal-adjusted time series

The slope of the trend _{2} is estimated using OLS from the seasonal-adjusted time series:

Breakpoints are estimated on

The seasonal cycle (or annual cycle)

An important aspect of the experimental design was the prescription of time series properties in the surrogate (artificial) data that were observed in the NDVI datasets. In order to create surrogate time series that mimic the full range of possible real world data, the mean, trend, inter-annual variability, seasonality and short-term variability was estimated for all observed NDVI time series of Alaska in a simple step-wise approach (

The mean of each NDVI time series was calculated.

In the second step, monthly values were averaged to annual values and the trend was calculated according to method AAT but without computing breakpoints. Hence, the slope of the annual NDVI trend over the full length of the time series was estimated.

To estimate the inter-annual variability, the standard deviation and range of the annual anomalies were calculated. The mean of the time series and the derived trend component from step (2), were subtracted from the annual values to derive the trend-removed and mean-centred annual values (annual anomalies). If the trend slope was not significant (p > 0.05), only the mean was subtracted. The standard deviation and the range of the annual anomalies were computed as measures for the inter-annual variability of the time series.

In the next step, the range of the seasonal cycle was estimated. The mean, the trend component and the annual anomalies were subtracted from the original time series to calculate a detrended, centered and for annual anomalies adjusted time series. Based on this time series the seasonal cycle was estimated as the mean seasonal cycle and the range was computed.

In the last step, the standard deviation and the range of the short-term anomalies were computed. Short-term anomalies were computed by subtracting the mean, the trend component, the annual anomalies and the mean seasonal cycle from the original time series. The result is the remainder time series component. The standard deviation of the remainder time series component is a measure of short-term variability.

All the described time series properties were estimated on the full NDVI dataset including all observations (

Surrogate time series were simulated based on addition of different time series components that were estimated from observed time series properties:

Trend: Time series with strong and weak positive, strong and weak negative and without a trend were created. Different magnitudes of trend slopes were derived from the 1% percentile of the observed distribution of trend slopes (strong decrease), 25% percentile (weak decrease), median (no trend), 75% percentile (weak increase) and 99% percentile (strong increase), respectively.

Inter-annual variability: Time series with low, medium and high inter-annual variability were created based on normal-distributed random values with zero mean and a standard deviation according to the 1%, 50% and 99% percentiles of the observed distribution of the standard deviation of annual anomalies. Values outside the observed ranges of inter-annual variability were set to the minimum or maximum of the observed distribution, respectively.

Seasonality: Seasonal cycles based on a harmonic model with low, medium, and high amplitudes were created according to the observed 1%, 50% and 99% percentiles of the distribution of seasonal ranges.

Short-term variability: Different levels of short-term variability were created based on normal-distributed random values with zero mean and a standard deviation according to the 1%, 50% and 99% percentiles of the observed distribution of the standard deviation of remainder time series values.

To introduce trend changes in these surrogate time series, trend components with one and two breakpoints as well as gradual or abrupt changes were created. In case of one breakpoint, the break was introduced 120 months after the beginning of the time series and in case of two breakpoints after 107 and 215 months, respectively. That means one time series can have one to three time series segments with a length of 360 months (30 years) in case of no breakpoint, 120 and 241 months in case of one breakpoint, respectively, and 107, 107 and 146 months in case of two breakpoints, respectively. The type of trend change was considered as an additional factor, whereby gradual change and abrupt changes were distinguished. A gradual change is a change between two trend segments, for which the last value of the trend component in the first segment equals the first value of the following trend segment (

Type of trend and number of breakpoints/segments (maximum 2 breakpoints = maximum 3 segments per time series with positive, negative or no trend = 27 possibilities),

Trend magnitude (weak, strong),

Inter-annual variability (low, medium, high),

Short-term variability (low, medium, high),

Type of trend change (gradual, abrupt) and

Range of seasonal cycle (low, medium, high).

For each combination of these factors one surrogate time series was created. Because some combination are physically not possible (e.g., abrupt or gradual change but 0 breakpoints), in total 1377 surrogate time series were created.

To evaluate the performance of the methods regarding the estimated breakpoints, the difference in number and timing of breakpoints were compared. The difference between the estimated number of breakpoints and the number of real breakpoints was calculated. The number of real breakpoints is the amount of breakpoints that was used to simulate the surrogate time series.

The timing of an estimated breakpoint was compared against the timing of the real breakpoint. For each estimated breakpoint the nearest real breakpoint was selected and the absolute temporal difference (in months) between them was calculated. If the difference is larger than five years the real breakpoint was set as undetected.

In order to evaluate the direction and significance of an estimated trend, estimated trends were compared with the real trend in a trend segment of the simulated time series. The slope and p-value of the real trend was calculated for each method based on the known real breakpoints and time series segments. To compare direction and significance of trends, trend slopes and p-values of real and estimated trends in a time series segment were classified in six trend classes:

N3: significant negative trend (slope < 0 and p ≤ 0.05)

N2: non-significant negative trend (slope < 0 and 0.05 < p ≤ 0.1)

N1: no trend with negative tendency (slope < 0 and p > 0.1)

P1: no trend with positive tendency (slope > 0 and p > 0.1)

P2: non-significant positive trend (slope > 0 and 0.05 < p ≤ 0.1)

P3: significant positive trend (slope > 0 and p ≤ 0.05).

Confusion matrices of estimated and prior trend classes were computed for each method in order to evaluate the accuracy of the methods for trend estimation. Confusion matrices (alternatively called contingency table or error matrix) are standard tools to compare errors between two classifications [

The overall performance of a method was quantified by comparing the estimated with the real trend component (

This formulation involves both an effect of the estimated trend and the estimated breakpoints. An analysis-of-variance (ANOVA) was calculated for the RMSE in order to identify the factors that explain the highest fraction of the RMSE. Trend magnitude, inter-annual variability, seasonality, short-term variability, type of trend change, number of real breakpoints and method as well as their second-order interactions were used as explanatory variables in the ANOVA.

All trend and breakpoint methods were applied to real NDVI time series of Alaska and parts of Yukon to assess differences between methods based on real data. The application of the four methods (AAT, STM, MAC, SSA) allows creating a multi-method ensemble of NDVI trend estimates. As many NDVI observations in northern regions are affected from snow, clouds or other distortions, the use of such poor quality observations causes additional uncertainties in NDVI trend estimates. To account for the effect of snow-affected observation, all methods were applied on the NDVI time series with all observations (“all”) and on the NDVI time series excluding snow-affected values (“ex”) (see Section 2.1). Additionally, method AAT was applied on the annual peak NDVI (defined as the annual quantile 0.9) to analyse trends (called AAT-peak) because vegetation growth in high-latitude ecosystems is usually limited to the peak production period. This setup of trend methods on the real dataset resulted in nine trend and breakpoint estimates for Alaska (AAT-all, AAT-ex, AAT-peak, STM-all, STM-ex, MAC-all, MAC-ex, SSA-all, SSA-ex). From all the nine trend estimates, the ensemble mean and standard deviation of the number of detected breakpoints, of the duration of greening and browning trends and of the trend slope were calculated. The ensemble mean NDVI slope _{m}

Time series segments with a length _{m}

Additional datasets were used to assess the plausibility of detected breakpoints. Fire perimeter observations from the Alaskan Large Fire Database [

To simulate surrogate time series, statistical distributions of NDVI mean, trend, seasonality, inter-annual and short-term variability were computed from observed NDVI time series in Alaska (

To evaluate the performance of the methods to detect breakpoints in trends, the real and estimated breakpoints were compared. For this purpose, the difference between the estimated and real number of breakpoints was calculated and analysed grouped by methods and factors (

Furthermore, the temporal difference between a detected and the closest real breakpoint was calculated, to evaluate the performance of methods regarding the timing of breakpoints (

In order to evaluate if methods detect the correct trends, the direction and significance of estimated trends were compared against the direction and significance of real trends in a time series segment (

Confusion matrices were calculated to evaluate the accuracy of trend classes based on the direction and significance of a trend. Method AAT had usually higher class accuracies as well as a higher total accuracy (37.6%) and Kappa coefficient (K = 0.25) than other methods (

To quantify the overall error of breakpoint and trend detection, the root mean square error (RMSE) between the estimated and real trend component was computed. The distribution of RMSE for the different experimental factors and methods is shown in

The contribution of different factors to the error between estimated and real trend component was analysed by an analysis-of-variance (

To compare breakpoint and trend estimates of the different methods under real conditions, all methods were applied to GIMMS NDVI3g time series of Alaska and the number and timing of breakpoints as well as the duration of significant greening and browning trends were calculated (

The correct timing of breakpoints does not depend on the temporal resolution of the time series but on how full-temporal resolution methods deal with seasonality. Two types of temporal resolution of NDVI time series were explored in this study: Method AAT makes use of a low temporal resolution based on annual aggregated data and methods STM, MAC and SSA were using a monthly temporal resolution of the time series. A more accurate detection of breakpoints was expected if a method uses the full temporal resolution than annual aggregated data. Nevertheless, the annual aggregation approach (method AAT) compared well in the timing of breakpoints like one full-temporal resolution method (method STM) although it largely under-estimated the number of breakpoints. Although the other full-temporal resolution methods (methods MAC and SSA) detected more often the right number of breakpoints, they had larger errors in the timing of these breakpoints (

The temporal resolution of the time series affects the estimation of the trend significance. The major problem of using annual aggregated data rather than full-resolution time series is the reduction in the number of observations. This involves an underestimation of the significance of the trend [

The performance of the four methods to estimate trends is lower in time series with breakpoints. All methods estimate trends with a lower error in case of simple time series with no breakpoints or in case of gradual than abrupt changes (

The capability to estimate trends and breakpoints depends mostly on the robustness of a method against inter-annual variability (

However, we have to be cautionary in the assessment of the effect of inter-annual variability on the method performance: We assumed that the inter-annual variability as well as the short-term variability are independent,

Alaska is of special interest for the analysis of trend change detection methods because previous studies reported greening NDVI trends in tundra ecosystems of the Alaska North Slope as well as browning trends in the Alaska boreal forests [

To evaluate the plausibility of detected breakpoints in NDVI time series of Alaska, the temporal dynamics and spatial patterns of breakpoints were compared against quality flags of the GIMMS NDVI3g dataset, temperature and precipitation anomalies as well as burnt areas from the Alaskan Large Fire Database (

Based on our results we want to summarize advantages and limitations of the methods and give recommendations for practical applications of trend and breakpoint detection methods on long-term NDVI time series. All tested methods offer advantages but involve also different limitations for trend and breakpoint estimation. Removing a mean annual cycle from seasonal time series (method MAC) in order to calculate trends is an often applied method. However, even if this trend analysis on seasonal-adjusted time series had the highest number of correct detected breakpoints, it involves also the highest number of false positive detected breakpoints and had a low overall performance for trend and breakpoint detection. The method that removes a modulated annual cycle as detected by singular spectrum analysis (method SSA) allows distinguishing and quantifying changes that are caused by changes in seasonality or caused by the long-term NDVI trend. Although this method resulted in a high proportion of correct detected breakpoints, it involves a high number of false positive detected breakpoints as method MAC. Additionally, the de-seasonalisation by a modulated annual cycle can remove the inter-annual variability that is related to trends and results in a low overall performance of this method. Trend and breakpoint estimation based on a season-trend model (method STM) quantifies trends while taking into account the seasonality and noise of the NDVI time series. Thus, it allows detecting, distinguishing and quantifying changes in the phenological cycle as well as in the long-term NDVI trend [

Based on different advantages and limitations of all methods, we recommend using method AAT on mean growing season or peak NDVI for regions where the time series are often affected by distortions. If the seasonal NDVI time series values outside the peak NDVI period are credible, the calculation of a multi-method ensemble based on full time series could help to detect robust trends and breakpoints assuming that the agreement of multiple methods is more reliable than a single method. The later approach allows not only to detect trends but also to quantify the uncertainty of the trend estimate based on the choice of the trend method. Breakpoints can be considered as more robust if they were detected by multiple methods. Nevertheless the environmental plausibility of detected breakpoints needs to be assessed. Breakpoints with abrupt changes,

As the detection of breakpoints causes additional uncertainties in trend estimates, the purpose of the breakpoint detection in analysis of NDVI trends needs to be clearly defined: Are trends or trend changes (breakpoints) in the focus of a study? Although the detection of breakpoints offer the potential to detect disturbances in NDVI time series, trend changes and trends in sub-segments of the NDVI time series, a false detection of non-existing breakpoints can result in wrong or even opposite NDVI trend estimates.

Inter-annual variability is the most important factor for the performance of methods to detect trends and breakpoints in NDVI time series. Main sources for inter-annual variability in NDVI time series are (1) contaminants like insufficient pre-processed data or insufficient harmonized multi-sensor observations, (2) meteorological distortions like clouds, dust, aerosols or snow cover and (3) environmental processes like climate variability, disturbances and land cover changes with associated changes in ecosystem structure and productivity. Usually, only the later source of inter-annual variability is of interest in NDVI time series analyses. Users of long-term NDVI datasets rely on the pre-processing and harmonization of multi-sensor observations performed in all conscience by dataset providers. Meteorological distortions can be excluded from analyses by excluding NDVI observations that are flagged as snow or poor quality; by aggregating the bi-monthly GIMMS NDVI3g dataset to monthly temporal resolution; or by analysing only annual peak NDVI observations. As snow cover and clouds have low NDVI values, an extended snow cover can likely cause a detection of weaker NDVI greening or even the detection of browning trends. Thus, the use or non-use of snow-affected and low quality NDVI observations directly affects the inter-annual variability of the NDVI time series and such NDVI values should be excluded from trend and breakpoint analyses.

We demonstrated that increasing inter-annual variability in Normalized Difference Vegetation Index (NDVI) time series decreases the performance of methods to detect trends and trend changes in long-term NDVI time series. Trend estimation based on annual aggregated NDVI time series and the season-trend method had good overall performances. Hence, in order to detect trend changes in NDVI time series with higher precision and accuracy, one needs to improve methods that work on the full temporal resolution time series regarding the robustness against inter-annual variability. Inter-annual variability of NDVI time series can be caused by artefacts from the harmonization of a dataset from different sensors, meteorological distortions like clouds or snow and environmental processes such as climate patterns or disturbances. As a consequence, snow-affected NDVI observation or observations with poor quality need to be excluded from trend and breakpoints analyses as the performance of trend and breakpoint estimation methods decreases with increasing inter-annual variability. Methods can detect wrong or even opposite NDVI trends if they detect breakpoints in time series that have no breakpoints. Nevertheless, the detection of breakpoints offers the potential to detect trend changes or disturbances in NDVI time series.

We evaluated for the first time different methods to detect trends and trend changes in newly available 30 year GIMMS NDVI3g time series. Future studies of trends and breakpoints in long-term NDVI time series should assess the plausibility of detected breakpoints against multi-method ensemble estimates of breakpoints, quality flags of the NDVI time series and further environmental data streams, in order to prevent a detection of wrong NDVI trends.

We thank Compton Tucker, Jorge Pinzon, Ranga Myneni and the GIMMS group for producing and providing the GIMMS NDVI3g dataset. We thank Martin Jung for his comments on this work. We are very thankful to the comments from six anonymous reviewers that helped improving the quality of the manuscript.

We thank the community of the R statistical software for providing a wealth of functionality. The methods described in this article are available as R package under the GNU General Public License on

M.F. received funding from the Max Planck Institute for Biogeochemistry and from the European Commission’s 7th Framework Programme project CARBONES (grant agreement 242316). N.C. was supported by the European Commission’s 7th Framework Program project Carbo-Extreme (grant agreement 226701). J.V. was supported by a Marie-Curie IRG grant of the European Commission’s 7th Framework Program (grant agreement 268423). M.M. was supported by the European Commission’s 7th Framework Program project GEOCARBON (grant agreement 283080). C.N. was supported by NASA’s Terrestrial Ecology and Carbon Cycle Science Programs (grant agreement NNH07ZDA001N-CARBON). M.F conducted this work under the International Max Planck Research School for Global Biogeochemical Cycles.

The authors declare no conflict of interest.

Estimated time series components for a random-selected example grid cell in central Alaska (3*3 grid cells averaged around central pixel 146.424°W, 64.762°N). The upper panel shows the original Normalized Difference Vegetation Index (NDVI) time series with its mean value (red line). The next panels show the estimated trend, inter-annual variability (IAV) (

Spatial and statistical distributions of NDVI time series properties in Alaska and time series components of the simulated NDVI time series. The left panel shows from top to bottom maps of the following time series properties: mean annual NDVI, slope of the annual trend (ΔNDVI/year), standard deviation of the inter-annual variability (iav), range of the seasonal cycle (seas), and the standard deviation of the remainder component (rem). The middle panel shows the statistical distribution of these properties, respectively. The right panel shows examples of the respective surrogate time series components.

Examples of simulated time series with different components of trend, IAV, seasonal and remainder referring to the simulated trend, inter-annual variability, seasonal and remainder time series components, respectively. The sum of these time series components gives the total simulated surrogate NDVI time series (upper panel). Left: time series with one breakpoint and gradual change (e.g., caused by gradual changes in environmental conditions), no trend in the first segment and decreasing trend in the second segment, medium inter-annual variability, medium seasonality and medium short-term variability. Right: Time series with one breakpoint and abrupt change (e.g., caused by a few years with exceptional favourable growing conditions), increasing trend in first segment and decreasing trend in second segment, high inter-annual variability, medium seasonality and low short-term variability.

Frequencies of differences between real and estimated number of breakpoints for the different methods from all experiments (blue indicates underestimation, red overestimation of the number of real breakpoints). (

Distribution of the temporal absolute difference between real and estimated breakpoints. (

Comparison of real and estimated slopes from different methods, all time series segments and all experiments. Slopes are coloured blue if both real and estimated slopes are not significant, green if only the real or estimated slope was significant and red if both slopes were significant (0.95 significance level).

Distribution of the root mean square error (RMSE) between real and estimated trend component for the different methods from all experiments. (

Ensemble of breakpoint and trend estimates from all methods in Alaska. AAT, STM, MAC and SSA are the four applied trend methods. ‘all’ indicates that all NDVI values were used (

Comparison of detected breakpoints with temporal fire and climate patterns in Alaska. (

Comparison of detected breakpoints of the year 2004 from four different methods with 2004 burnt areas and

Normalized confusion matrices of estimated and real trend classes for each method. N3: significant negative trend, N2: non-significant negative trend, N1: no trend with negative tendency, P1: no trend with positive tendency, P2: non-significant positive trend, P3: significant positive trend. ToAcc: total normalized accuracy, Kappa: Kappa coefficient.

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Est.N3 | 55.24 | 11.18 | 15.57 | 8.44 | 5.95 | 3.62 | 100.00 |

Est.N2 | 12.48 | 43.27 | 26.76 | 11.11 | 0.00 | 6.38 | 100.00 |

Est.N1 | 13.27 | 14.55 | 24.55 | 17.46 | 17.74 | 12.42 | 100.00 |

Est.P1 | 10.37 | 10.57 | 15.29 | 24.43 | 24.85 | 14.49 | 100.00 |

Est.P2 | 5.54 | 13.72 | 11.98 | 22.01 | 31.01 | 15.74 | 100.00 |

Est.P3 | 3.09 | 6.70 | 5.85 | 16.56 | 20.45 | 47.34 | 100.00 |

Sum | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 600.00 |

ToAcc = 37.64, Kappa = 0.25 | |||||||

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Est.N3 | 47.90 | 20.68 | 13.18 | 7.58 | 6.07 | 4.59 | 100.00 |

Est.N2 | 20.58 | 32.21 | 14.54 | 11.05 | 15.14 | 6.48 | 100.00 |

Est.N1 | 14.60 | 18.92 | 22.68 | 14.79 | 18.47 | 10.54 | 100.00 |

Est.P1 | 10.37 | 11.09 | 20.22 | 25.48 | 17.20 | 15.65 | 100.00 |

Est.P2 | 1.15 | 8.16 | 19.91 | 25.21 | 30.22 | 15.35 | 100.00 |

Est.P3 | 5.41 | 8.94 | 9.47 | 15.89 | 12.89 | 47.39 | 100.00 |

Sum | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 600.00 |

ToAcc = 34.31, Kappa = 0.21 | |||||||

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Est.N3 | 48.08 | 22.05 | 11.81 | 7.56 | 4.37 | 6.13 | 100.00 |

Est.N2 | 13.24 | 29.18 | 14.06 | 10.84 | 26.98 | 5.69 | 100.00 |

Est.N1 | 15.15 | 19.12 | 27.35 | 14.75 | 10.87 | 12.76 | 100.00 |

Est.P1 | 10.91 | 16.97 | 15.94 | 25.79 | 18.33 | 12.06 | 100.00 |

Est.P2 | 7.14 | 4.45 | 22.71 | 26.33 | 21.16 | 18.22 | 100.00 |

Est.P3 | 5.48 | 8.23 | 8.13 | 14.73 | 18.29 | 45.15 | 100.00 |

Sum | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 600.00 |

ToAcc = 32.79, Kappa = 0.19 | |||||||

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Est.N3 | 48.08 | 17.79 | 14.94 | 6.76 | 6.21 | 6.22 | 100.00 |

Est.N2 | 9.07 | 37.14 | 19.66 | 11.88 | 18.57 | 3.69 | 100.00 |

Est.N1 | 15.20 | 20.16 | 24.72 | 14.54 | 14.08 | 11.31 | 100.00 |

Est.P1 | 13.80 | 9.59 | 13.99 | 24.52 | 24.76 | 13.34 | 100.00 |

Est.P2 | 7.88 | 6.19 | 18.57 | 25.12 | 22.70 | 19.55 | 100.00 |

Est.P3 | 5.98 | 9.13 | 8.12 | 17.17 | 13.69 | 45.90 | 100.00 |

Sum | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 600.00 |

ToAcc = 33.84, Kappa = 0.21 |

Analysis of variance table for the RMSE between real trend and estimated trend. IAV and STV denote inter-annual and short-term variability, respectively.

IAV | 2 | 0.2136 | 0.1068 | 4096.7 | <2.2e-16 | 30.73 |

Type of change | 1 | 0.0511 | 0.0511 | 1959.3 | <2.2e-16 | 7.35 |

IAV * Method | 6 | 0.0469 | 0.0078 | 299.8 | <2.2e-16 | 6.75 |

Trend magnitude | 1 | 0.0252 | 0.0252 | 966.5 | <2.2e-16 | 3.62 |

IAV * STV | 4 | 0.0153 | 0.0038 | 146.8 | <2.2e-16 | 2.20 |

Type of change * Method | 3 | 0.0121 | 0.0040 | 154.6 | <2.2e-16 | 1.74 |

Method | 3 | 0.0108 | 0.0036 | 137.8 | <2.2e-16 | 1.55 |

Trend magnitude * Method | 3 | 0.0073 | 0.0024 | 93.9 | <2.2e-16 | 1.06 |

Number of breakpoints | 2 | 0.0072 | 0.0036 | 137.6 | <2.2e-16 | 1.03 |

STV * Type of change | 2 | 0.0061 | 0.0030 | 116.5 | <2.2e-16 | 0.87 |

STV | 2 | 0.0024 | 0.0012 | 46.1 | <2.2e-16 | 0.35 |

Trend magnitude * Type of change | 1 | 0.0022 | 0.0022 | 86.3 | <2.2e-16 | 0.32 |

Trend magnitude * Number of breakpoints | 2 | 0.0022 | 0.0011 | 41.7 | <2.2e-16 | 0.31 |

Type of change * Number of breakpoints | 1 | 0.0022 | 0.0022 | 83.4 | <2.2e-16 | 0.31 |

Trend magnitude * STV | 2 | 0.0022 | 0.0011 | 41.3 | <2.2e-16 | 0.31 |

IAV * Type of change | 2 | 0.0005 | 0.0003 | 10.4 | 2.962E-05 | 0.08 |

Seasonality * Number of breakpoints | 4 | 0.0005 | 0.0001 | 5.0 | 4.945E-04 | 0.08 |

STV * Number of breakpoints | 4 | 0.0005 | 0.0001 | 4.5 | 1.238E-03 | 0.07 |

Trend magnitude * IAV | 2 | 0.0004 | 0.0002 | 7.4 | 0.001 | 0.06 |

STV * Method | 6 | 0.0003 | 0.0001 | 2.1 | 4.948E-02 | 0.05 |

Trend magnitude * Seasonality | 2 | 0.0002 | 0.0001 | 4.6 | 0.010 | 0.03 |

Seasonality * Type of change | 2 | 0.0002 | 0.0001 | 4.2 | 1.526E-02 | 0.03 |

IAV * Number of breakpoints | 4 | 0.0002 | 0.0001 | 2.0 | 8.910E-02 | 0.03 |

Seasonality | 2 | 0.0000 | 0.0000 | 0.2 | 0.799 | 0.00 |

Residuals | 10,952 | 0.2855 | 0.0000 | 41.07 |