Study Area

The study area, comprising the counties of Jingzhou and Tongdao, is located southwest of Hunan Province, China (Fig. 1(a-c)). These counties are key forested regions of China, with forest coverage rates exceeding 70%. The subtropical monsoon humid climate in the study area leads to frequent cloudy and rainy weather, contaminating satellite optical data and forming sparse Landsat time series. Due to severe karst rocky desertification, the forest ecosystem in the study area is fragile and highly susceptible to climate change and human activities. The primary forest disturbance targets for detection in this study area include deforestation (such as clearcut and selective logging), insects, and fire, which lead to different change magnitudes in the forest spectrum. Hence, this study area provides an ideal condition for verifying the feasibility of detecting diverse disturbance agents from sparse Landsat time series using the proposed AEWMATCD algorithm.

Fig. 1.

Location, samples, forest cover, and images of study area: a) location within China, and b) Hunan Province; c) a Landsat 8 OLI image of study area and distribution of disturbed plots for validation; d) forest benchmark mask and the annual average of clear observations in each forest pixel.

Landsat Data and Forest Benchmark Mask

Landsat TM5, ETM+7, and OLI8 surface reflectance (SR) time series from 2001 to 2020, consisting of 115 images with less than 20% contaminated pixels, was collected from the US Geological Service (USGS). The three datasets are coordinated in a sequential order based on time. The annual average number of clear observations for 78.5% of pixels is 5 (Fig. 1d)), which is insufficient to construct a reliable harmonic model to eliminate the interference of phenological changes. The SLC-off gaps in the ETM+7 images were filled using a spatiotemporal interpolation method [43], and the function of mask products (Fmask) was applied to mask out clouds and cloud shadows. A forest benchmark mask was delineated using the random forest classification algorithm based on the Landsat image taken on October 3, 2002 (the date corresponding to the maximum training length for most forest pixels), to remove the non-forest pixels (Fig. 1d)). The forest benchmark mask maximizes the likelihood of selecting forest pixels as analysis targets and minimizes the possibility of stand-replacing disturbances occurring during the training stage.

Validation Data

The validation dataset, consisting of 345 disturbed plots (Fig. 1c)) and 345 undisturbed plots, were collected to evaluate the detection accuracy of the AEWMATCD algorithm. The type and initial disturbance date for each disturbed plot in the Landsat time series were determined through visual interpretation of the time series data (multispectral composite images and time series curves) and high-resolution images acquired from Google Earth, supported by additional materials. Specifically, MODIS MCD14ML active fire product was used to assist in collecting fire samples; insect samples were collected assisted by local historical statistics and relevant news and articles; and the clearcut and selective logging samples entirely collected relied on visual interpretation of Landsat time series data and high-resolution images. Finally, a total of 345 disturbed plots, including 219 clearcut, 40 selective logging, 59 fire, and 27 insect samples separately, were collected. In addition, 345 undisturbed plots were sampled from the non-disturbance forest region, which were also confirmed using Landsat time series data and Google Earth imagery.

Methodology

The flowchart of detecting diverse forest disturbance agents with different change magnitudes using the proposed AEWMATCD algorithm is shown in Fig. 2. First, to eliminate the interference of forest seasonal variations in disturbance detection, the Normalized Difference Moisture Index (NDMI) was spatially normalized using the spatial context to finish subsequent model initialization using sparse clear observations. Second, in order to meet the requirement for AEWMA-t chart input to follow an independently normal distribution in both the temporal and spatial dimensions, the spatial errors model (SEM) was established through fitting temporal-spatial observations in the training stage. The residual time series were then generated by subtracting the observed values from the fitted values, yielding normally distributed residuals. Third, the residual time series were input to the AEWMA-t chart to detect diverse disturbance agents, and disturbances were labeled if the AEWMA-t values consecutively exceeded the control limits. The crucial procedures are described in more detail in the following sections.

Fig. 2.

Flowchart of the proposed AEWMATCD algorithm.

Spatial Normalization of NDMI for Model Initialization

By contrasting SWIR1 and NIR bands, NDMI (1) [44] has been proven to be sensitive to forest insects [25, 27, 45]. NDMI has also been widely used in detecting deforestation, including clearcut, small-scale deforestation, and selective logging [7, 9, 10, 46, 47]. In addition, NDMI also has the ability to detect fire [48- 50]. Therefore, NDMI was selected as the spectral input of the change detection algorithm for detecting diverse forest disturbances with different change magnitudes, including clearcut, fire, selective logging, and insects in this study.

NDMI was calculated as:

To reduce the impact of phenological variations on change detection, the spatially normalized NDMI (SNDMI) was calculated as (2). First, NDMI_median was then obtained by calculating the median NDMI of the pixels exceeding a certain percentile P (set to 90% in this study) within a moving window. Then, the SNDMI of the central pixel was obtained by dividing the NDMI value of the central pixel (NDMI_pixel) by NDMI_median. This approach assumes that the upper tail of the pixels within the moving window are forested, and their seasonal variations are similar to that of the central pixel. Therefore, SNDMI can remove the phenological variations. SNDMI time series were calculated from 2001 to 2020 for each forest pixel.

The spatial moving window size is important for normalization. Based on the analysis of the collected sample data and statistical data on insects and fires in the study area, the areas of forest deforestation, fire, and insect patches are generally smaller than 35 ha. Therefore, the window size was set to 21Í21 pixels (39.69 ha) to avoid smoothing out the impact of disturbances when calculating the spatially normalized index while preserving the temporal dynamics similarity between the central and neighboring pixels.

Considering that the SNDMI time series has eliminated the seasonal changes described by a harmonic model in previous studies, the harmonic model was superseded by a simple linear model (3).

where a is theoretically close to 1 and estimated using ordinary least squares, and u_i is the residual at date t_i. Fitting the simple linear model requires only six clear observations [51], thereby shortening the length of the training stage in regions with insufficient data.

Acquisition of Independently Normally Distributed Residual Time Series Using SEM Model

Diverse forest disturbance agents were detected using the AEWMA-t chart, which requires the input data in the temporal-spatial domain to follow an independently normal distribution. However, due to strong spatial correlation, the assumption that the n spatially adjacent residuals at the same time step follow an independently normal distribution may fails [52]. Therefore, instead of (3), SEM (4) was performed to remove the spatial correlation of the regression residuals:

where SNDMI denotes SNDMI observations with the size of m (length of time series) Í n; a represents n regression coefficients a; u represents the matrix of spatially correlated regression residuals u_i; γ is the spatial dependence parameter estimated by maximum likelihood method; W is the spatial weight matrix filled with 1 for neighboring forest pixels and 0 otherwise; ε is the independently normally distributed residuals in the temporal-spatial domain, and I denotes the identity matrix. Therefore, instead of the regression residuals u_i estimated by the simple linear model (3), the independently normally distributed residuals ε can be entered into the AEWMA-t chart for disturbances detection.

The training stage is limited to six time steps, which reduces the likelihood of disturbances occurring and affects fitting accuracy. To avoid a disturbance or noise during the training stage, we adopted the approach of [20, 31]: a moving window with six time steps, initially sequentially until the fitting accuracy reached the required precision R²_min (0.7) or the window moves to the date corresponding to the maximum training length (12 time steps). Since some outliers or contaminated pixels in the training stage may be not removed by using Fmask, a two-step fitting procedure was employed for each model fitting: 1) all clear observations within the moving window were utilized to fit the SEM model, 2) the SEM model was fitted again by using the remaining observations after removing the observations whose fitting residuals ε are greater than three times the standard deviation of all residuals at the first time.

Diverse Disturbance Agents Detection Using AEWMA-t Chart

EWMA-t chart, designed for short production runs, can detect outliers using limited samples. Some studies have proven that the EWMA-t chart has the ability to detect forest disturbances in cloudy and rainy regions [40]. To build the reliable control limits using a limited number of observations, the statistic T_i replaced the residual ε_i in [30] and is treated as the input for the EWMA-t chart:

where X_i represents the subgroup mean, and S_i represents the standard deviation of subgroups ε_i,n at date t_i. Therefore, the EWMA-t statistic, EWMA-t_i is defined as:

where the smoothing parameter λ, ranging from 0 to 1, is used to measure the retrospective nature of the chart. Specifically, more weight is assigned to the current residual statistic (T_i) when λ is close to 1, and the EWMA-t_i value principally depends on previous values EWMA-t_i-1 when λ is close to 0. The initial value of EWMA-t₀ is normally set to 0.

Based on the principle of effectively detecting low-magnitude disturbances, the value of λ was set to a small value of 0.25, which is one of the determining factors of the control limits (CL) (7). The forest pixels within the 3Í3 patch were labeled as disturbed if EWMA-t_i crosses the lower CL [53]. The value of L was set to 2.

The EWMAT index was calculated to signal disturbances (8).

where sign() is a sign function , || represents the absolute value, and int[] is used to round down the absolute value. A forest patch is marked as undisturbed if its EWMAT value is equal to 0, and a possible disturbance occurs when the EWMAT value is less than 0.

Similar to the EWMA chart, the inertia problem of the EWMA-t chart with a fixed small value of λ (0.25) will also cause a temporal delay in detecting high-magnitude disturbances. For resolving the ‘inertia problem’, the AEWMA chart where smoothing parameter λ is adaptively optimized according to the change magnitude has been developed [32], and this adaptive strategy is also introduced to the EWMA-t chart to establish the AEWMA-t chart (9) [42].

where e_i =T_i -AEWMA-t_i-1 is the estimation error. ϕ is the function of e_i, and a widely used score function (10) was adopted [32].

where k is the deviation threshold and was set to 3 in this study. Using the definition of ω(e_i) = ϕ (e_i)/e_i, AEWMA-t chart can be rewritten as follows:

ω(e_i) is equivalent to the smoothing coefficient λ in (6). ω(e_i) is equal to λ and the AEWMA-t chart was converted to EWMA-t chart when there is a low-magnitude disturbance in the process (|e_i|≤k). When a low-magnitude disturbance occurs (|e_i|≤k), the score function makes the equivalent smoothing coefficient ω(e_i) smaller. Because the lower CL’s absolute value is small, AEWMA-t_i can exceed the lower CL, which means the AEWMATCD algorithm is sensitive to low-magnitude disturbances. Conversely, when a high-magnitude disturbance agent occurs (e_i<-k), the sudden drop in the current chart value AEWMA-t_i makes the high-magnitude disturbance quickly detected, effectively overcoming the inertia problem and making the algorithm suitable for detecting both low- and high-magnitude disturbances. The AEWMAT index was calculated to signal disturbances:

Like the EWMA-t chart, a forest patch is labeled as undisturbed if its AEWMAT value is equal to 0, and a possible disturbance occurs if the AEWMAT value is less than 0. A disturbance is determined when consecutive out-of-control signals are detected, effectively lowering the false positives due to ephemeral factors, such as clouds that were not removed by Fmask [20, 30]. The number of consecutive out-of-control signals for determining disturbance is half of the annual average number of clear observations [31]. Considering the small size of the forest patch, the likelihood for the rest within the patch to be disturbed subsequently is high when some forest pixels are disturbed at the current time step. Therefore, the current time step is treated as the occurrence time of forest disturbance in the patch.

Feasibility Analysis of Detecting Diverse Disturbances in Sparse Landsat Time Series Using AEWMATCD Algorithm

AEWMATCD algorithm was performed to detect clearcut, fire, selective logging, and insect agents separately to analyze the feasibility of detecting diverse disturbances (Fig. 3). Because clearcut and fire agents both result in stand-replacing transition, change magnitudes of SNDMI for clearcut (the SNDMI median of the pixels within the patch dropped from 0.80 to -0.54) and fire agents (dropped from 0.83 to -0.19) were both high (Fig. 3(a-b)). When clearcut or fire agent with high-magnitude occurred, the equivalent smoothing coefficient ω(e_i) adaptively get larger from initial 0.25 to 0.53 for clearcut and from initial 0.25 to 0.59 for fire. Then a sudden drop in the current chart value AEWMA-t_i with more weights makes current AEWMAT value quickly less than 0 (-2 for clearcut and -4 for fire). The high-magnitude disturbances quickly detected, effectively overcoming the inertia problem. Selective logging or insect agents leads to subtle changes in structure or condition with a persisting forest cover and, therefore, change magnitudes of SNDMI for selective logging (the SNDMI median of the pixels within the patch dropped from 0.72 to 0.35) and insect agents (dropped from 0.76 to 0.12) were both low (Fig. 3(c-d)). When selective logging or insect agents with low magnitude occurred, ω(e_i) still kept a small value (initial λ=0.25). Because the absolute value of the lower CL is small, it makes the current chart value AEWMA-t_i can cross the lower control limits, and the current AEWMAT value less than 0 (-1 for both selective logging and insects), which means the AEWMATCD algorithm is sensitive to selective logging or insects agent with low-magnitude. The results proved that the AEWMATCD algorithm is feasible for detecting both low- and high-magnitude disturbances based on the adaptive adjustment of the smoothing coefficient ω(e_i) for different change magnitudes.

To verify the applicability of the AEWMATCD algorithm to detect disturbances using sparse Landsat time series, the AEWMA chart was performed to detect the clearcut agents in Fig. 3a), wherein the annual average of clear observations is equal to 5, for comparing with the result using the AEWMATCD algorithm (Fig. 4). Like the EWMA chart in Brookes et al. (2014), the AEWMA chart also needs dense, clear observations to establish a reliable baseline by fitting the harmonic model during the training stage and control limits that depend on an accurate estimation of the standard deviation of fitting residuals. However, when the observations at six time steps, the same number of time steps used to estimate 1 fitting parameter in (4) in the AEWMATCD algorithm were applied to fit the harmonic model with 2 harmonic terms (i.e. 5 fitting parameters) in AEWMA chart, overfitting of the harmonic model influenced the removal of seasonality. This resulted in an inaccurate estimation of the standard deviation of fitting residuals, which led to false alarms (or omission errors) (Fig. 4a)). Although the AEWMA chart can accurately detect disturbances when the observations at 15 time steps that are thrice larger than 5 fitting parameters were used (Fig. 4b)), the long training stage with nearly 4 years in this sample introduces the challenge in online detecting multiple disturbances in regions with low data availability or with frequent disturbances. On the contrary, the proposed AEWMATCD algorithm only needs the observations with the size of 3Í3 (spatial window) Í6 (time steps) to fit the SEM model. Then, it can accurately detect the clearcut agent (Fig. 3a)). Therefore, the AEWMATCD algorithm can also detect disturbances in regions with insufficient data.

To further assess the ability to overcome the delay in detecting high-magnitude disturbances using the proposed AEWMATCD algorithm, the EWMATCD algorithm and the EWMA-t chart with a fixed small value of λ (0.25) were executed on the high-magnitude disturbance agents in Fig. 3(a-b) (Fig. 5). Compared with the result of timely detection using the AEWMATCD algorithm, the disturbance was detected with the delay of one or two time steps when the EWMATCD algorithm was executed. More seriously, when the disturbance agent was only recorded on the limited time steps of the time series because of low data availability, the limited clear observations and inertia problem of the EWMA-t chart led to the number of consecutive signals crossing the CL for labeling disturbances not enough, resulting in omission error. As shown in Fig. 6, clear observations at only three time steps (corresponding to the second, third, and fourth dashed lines) were recorded in the duration of a clearcut agent, and the inertia problem of the EWMA-t chart resulted in the lack of three consecutive out-of-control signals for determining disturbance (Fig. 6b)). Meanwhile, the AEWMATCD algorithm can detect the clearcut agent in a timely manner, even if clear observations are limited (Fig. 6a)).

Assessment of Disturbance Detection Accuracy in the Spatial Domain

The assessment results of the spatial accuracy of detecting disturbances using the AEWMATCD algorithm was shown in Table 1. The producer’s and user’s accuracies for the undisturbed samples are 80.0% and 88.2%, respectively, while those for the disturbed samples are 89.3% and 81.7%, respectively. The absolute value of the lower CL is set as a low value for effectively detecting the low-magnitude disturbances, and therefore, the commission error rate (69/377 = 18.3%) is larger than the omission error rate (37/345 = 10.7%) for the disturbances. The overall accuracy of 84.6% indicates that the AEWMATCD algorithm can effectively detect diverse disturbance agents with different change magnitudes.

Fig. 3.

Detection of diverse forest disturbance agents within the 3×3 spatial window (yellow boxes in high-resolution images or Landsat images before and after disturbance) using the proposed AEWMATCD algorithm: a) clearcut, b) fire, c) selective logging, and d) insects. The dashed lines in the AEWMA-t chart represent the initial dates of disturbances labeled by AEWMATCD algorithm. RGB: R= band NIR, G=band Red, B=Green. We displayed Google Earth Pro (GEP) images if the date near the disturbance occurs has available images for better intuitiveness.

Considering each disturbance type (Table 1), the producer’s accuracy is highest for clearcut (92.7%), and it was followed by fire (89.8%), which means that a high proportion of high-magnitude disturbance agents were correctly detected (low omission error). Although the producer’s accuracy was relatively low for selective logging (80.0%) and insects (74.1%) compared to clearcut and fire, disturbance detection was still moderately successful for low-magnitude disturbance agents. A comparison of different disturbance agents showed expected patterns of detection accuracies for high-magnitude disturbances that were higher than low-magnitude disturbances.

Fig. 4.

Detection of forest clearcut agent in Fig. 3a) using AEWMA chart: the number of training data is equal to a) 6 and b) 15, respectively. The dashed line in the picture represents the clearcut date labeled by the AEWMA chart.

Fig. 5.

Detection of forest high-magnitude disturbance agents in Fig. 3(a-b) using EWMATCD algorithm: a) clearcut, b) fire. The black and red dashed lines in EWMA-t chart represent the initial dates of disturbances and the dates of disturbances detected by the EWMATCD algorithm, respectively.

Most of the commission errors can be ascribed to:

1) the consecutive noise and 2) the difference in forest seasonal variations. Consecutive noises that Fmask did not remove may be falsely detected as a disturbance. As shown in Fig. 7, consecutive shadows that appeared on October 31 and December 18, 2018 (second and third dash lines) resulted in three consecutive out-of-control signals (from third to fifth dash lines). Because of the inertia problem caused by the small value of the equivalent smoothing coefficient ω(e_i), the AEWMAT values on the dates corresponding to the fourth and fifth dash lines were determined by historical values on the previous dates when shadows appeared, and then less than 0 even though shadows disappeared on the current two dates. Therefore, the AEWMATCD algorithm more easily mistakes consecutive (even less than three times) noise for disturbance. The difference of seasonal variations among mixed forests may result in spatially normalized index SNDMI largely deviating from 1, thereby generating a false alarm. As shown in the high-resolution images of Fig. 8, the seasonality of the forest within the patch with 3Í3 pixels or spatially normalized windows was visually different in different seasons. Every month for 20 years (from 2001 to 2020), the SNDMI of the forest within the patch deviated from 1 at different levels, especially from December to March (Fig. 8a)). Therefore, the large deviation of SNDMI caused by the difference in seasonality in these months generated a false positive (Fig. 8b)). One possible solution to this problem is to select the NDMI value of the forest pixels with the same tree species as the central pixel as the median NDMI_median according to the tree species classification map. However, it would make the algorithm complicated and time-consuming.

The omission error was mostly due to the following reasons: 1) excessively low disturbing signals; 2) the extremely sparse clear observations during disturbance; and 3) the relatively small spatially normalized window resulting in the covering up of disturbance with a wide range. Although the AEWMATCD algorithm can effectively detect disturbance agents with low-magnitude change, some disturbance agents (e.g., selective logging and insects) with excessively low disturbing signals are still hard to characterize. As shown in Fig. 9, insect agents lead to excessively subtle changes: the SNDMI median of the pixels within the patch drops from 0.79 at the previous time step before disturbance to 0.50 in the duration of disturbance (the black box), and the medians at each time step in the black box are between 0.40 and 0.61. Although the absolute value of the lower CL is small (-0.873), excessively low severity makes nearly all chart value AEWMA-t_i cannot cross the lower CL, and only the last AEWMAT value in the duration of the disturbance is equal to -1. Extremely sparse clear observations would make disturbance hard to detect since the number of clear observations during disturbance is less than the requested number of consecutive signals for determining disturbance. As shown in Fig. 10, only one clear observation on the date corresponding to the second dash line recorded a disturbance due to the absence of clear observations in 2012 and a possible recovery in 2013. Therefore, the number (1) of out-of-control signals is below the requested number (3) of consecutive out-of-control signals for determining disturbances, resulting in omission error. When the spatial range of the disturbance agent is larger than the size of the spatially normalized window, the SNDMI of disturbed pixels is close to 1 because the forest pixels corresponding to NDMI_median are also disturbed. Then, it smoothed out the influence of disturbance. As shown in Fig. 11, the NDMI of forest patches from April to June in 2008 were generally lower than those in other years (Fig. 11a)). The SNDMI of disturbed pixels largely deviated from 1 when insect outbreaks occurred in the partial forest pixels within the spatially normalized window on April 26 and May 12, 2008 (second and third dash lines in Fig. 11b)). Then, the SNDMI of disturbed pixels is close to 1 when the insect occurred throughout the spatially normalized window on June 29 (fourth dash line in Fig. 11b)), followed by gradual and full recovery in September and October (fifth and sixth dash lines in Fig. 11b)). This resulted in the lack of three consecutive out-of-control signals for determining disturbance during the insect outbreaks. Therefore, to avoid such a situation, the proper size of the normalized window should be defined according to the extent of disturbance agents in the specific region.

Fig. 6.

Timely detection of high-magnitude disturbance agent (clearcut) within a 3×3 spatial window (yellow boxes) using AEWMATCD algorithm a) and omission error in detection using EWMATCD algorithm with a fixed small value of λ(b): sparse clear observations during disturbance and inertia problem of EWMA-t chart. The dates corresponding to six dashed lines in the charts correspond to those of Landsat images in turn.

Fig. 7.

Commission error of detecting disturbance agent within a 3×3 spatial window (yellow boxes) using AEWMATCD algorithm: consecutive shadows. The dates corresponding to five dashed lines in AEWMA-t chart correspond to those of Landsat images in turn.

Assessment of Disturbance Detection Accuracy in the Temporal Domain

Given that Landsat time series are sparse, the date corresponding to the first image in which disturbance was identified through visual interpretation was treated as the initial occurrence date. Then, the temporal accuracies of the 308 reference disturbed samples detected by the AEWMATCD algorithm were further assessed (Table 2). 78.9% of disturbed samples were detected by the AEWMATCD algorithm on the initial date of disturbance (same time step). If a one time step delay (late = 1 time step) in detecting disturbances is acceptable, 89.3% (78.9%+10.4%) of disturbance samples were correctly signaled within two time steps after disturbance occurrences, showing a rapid response of the AEWMATCD algorithm to disturbances.

Fig. 8.

Commission error of detecting disturbance agent within a 3×3 spatial window (yellow boxes) using AEWMATCD algorithm: difference of forest seasonal variations. a) SNDMI of forest patch with the 3×3 spatial window in every month of 20 years (from 2001 to 2020); b) AEWMA-t chart. The dates corresponding to four dashed lines in AEWMA-t chart correspond to those of Landsat images in turn, and the black boxes in the high-resolution images represent the spatially normalized window.

Considering each disturbance type (Table 2), 84.2% of clearcut were detected by the AEWMATCD algorithm on the initial date of disturbance and followed by fire (81.1%), meaning the timely response of AEWMATCD algorithm to high-magnitude disturbances. The comparison of different disturbance agents showed that detecting clearcut and fire with high magnitude on the same time step was earlier and more timely than selective logging (56.3%) and insects (50.0%) with low magnitude. The reason is that the change severity and equivalent smoothing coefficient ω(e_i) of high-magnitude disturbances are both higher than those of low-magnitude disturbances, resulting in quicker detection of the high-magnitude disturbances. However, 71.9% (56.3%+15.6%) of selective logging and 75.0% (55.0%+20.0%) of insects were still correctly signaled within two time steps after disturbance occurrence, showing moderate success for low-magnitude disturbance detection and the potential for early warning.

For further verifying whether the AEWMATCD algorithm effectively overcomes the inertia problem, the EWMATCD algorithm with a fixed small value of λ = 0.25 was executed on 308 reference disturbed samples detected by the AEWMATCD algorithm. As shown in Table 2, regardless of whether it is the same time step or within two time steps, the temporal accuracies (58.8% or 58.8%+16.5% = 75.3%) of disturbed samples detected by the EWMATCD algorithm are both lower than those (78.9% or 89.3%) detected by the AEWMATCD algorithm. More seriously, several disturbed samples (5.8%) were undetected by the EWMATCD algorithm because of sparse, clear observations during the disturbance and inertia problem of the EWMA-t chart (Fig. 6b)). For high-magnitude disturbances, due to the adaptive adjustment of the equivalent smoothing coefficient ω(e_i), the temporal accuracies of both clearcut and fire detected on the initial occurrence date are raised by more than 20% using the AEWMATCD algorithm, compared with the EWMATCD algorithm. For low-magnitude disturbances, the temporal accuracies of both selective logging and insects detected on the initial occurrence date using the AEWMATCD algorithm are basically the same as those using the EWMATCD algorithm. The reason is that ω(e_i) in the AEWMATCD algorithm generally keeps its initial small value of 0.25 due to the low severity of selective logging and insects, which is the same as the fixed small value of λ in the EWMATCD algorithm. These results further indicated that the AEWMATCD algorithm could effectively solve the inertia problem and temporal delay of high-magnitude disturbance detection.

Fig. 9.

Omission error of detecting disturbance agent (insects) using the AEWMATCD algorithm: excessively low disturbing signals. The black box represents the duration of disturbance.

Fig. 10.

Omission error of detecting disturbance agent (clearcut) within a 3×3 spatial window (yellow boxes) using the AEWMATCD algorithm: the extremely sparse clear observations during disturbance. The dates corresponding to three dashed lines in AEWMA-t chart correspond to those of Landsat images in turn.

The temporal errors of the AEWMATCD algorithm are mainly due to low-magnitude disturbances initially occurring in partial pixels, resulting in excessively low disturbing signals (AEWMA-t_i) at the first few time steps. This makes the AEWMATCD algorithm unable to detect the disturbance until the disturbing signals are accumulated and amplified. Fig. 12 shows selective logging started to occur in the partial pixels (5/9) of the 3Í3 spatial window on September 4, 2009 (corresponding to the second dash line in the AEWMA-t chart). This leads to the relatively low absolute values of the current T_i and chart value AEWMA-ti that cannot cross the lower CL in a timely manner. As selective logging occurred in the rest of the pixels and even clearcut occurred in the partial pixels, the accumulated disturbing signal (AEWMA-ti) was gradually enhanced. It became large enough to identify the disturbance on November 23, 2009 (fifth dash line in the AEWMA-t chart), resulting in a temporal delay of three time steps.

Fig. 11.

Omission error of detecting disturbance agent (insects) within a 3×3 spatial window (red boxes) using AEWMATCD algorithm: the relatively small size of spatially normalized window resulting in the covering up of disturbance with a wide range. a) NDMI of forest patch with the 3×3 spatial window under insects stress in 2008 and other years; b) Insects detection using AEWMA-t chart. The dates corresponding to six dashed lines in AEWMA-t chart correspond to those of Landsat images in turn, and the black boxes are the spatially normalized windows.