Application of the Thermo-RAdiometric Normalization of Crop Observations (TRANCO) Back in Time: An Assessment of the Potential for Crop Time-Series Generalization to Past Years Using Wheat as a Proxy

Highlights

What are the main findings?

• The TRANCO approach is able to normalize time-series through time.
• The addition of TRANCO into a classifier improves its performance.

What are the implications of the main findings?

• The tests performed in this research show that the TRANCO approach is able to generalize information outside its time component, allowing normalized time-series outside its year of origin to be used by classifiers.
• Such normalization of time-series could allow improving deeper classifiers, even empower the classification of past years’ crops, in which ground truth data could be scarce, by training in recent years.

Abstract

Crop type maps are essential for food security. However, there is a gap in information for worldwide maps that, at the same time, cover a wide period of time. The inability of classification algorithms to generalize information across years is one of the main reasons for this lack of information. This study aims to advance this direction by normalizing annual time series of wheat crops using the accumulation of Growing Degree Days (GDDs). Based on the Crop Data Layer (CDL) crop-type maps and Landsat 5, 7, and 8 imagery, we built yearly time series for the period 2008–2020. Then, we tested the performance of two normalization approaches: TRANCO, which uses Growing Degree Days (GDDs) and Crop Calendars to normalize time-series data; and Time Windows, which uses Crop Calendars to define wheat’s biofix dates and normalize time-series data. Furthermore, we compared them with a Baseline, meaning a time series without further processing. Such performance was tested in two main ways: By computing the Jeffries–Matusita (JM) distances between time series and their average behavior, and by training random forest classifiers. For the latter, we defined a training period (2017–2020) during which we trained the models, and a validation period (2008–2016), during which we validated them on years the models were not trained on. We found that TRANCO was the best normalization approach for bringing the time-series closer to a common behavior (JM = 0.3), compared to Time windows (JM = 0.4) or the Baseline. Also, it achieved the best classification results (F1 = 0.779), compared to Time windows (F1 = 0.71) or the Baseline (F1 = 0.73), and, in addition, TRANCO’s classifier was the most stable throughout the validation period, empowering past crop type classifications with classifiers trained in recent years.

1. Introduction

Food security is facing challenges worldwide, such as adaptation to climate change impacts [1,2,3,4], a growing global population [4,5], famines in developing countries [6] or armed conflicts in producing countries [7,8]. In this context, knowing the location of specific crop types can help minimize disruptions to food security or, at least, minimize the effects of unwanted phenomena through improved market transparency [9]. Furthermore, this kind of information is useful to explain processes of agricultural intensification [10,11], land use change [12,13], land degradation [14], or desertification [14], as well as to improve the application of surface energy balance algorithms [15].

1.1. Literature Review

Crop Type Maps

The description of crops in a given area and for specific years is crucial for agronomy applications such as crop monitoring or yield prediction. Nonetheless, describing a crop species or variety distributed across space (e.g., global scope) and time (e.g., crop seasons) presents several problems. Also, each crop has a unique set of requirements, such as nutrient ratios, soil moisture, and pH, or a range of maximum and minimum temperatures, which can affect the crop’s signal sensed from satellite in different ways. On top of that, from a global perspective, crop datasets are usually spatially biased and very limited in time.

This description of crop type locations, from coarse to fine resolution, mostly lies on crop type maps [16,17,18,19]. While there are plenty of studies in the literature on building crop-type mapping algorithms, most are applied regionally, are not transferable to other regions, and are limited to a specific year or period. As an example of global crop type maps, we have Crop Monitor’s Best Available Crop Specific Masks with coarse spatial resolution and not limited to a specific year or period [20,21]. As far as finer spatial resolution comes, we only found crop type studies for specific years and at local [16,17,22,23] or at regional and national [24,25,26,27,28,29,30,31,32,33] scale, with the global scale exception to WorldCereal’s ones [34,35].

Our previous study [36] shed light on the reasons for the scarcity of fine-resolution global crop-type maps and the most common approaches to their classification. We could sum it up in three crucial problems:

1.

The classification approach used, which at a global scale and fine resolution can result in a high economic cost and large power processing capabilities. Although the latter can be solved with current processing platforms such as Google Earth Engine [18,37,38,39,40,41,42,43,44,45,46,47].

2.

The phenology shift among distant areas. Mainly caused by the natural change of the climate with latitude, although we also had to take into account areas with altitudes well differentiated on a regional scale. This also influences the type of classification approach used, which must account for these phenomena [18,37,44,48,49,50,51,52,53,54,55,56,57,58,59,60,61].

3.

The spatial bias toward the Northern Hemisphere in crop type observations and, more specifically, wheat crop types observations [34,35,36].

Given the aforementioned limitations, crop type maps are not as commonly produced at high spatial resolution as land cover maps (i.e., 30 or 10 m). However, there is a need for global crop-type maps at fine resolution [18,56]. Moreover, crop-type maps covering long periods are scarce; the Crop Data Layer (CDL) from the United States Department of Agriculture (USDA) is an example. Nonetheless, we did not find any map or dataset of crop types covering a few years while maintaining a global scope. Similar to the difficulties of spatial extrapolation of crop observations, in the temporal case, climatic conditions cause interannual variability in crop signals, which limits their generalization. Furthermore, sharing a location through the years adds a new source of autocorrelation that the models have to deal with [62].

The relation between temperature and crop growth is well-known [47,63], and we leveraged it to reduce spatial autocorrelation and normalize global time-series [36]. In fact, through the accumulation of Growing Degree Days (GDDs), we not only normalized (i.e., generalized) the crop phenology throughout the world, but also classified wheat over block samples distributed throughout the entire world with satisfactory results [36]. Furthermore, our results empowered further and better classifications of winter and summer cereals, such as wheat or maize [34,35,64]. Yet, the performance of such normalization over time remains to be explored. In order to do that, we had to abandon the global scope in search of a crop type dataset populated over a wide period of time: the CDL.

2. Objectives and Questions

The main objective of this study is to test whether the Thermo-Radiometric Normalization of Crop Observations (TRANCO) approach, previously validated in a spatial context, can normalize yearly time series using wheat crops as a proxy. Also, assuming that a better normalization implies a better quality of the data fed into a classifier, hence relating both performances: the one of the normalization and the one of the classifier, we will train a random forest classifier with the normalized time-series to approximate the normalization performance.

3. Materials

3.1. Crop Calendars

The TRANCO approach [36] uses the accumulation of GDD to relate the growth stage of wheat crops to air temperature. Nonetheless, such accumulation must begin at some point in time, usually known as the biofix date [65]. This moment is usually defined as the planting or sowing date of the crop, which is commonly defined in crop calendars. These have their own problems (e.g., lack of documentation, low spatial resolution, being outdated), hence we used our own modelled crop calendars that are based on the existing information at the time, aiming for a better definition of the spatial variations, the extrapolation of information to fill undocumented gaps in the knowledge, and an increase of the spatial resolution [66,67]. In this study, we used these crop calendars to determine the dates on which we began and ended accumulating GDD.

3.2. Crop Data Layer

The CDL is a crop-type and land-use classification of the USA at 30 m resolution. For its development, they used EO satellites such as MODIS, AWiFS, and Landsat, as well as NASS and FSA field surveys. Since 2007, they have offered a complete raster dataset, including the seasonality of crop types and land uses, which extends across the USA mainland [25]. As for their error, Boryan [25] reported a precision of 95% and a recall of 85%, yielding an F1 of 0.90% for the major crop categories. However, there are doubts about the representativeness of such errors due to the methodology employed [68,69].

3.3. ERA-5

Our model relies on a reanalysis database to obtain the required information on 2-m air temperature. Such databases use data assimilation strategies—i.e., they rely on model-based forecasts and observations—to fill gaps in space and time dimensions [70]. In addition, the mentioned models are validated on the ground using known error estimates and are fully updated when new observations and variables become available. Specifically, we used the Agrometeorological indicators from 1979 to present derived from reanalysis (AgERA5) database, since its variables are designed for agricultural purposes. AgERA5 [71] is the result of downscaling the ERA5 database [72] to 0.1° (i.e., about 1 km) spatial resolution, enabling ERA5 to be used in agriculture.

3.4. Landsat

We used the Landsat constellation because of its extensive spatial and temporal coverage, which matches the CDL database’s extent and years. Because of the latter, we downloaded information distributed throughout the USA’s mainland for the period 2008–2020. Specifically, we used imagery from the Landsat-5, Landsat-7, and Landsat-8 satellites and harmonized their bands using Landsat-8 as the reference. Each one of them has 30 m of resolution and a revisit time of 16 days.

From them, we use all the bands they offered, except those related to Land Surface Temperature (LST), since we wanted to be as comparable as possible with our previous work [36], which did not use LST information.

4. Methodology

In this study (Figure 1), we leverage satellite, climatology, and crop information to test the ability of the TRANCO approach to normalize yearly time series. The overall methodology, explained further below, trains a random forest classifier to detect wheat through a period of years it did not see before (i.e., the validation period). The performance of the classifier fed with TRANCO’s normalized time-series is then linked to its normalizing ability.

4.1. Creating the Analysis Ready Dataset

We organized an Analysis Ready Dataset (ARD) covering the entire USA mainland and the period 2008–2020. Taking advantage of the CDL, we computed the level of wheat aggregation within 12 km pixels and selected 40 of them (Figure 2) to download Landsat information using the Python API of Google Earth Engine (earthengine-api package, version 0.1.338).

Figure 2. Aggregation of the CDL wheat labels, as considered in Table 1, through the USA mainland. The white points are the 40 blocks created, while the red Xs reference the blocks shown in Figure 7a–d, whose identifiers are shown in green.

Figure 2. Aggregation of the CDL wheat labels, as considered in Table 1, through the USA mainland. The white points are the 40 blocks created, while the red Xs reference the blocks shown in Figure 7a–d, whose identifiers are shown in green.

Table 1. CDL wheat codes.

CDL Code	Crop
22	Durum wheat
23	Spring wheat
24	Winter wheat
26	Winter wheat/Soybeans
225	Winter wheat/Maize
230	Lettice/Durum Wheat
234	Durum Wheat/Sorghum
236	Winter wheat/Sorghum
238	Winter wheat/Cotton

Table 1. CDL wheat codes.

CDL Code	Crop
22	Durum wheat
23	Spring wheat
24	Winter wheat
26	Winter wheat/Soybeans
225	Winter wheat/Maize
230	Lettice/Durum Wheat
234	Durum Wheat/Sorghum
236	Winter wheat/Sorghum
238	Winter wheat/Cotton

Definition of the Study Blocks

Though wheat crops are well distributed throughout the USA, their distribution varies by location and, to some extent, by year. Because of that, deciding which areas to study required a good representation of that variability. We adapted the work of King et al. [29] to match our case.

Specifically, we were focused on wheat crops, as defined in the CDL (Table 1), for our study period (i.e., 2008–2020). Then, within pixels of 12 km wide, we computed the proportion of wheat pixels with respect to the total of cropland pixels. Next, we averaged the entire period and selected values below the 99.99% percentile to form 4 groups using the unsupervised K-Means algorithm. Furthermore, we reduced potential autocorrelation by using K-Means to sample 10 pixels from each aggregation group, based on the coordinates of the 12 km pixels. As a result, we obtained 40 pixels of 12 km each, hereafter blocks, as far as possible from one another.

4.2. Data Acquisition and Preprocessing

Once our study blocks were selected, we populated them with information for the study period (i.e., 2008–2020): Landsat imagery, AgERA5 2-m temperatures, crop calendars, and crop types. Specifically, for satellite data, we downloaded Landsat imagery (Landsat-5, Landsat-7, and Landsat-8) processed at Level 2, using Google Earth Engine’s Python API. Yet, to use the imagery as a whole, we had to harmonize the bands’ nominations; thus, we used Landsat-8 as a reference (

Table 2. Harmonization of Landsat bands to a common band reference, led by the Landsat-8 configuration.

Region	Landsat-5	Landsat-7	Landsat-8	Harmonized
Blue	B1	B1	B2	B2
Green	B2	B2	B3	B3
Red	B3	B3	B4	B4
NIR	B4	B4	B5	B5
SWIR1	B5	B5	B6	B6
SWIR2	B7	B7	B7	B7

). We preprocessed the entire image pixel-wise, addressing cirrus, clouds, and cloud shadows. Furthermore, we averaged the time-series monthly and interpolated it on a daily basis. After that, we smoothed the time series using a moving window average over time for each Landsat pixel, with a 30-day window width. However, since our scope is time-series normalization rather than classification, we did not account for the differences in the three satellites’ sensors, nor did we address Landsat-7’s striping problem.

4.2.1. Band Combinations

We used a total of 20 band combinations (e.g., remote sensing indices) of multispectral or radar imageries that derive information related to the vegetation or the soil: NDVI, NDMI, EVI, aNIR, NIRV [54], AUC, NAUC [73], NDWI [74], NBR [75], NBR2 [76], GNDVI [77], NDRE [1,2,3,4,5,78], EVI2 [79], SAVI [80], REP [81], SIPI [82], RVH [83], and RVI [84].

4.2.2. Normalizations

Once the time series were created, we applied two time-series normalization (or generalization) approaches to make them independent of location and year, and left a Baseline without further processing for comparison.

• TRANCO. Vegetation metabolism is related to daily temperature accumulation within maximum and minimum boundaries. If any of these boundaries is surpassed, the metabolism of a plant is reduced to a minimum (minimum boundary) or reaches the maximum activity (maximum boundary) [85,86]. These boundaries, which vary among plant species [87], are used by the GDD to compute effective temperatures, meaning temperatures at which vegetation metabolizes. In our approach, we followed the mathematical definition of [88]:

  $$GDD={\displaystyle \frac{T_{max}+T_{min}}{2}}-T_{base}$$

  (1)

  $$\mathrm{if}{T}_{min}<T_{base}:GDD=T_{base}$$

  (2)

  $$\mathrm{if}{T}_{max}>T_{mb}:T_{max}=T_{mb}$$

  (3)

  where $GDD$, $T_{max}$, $T_{min}$, $T_{base}$, and $T_{mb}$ are Growing Degree Days, maximum temperature, minimum temperature, base temperature, and maximum boundary, respectively. Specifically for wheat, the $T_{base}$ is 0 °C, and the $T_{mb}$ is 25 °C. Although we explored this, we did not consider the maximum boundary here, as our ARD is located in the Northern Hemisphere, where wheat crops develop through winter and early spring, and temperatures usually do not reach the maximum boundary. In fact, generally, the maximum boundary can be omitted and still achieve good results [18,65,67].
  Furthermore, to accumulate GDD temperatures, it is necessary to know the biofix date, or the date when a phenological cycle begins. In the specific case of wheat crops, this date corresponds to the sowing date, which can be derived from LSP analysis and interpolation or obtained from existing crop calendars [67].
  TRANCO used Cintas et al. [66] predicted Crop Calendars to define when the accumulation process starts (SOS) and finishes (EOS). We computed the GDD from the AgERA5 2-m air temperature time series [71] and accumulated it from the SOS to the EOS. Then, we translated the time coordinates into temperature ones, defining 140 °C steps: from 0 °C to 2520 °C, and averaged the radiometric signals at each step. When the accumulated GDD series stopped before reaching 2520 °C, the subsequent steps were filled with 0 values. The 2520 °C limit and the 140 °C steps were defined to match the number of model features in the Time windows normalization.
• Time windows. We compared the performance of the TRANCO against a simpler normalization based on time windows. Such time windows limit the wheat time-series to the SOS and EOS dates defined in the predicted Crop Calendars. In other words, a Time windows’ time-series starts at the SOS and grows until it reaches the EOS. In addition, we averaged the radiometric signal inside the time windows into 10-day composites (i.e., dekads).
• Baseline. We evaluated how well both normalizations performed compared with an approach without any normalization, starting the time series on 1 January. and finishing on the 31 December. As in the Time windows case, we averaged the radiometric signals into dekads.

4.3. Maximum Separability Minimum Distance

Khosravi et al. [89] proposed a method based on Jeffries–Matusita (JM) distances to measure the separability of the features among classes, removing correlated features and giving priority to the radar ones. We used their Maximum Separability Minimum Distance (MSMD) algorithm to select features for our model; however, we did not use radar features or define a minimum distance, and instead sorted them by their JM distance. Next, we assessed correlations among the features, retaining only those with a greater JM’s distance when the correlation exceeded 0.85. As we used spatial cross-validation, the JM distances were computed inside each group and in each iteration.

4.4. Spatio-Temporal Stratified Sampling

Although we accounted for spatial autocorrelation when selecting our 40 blocks, we must also be careful about spatio-temporal autocorrelation within each block to avoid overoptimistic results. In our application, the yearly time series are independent of year, but the crop-type classes are not. Because of that, we applied a sampling rotated algorithm [62] to avoid sampling the exact same location within a block each year. In their work, ref. [62] defined a matrix of inclusion probabilities ∏ of K × T dimensions, with K representing the k_th location (columns) and T the t_th time step (rows):

$$\prod =\left(\begin{array}{ccccc}{\pi }_1^1& \dots & {\pi }_1^t& \dots & {\pi }_1^T\\ ⋮& & ⋮& & ⋮\\ {\pi }_k^1& \dots & {\pi }_k^t& \dots & {\pi }_k^T\\ ⋮& & ⋮& & ⋮\\ {\pi }_K^1& \dots & {\pi }_K^t& \dots & {\pi }_K^T\end{array}\right)$$

where ${\pi }_k^t$ is the probability of a cell to be sampled; k is a spatial location in K; and t is a moment in time in T. Then they generated the matrix A, where each element $a_k^t$ takes the value 0 or 1, and cells that are coincident in time and/or space receive the value 0. In other words, once an element $a_k^t$ is selected, the rest of the elements at $a_k$ and $a^t$ are ignored.

$$A=\left(\begin{array}{ccccc}{a}_1^1& \dots & a_1^t& \dots & a_1^T\\ ⋮& & ⋮& & ⋮\\ a_k^1& \dots & a_k^t& \dots & a_k^T\\ ⋮& & ⋮& & ⋮\\ a_K^1& \dots & a_K^t& \dots & a_K^T\end{array}\right)$$

For a correct rotated sampling, the authors defined the following requirements [62]:

1.

The sampling design satisfies the inclusion probabilities given in ∏ (i.e., $Ep\left(A\right)\prod$).

2.

The longitudinal sample $a_k=(a_k^1,\dots ,a_k^t,\dots ,a_k^T)$ is as spread over time as possible for all the observations, in the sense that once a unit has been selected, it should remain out of the following samples as long as possible.

3.

The cross-sectional sample $a^t={(a_1^t,\dots ,a_k^t,\dots ,a_K^t)}^T$ is as spread in space as possible, for all $t\in \{1,\dots ,T\}$, in the sense that we avoid selecting geographically neighboring units.

To satisfy these requirements, we created an initial matrix A with all its elements as 1, i.e., all the elements had the same probability of being sampled (Requirement 1). To initiate the algorithm, we used K-Means to create a spatially distributed sample in the first column (first year) (Requirement 2), assigning 0 to all the sampled elements. Then, in the remaining columns (years), we set the elements of the rows that matched the sampled ones to 0 and increased the values of the sampled columns by 0.1 (Requirement 3). In the next iteration, i.e., the same algorithm applied over the next column, we did the same as in the initial one, but sampling for maximum probabilities, ensuring they are as far as possible in space but also in time (Requirements 2 and 3). This algorithm will continue until all the columns have been sampled.

4.5. Time-Series Normalization Assessment

4.5.1. Based on Jeffries–Matusita Distances

To assess performance in normalizing TRANCO and Time windows, we computed, for each approach (including the Baseline), the JM distances between time series and their average behavior. In addition, we check if there was a significant difference among JM distances.

4.5.2. An Approximation with a Random Forest Classifier

Random forest is a versatile machine learning algorithm able to adapt to different problems. In fact, its performance usually depends more on the quality of the data passed than on the selected hyperparameters [90,91,92]. Because of that, it was ideal to use it as a proxy for normalization performance, assuming that better normalization implies higher data quality. In this study, we use the implementation of a random forest classifier in Python’s Scikit-learn library Pedregosa et al. [93]. Furthermore, we used a spatial cross-validation strategy to address spatial autocorrelation; however, we did not consider a temporal variant of cross-validation, as we wanted our results to be as comparable as possible with our previous study in Cintas et al. [36]. Hence, each approach’s ability to generalize through the years will be shown in the validation step.

• Spatial cross-validation strategy. Cross-validation is a key algorithm used throughout this study, from feature selection to error assessment. It is useful for training a model and assessing its performance on data it has never seen before, since it avoids overfitting to the training partition. Cross-validation approaches involve sampling a dataset iteratively, usually from the training partition. In each iteration, the training partition is split into training and test sets to train the model and assess its performance. Commonly, the aggregated results of all the iterations describe better the performance of the model and reduce its variance, ensuring that the model is able to predict new data within an acceptable error [94,95,96].
  In addition, when dealing with large amounts of data, samples can be correlated, leading to overoptimistic results if the sampling process is not carefully designed. Although a good sampling strategy can be implemented, in some cases, such as when the dataset is heavily biased, it is difficult to eliminate autocorrelation. In order to solve that, we use a specific cross-validation algorithm to minimize the autocorrelation among samples, while keeping as much information as possible. In this study, we used an implementation of the spatial cross-validation algorithm of Brenning [97] but using the Leave One Group Out (LOGO) strategy with the groups defined by the latitude and longitude coordinates of each observation. In the LOGO cross-validation algorithm, k groups are created in each iteration. These groups are based on a defined property of the data, such as color, height, altitude, longitude, or latitude. Once the groups are created, the data associated with k − 1 groups are assigned to the training set, while the remaining group is assigned to the test set; this process is repeated until all the groups have taken the test set role. Then cross-validation continues until the predefined number of iterations is reached. We used the scikit-learn implementation of LOGO found in Pedregosa et al. [93].

4.5.3. Training and Validation Strategies

We split our ARD into a training period, during which three random forest classifiers were trained, and a validation period, during which the three models were applied to the years they had not been trained on. To be comparable with the spatially normalized results in Cintas et al. [36], we defined the training period as the four years 2017–2020, both included, and the validation period as the years 2008 to 2016, also both included.

• Training strategy. The spatial cross-validation strategy needs to split the training partition, i.e., the ARD limited to the training period, into a given number of spatial groups. Hence, for each approach, we assessed 11 spatial configurations: 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, and 40 groups, to keep those configurations free of spatial autocorrelation. This autocorrelation was measured by means of two methods: ${\chi }^2$ test of independence [98] and Crammer’s V [99]. Once we selected the best configurations, we split the training partition into training (70%) and validation (30%) sets. Then, we trained a random forest classifier on the training set using spatial cross-validation, with groups defined by the selected configurations, for TRANCO, Time windows, and the Baseline. Hence, because we used the full four years of the training period, we did not account for temporal autocorrelation. Furthermore, we computed the MSMD feature scores during the training. This process was repeated 20 times for each approach and configuration.
• Validation strategy. The validation was performed in two ways and using typical classification score metrics: F1 [48], precision [100], recall [100], accuracy [101], and $\kappa$ [102]. First, we assessed the performance of the best model configuration on the validation set during the training period (2017–2020), which represents the best combination of groups and number of features. Secondly, the best models were used to predict the crop labels within the blocks and for each year in the validation period (i.e., 2008–2016); meaning that each validation was year independent. In this way, we wanted to evaluate how TRANCO performs over time and whether it can normalize better than other approaches, such as Time windows or the Baseline. Such validation was also performed using the spatial cross-validation algorithm, with the group configuration of their respective models. Also, this process was repeated 20 times at random to assess the model’s stability under input variability.

5. Results

5.1. Normalization Performance

Time-series normalization performance can be approximated by measuring the similarity between each location’s time series and its average behavior (Figure 3). The JM distances quantify this resemblance across normalization approaches: As the JM distances increase, the separation among the observations also increases. In the case of TRANCO, we find curves with their peaks centered around 1200 accumulated GDD and the best JM (0.3) of the three approaches. The maximum of the Time windows normalization is around DOY 100; however, uniformity is worse than with TRANCO, so the JM distance is higher (0.4). In the Baseline case, the curves have almost lost their shape relative to the other two approaches, with the JM distance increasing to 0.53 and a peak around DOY 125.

In addition, when testing for differences in JM distances, we found that the three approaches differed significantly, suggesting they exhibit distinct behaviors. This is especially important when comparing TRANCO and Time windows, confirming that their normalization of the time series is different.

5.2. Autocorrelation

The analysis of the spatial autocorrelation in the groups created by the cross-validation algorithm is shown in

Table 3. Autocorrelation results from the analysis performed over the eight spatial groups considered.

Spatial Groups	${\mathit{\chi }}^2$	p-Value	Cramer’s V
2	3.36	0.07	0.017
3	7.26	0.03	0.024
4	13.67	0.00	0.033
5	7.89	0.10	0.025
10	21.55	0.01	0.042
20	31.80	0.03	0.051
40	45.93	0.21	0.061

. The results show that the number of groups is important to determine if a set is autocorrelated or not. The ${\chi }^2$ and the Cramer’s V measure the autocorrelation between categorical pairs, as the labels we are using. Hence, lower values of both would indicate lower autocorrelation. However, the p-value of the ${\chi }^2$ test indicates whether that measure is significant between the pairs, with the null hypothesis that there exists dependence between pairs. Taking that into consideration, we found that the approaches without autocorrelation are those with 2, 5, and 40 groups.

5.3. Training Results

In the training step, the Baseline shows the best performance (Figure 4a), followed by TRANCO and time-window normalization. Across the three approaches, the best model configuration has 15 features but differs in how many groups it uses for spatial cross-validation during training. In this regard, the best configuration for the Baseline and Time windows was to use 5 groups; however, TRANCO achieves the best performance with 40 groups.

The Baseline has the best results in F1 (0.821), Precision (0.855), Accuracy (0.834), and $\kappa$ (0.669); except for Recall (0.804), which is surpassed by TRANCO (0.824). Nonetheless, the latter has the second-best score for F1 (0.807), Precision (0.803), Accuracy (0.806), and $\kappa$ (0.611). Hence, the Time windows approach holds the worst values for F1 (0.728), Precision (0.729), Recall (0.762), Accuracy (0.73), and $\kappa$ (0.461). These results indicate that the better performance of the Baseline, and if we give more weight to F1 than to the Accuracy and $\kappa$ metrics, comes from its Precision, i.e., for its ability to detect wheat without confusing it with anything else, and not from its Recall metric, or its ability to not confuse other crops with wheat. In this latter metric, TRANCO shows the best statistics (Figure 4b). In addition, TRANCO variability is lower across the five metrics than across the time windows or the baselines, indicating greater stability in its model.

5.4. Features Importance

We assessed the average importance of each feature used in the classification model using the MSMD methodology, which is based on JM distances (Figure 5). For TRANCO, the most important features, the top three, are the EVI at 0 °C GDD accumulated and the SIPI at the beginning and during the peak of the season, i.e., at 140 °C and 1450 °C of accumulated GDD. As far as the Time windows approach is concerned, the most important features are the SIPI at the beginning of the season (DOY 10), and the EVI at the beginning and the peak of the season (DOY 20 and 80). For the Baseline, the 2 top features are the EVI at the beginning and the peak of the season (DOY 20 and 120). All of the above could indicate the importance of when the season’s maximum occurs for the models to discern wheat properly. Also, the initial values of the EVI and SIPI are important in the initial steps of TRANCO and Time window-based models.

5.5. Performance in the Validation Period

The performance of the three normalization approaches in the validation period (i.e., 2008–2016), which can be found in Figure 6a,b, shows that not only does TRANCO achieve the best results in almost all the years considered, but also its results are the most stable across time. Specifically, TRANCO achieves the highest F1 scores across all years, except in 2013 and 2015, when the Baseline performs slightly better. The latter is the second-best model, except for the said years and 2009, 2010, and 2015, when its performance is worse than that of the Time windows’ best model (Figure 6a). This one has the worst metrics of F1 during the entire validation period, except for the years when it achieved higher scores than the Baseline. In addition, TRANCO’s best model closely follows the dynamics of the average performance of the 20 models, a level of agreement not found in Time windows or the Baseline. For example, the performance of the best and most stable Time window models follows the average performance back to 2011, when they begin to diverge from the average. This dissimilarity between models is greater for the Baseline approach, whose best and most stable models do not follow the same dynamics, and the most stable and averaged performance also diverge in 2011. Furthermore, while TRANCO and Time windows approaches have the highest F1 scores in 2016, i.e., closer to the training period, the Baseline’s best score happens in 2011. However, its dynamics over the years have been heterogeneous. Attending to this dynamic over time, after an initial decrease in the F1 score in 2015, the TRANCO and Time windows approaches maintain their performance over time under certain variance, with the former achieving the highest F1 scores and the latter the lowest.

When looking at the average performance of the normalization approaches in the validation period (Figure 6b), TRANCO achieves the best scores in the metrics F1 (0.779), Recall (0.806), Accuracy (0.783), and $\kappa$ (0.566); but in the Precision (0.791), TRANCO is slightly surpassed by the Baseline (0.793). The latter achieves the second-best scores in F1 (0.73), Accuracy (0.759), and $\kappa$ (0.518), but the lowest Recall (0.706), whereas Time windows achieves the second-best score (0.74). Besides the cited exceptions, Time windows have the worst values of F1 (0.71), Precision (0.723), Accuracy (0.715), and $\kappa$ (0.432).

We also classified four blocks at four levels of wheat aggregation to assess how normalization affected the classification’s spatial and temporal certainty (Figure 7). Specifically, in the Northwest (Figure 7a), it can be observed that TRANCO achieves higher probabilities for wheat crops in scenes from 2008 onward, while the other two approaches have probabilities closer to 0.5 in most cases. Nonetheless, in 2013, TRANCO tended to misclassify other crops as wheat, at least stronger than in the rest of the years. Note that this year shows the least proportion of wheat in the selected scene. Furthermore, as scene 8 is located in the Northwest of the USA, Time windows and the Baseline could be affected by spatial bias. In the East of the USA (Figure 7b), TRANCO has a heavier tendency to misclassify other crops as wheat, while the Baseline reduces these confusions in most of the cases, although it also suffers from the same problem through the different years. In contrast, in the Southeast of the USA (Figure 7c), TRANCO outperforms the Baseline and Time windows in all years and exhibits less class confusion. However, such misclassification persists across the three approaches. This could also be an effect of spatial bias in time window normalization and the Baseline. In the middle of the USA (Figure 7d), time-window normalization achieves better results; however, TRANCO and the Baseline probabilities better describe the CDL data. In addition, the Baseline is more variable over the years, while TRANCO shows more stable behavior.

6. Discussion

We have analyzed the applicability of the TRANCO algorithm in years for which it was not trained. The results show that TRANCO achieved generalizing the samples not only in space [36], but also in time. The JM distances, shown in Figure 3, are greater in Time windows and the Baseline with respect to TRANCO’s. Nonetheless, the TRANCO’s bell shape is softer than in previous results [36], likely due to an increase in the number of observations or poor phenological information. At the same time, the shape of the time window and the JM distance remained close to what we found before. In this respect, the Baseline improved, reducing its JM distance to 0.53 from 0.8 and showing a soft peak around DOY 125. The reason for the improvement of the Baseline is that, as we reduced our study area from the entire globe down to the USA extension, we are not expecting huge seasonality changes across the territory but in time. Yet, because of it, both normalizations, i.e., TRANCO and Time windows, should improve their own normalization performance; but that’s not the case. One possible reason for the lower normalization performance is the utilization of static Crop Calendars. In the Time windows approach, errors in the Crop Calendar for a specific year would lengthen the time series considered, thereby increasing the probability of introducing non-wheat signals. In the case of TRANCO, deviations in the Crop Calendar could increase the accumulated GDD. If the static Crop Calendars deviate in the EOS, the TRANCO curves are expected to lengthen and increase the total accumulated GDD, while also introducing greater variability from the temperature data. However, because temperatures are lower at the beginning of the wheat season, deviations in the SOS are not expected to significantly affect TRANCO performance. This could explain why JM distances in the Time windows approach do not decrease as much as TRANCO with respect to previous results, since larger errors in the EOS of the Crop Calendars are expected [67].

Although our main scope is not the development of a fine classification model, but use it as a proxy for the time-series normalization performance, it is interesting to check classification results in the literature. Neither of the approaches achieved results as high as those of other studies not contemplating the GDD, let them take care of spatial autocorrelation [36] or not [30,32,52,103,104]. Nevertheless, we have to take into consideration several issues:

1.

We are limited to the information common to Landsat-5, 7, and 8, which can lead to a reduction in the information needed to discern some crops. Also, to enable a limited comparison between what we obtained in this study and the results of our previous work [36], we omitted valuable information, such as the thermal bands from Landsat.

2.

The classification models are not the main focus of this thesis, but the normalization of the time-series through space and time. Thus, the classifiers act as an approximation of the performance of the normalizations, leaving the development of more thorough models to WorldCereal [34,35].

3.

Because of the temporal resolution of Landsat imagery (i.e., 16 days between passes) and the difficulties of finding enough cloud-free information, we aggregated Landsat information in composites of 30 days that we then interpolated daily to match AgERA-5 temporal resolution. Given the fast biophysical changes of crops, and especially cereals, along their growing season, this low temporal resolution might mask or minimize critical remote sensing signals. This risk is larger in the case of TRANCO, since we aggregated the accumulated GDD in 140 °C steps, which can mask more than 16 days depending on the daily temperatures. However, the accumulated GDD is used in a wide variety of studies to describe phenological stages; hence, it is not fully clear what effects such aggregation could have on TRANCO, and a more detailed study must be performed to clarify them.

4.

When aggregating Landsat 5 to 8 information, we did not account for algorithms to harmonize their data; hence, lower performance is expected. More importantly for classification, we did not fix Landsat-7’s strip problem, which could reduce the classification performance of the three approaches. Nonetheless, because of the averaging step in the normalization approaches, we expect this effect to be more pronounced in TRANCO, since each step does notcorrespond to a fixed number of days.

5.

We used the CDL as ground-truth data; however, its classification performances are not as high as other approaches found in the literature (F1 = 0.54), at least for the crops we considered as wheat (Table 1) and for the period considered. Nonetheless, some of the blocks considered, mainly those with high wheat aggregation, show high performance (F1 > 0.85). Hence, our classification performances do not strictly show how good classifiers are, but how well they describe the CDL dataset with its errors, which could make the interpretation of our results difficult.

For our classification approach, we assessed the best configuration of spatio-temporal groups to minimize autocorrelation in the models. A configuration of 2, 5, and 40 groups resulted as the best candidates to configure the models since they did not present spatio-temporal autocorrelation. Upon assessment, they determined that the best possible configuration is five groups and 15 features for Times windows and Baseline approaches, and 40 groups and 15 features for TRANCO. From these configurations, the Baseline seems to be the best approach, followed by the TRANCO-based model. However, once we applied these models to the validation period, TRANCO achieved the best results, followed by the Baseline-based model, and, with the worst performance, the Time windows model.

Across the three approaches, the JM distances indicating the importance of model features are similar for the top three features in TRANCO and Time windows. They differ in the moment of the season that the features describe and the source of such features, using TRANCO the EVI for the beginning of the season and the SIPI for the growing and peak of the season; while Time windows uses the SIPI and EVI for the beginning of the season and EVI for the peak of the season. In contrast, the top two and three features of the Baseline rely exclusively on the EVI. As SIPI is sensitive to the carotenoids to chlorophyll ratio, that would mean that TRANCO is giving more weight to such a ratio at the peak of the season than the other two approaches, which only rely on chlorophyll [105].

Furthermore, we deliberately created 40 areas distributed by spatial location and wheat label concentration, which we expected to represent wheat in both spatial and under areas with different wheat concentrations. In addition, within each block, we performed a sampling method specifically designed to address the spatio-temporal and categorical nature of the CDL dataset. Furthermore, both validations (i.e., in the training validation set and the validation period) made use of a spatial cross-validation approach to reduce as much as possible the spatial autocorrelation left in the samples. It should be noted that the validation period was evaluated year by year, meaning that errors from each year were independent of the others, whereas the validation performed during the training period considered all four years.

Also, climatology could affect the performance of the three approaches. However, declines in the classification performances (Figure 6a) do not follow the average dynamic of temperatures and precipitations in the blocks studied and during the study period. In addition, the variance of the CDL errors does not match our results, except for the 2013 and 2015 declines. In Figure 7a–d, it can be appreciated that in some years the errors of all the models worsen, probably because of the effects of a specific year on a specific location. For example, in the East of the USA (Figure 7b), the quality of the predictions in the year 2011 worsens with respect to the other years, while in the Northwest of the USA (Figure 7a), 2014 and 2008 are the worst years. Yet, there are other areas where the climate does not seem to have a strong effect (Figure 7c,d). These changes in prediction performance are likely due to climate, Landsat-7 striping issues, or CDL errors. Hence, further studies focused on classification should be performed.

Taking all that into account, and based on previous experiences [36], we suggest that the differences between the training and validation period errors are due to bias introduced by temporal autocorrelation in the training period, which artificially improves the Baseline’s results. In other words, the ability of TRANCO to keep the most relevant information about the crops allows it to have a more stable behavior over time. Yet, further and more detailed studies must be developed to ensure this.

Regarding time-series normalization with GDD, we note the study by Nyborg et al. [106], which was completely missed in our previous study [36]. However, although their approach is fully based on the performance of a more complex model than random forest, their results are pretty close to what we achieved for wheat in Europe with a jack-of-all-trades model (i.e., random forest). We think that such an endeavor has its roots in attending to key features of croplands when normalizing time-series: biofix date and basal temperatures; something that their study can benefit from. Even better, they achieved a remarkable feat: to discern winter wheat from winter barley relying only on Sentinel-2 imagery, which is a good result in itself. Nonetheless, no further crop-specific errors are shown. Based on this work, ref. [107] tested the approach’s sensitivity across different machine-learning models, including a temporal case. Focusing on the latter, their overall results for random forest match our average F1 metric for the unseen years (0.79), though both approaches are not exactly the same. Nonetheless, both studies provide evidence for the applicability of TRANCO across a wider range of crops and over time.

Finally, to our knowledge, no prior attempt to classify past years based on recent years has been performed. Hence, our normalization and classification results set this study apart.

7. Conclusions

In this work, we tested TRANCO’s performance in normalizing time series over different years. We also compared it with two other approaches: Time windows for time-series normalization, and a Baseline representing time-series without further processing. Although not central to this research, we also trained three random forest classifiers to approximate the quality of the normalization. The assumption for this approximation was that a better normalization implies a better quality of the data fed into the classifier and, hence, better classification results, at least for the random forest case.

Looking at normalization performance, measured in JM distances, we found that TRANCO had the best normalization (0.3) compared with Time windows (0.4). Moreover, based on the classification results (F1) for the validation period (2008–2016), we found that TRANCO performed best (0.779) compared with the Baseline (0.730) and Time windows (0.710) approaches. In addition, TRANCO showed the most stable behavior during the validation period, with the best model’s performance and the most stable model following the average performance of 20 iterations closely. This has not occurred to the same extent in the Time windows approach or in the Baseline. However, TRANCO’s performance during the training period (0.807) was lower than the Baseline’s (0.821). Since we did not account for temporal autocorrelation in this step, this suggests that TRANCO handles autocorrelation better; however, a more detailed analysis is still required.

Therefore, we conclude that TRANCO is applicable not only in space, but also through time. Yet, the performance in other crops, such as maize or soy, or at larger spatio-temporal scales, remains to be explored. Furthermore, these results also open the possibility for classifying years without categorical data, rebuilding the lost location of crop types through time.