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Figure 1 presents the average monthly energy expenditure at the household level based on USD across the 37 surveyed nations. The households in Singapore expend the most amount of energy, that is, 748 USD each month on average. The energy consumption appears positively associated with the economic development level; for example, households from high-income countries, including France, Italy, Japan and the US, tend to consume more energy than those from low-income countries (e.g., Kazakhstan, Myanmar, and Mongolia). In India, Indonesia, and Vietnam, households with higher income expend more on energy than rural/slum households. For the energy expenditure to household income ratio, strong trends were not found between developing and developed countries. Notably, middle-income countries (e.g., Greece, Chile, Brazil, Egypt) spend a relatively higher share of total income on energy.Figure 1Average monthly energy expenditure at the household level across the 37 surveyed nations. Data source: Original survey.Full size imageThe relationship between subjective well-being and energy consumption expenditure based on the ordered logit, ordered probit, and OLS models is shown in Table 2, panel A. The LR Chi-Square test and Pseudo R-squared for the ordered logistic regression model and the ordered probit model were applied to measure the goodness of the fit, whereas F-statistics and adjusted R-squared were used for the OLS model. For the validation of the measurement of subjective well-being, life satisfaction and happiness measures were used. Importantly, the results from variated regression models are consistent, indicating a positive relationship between household energy consumption expenditure and the improvement of individuals’ subjective well-being. Regarding the model’s goodness of fit, the LR Chi-Square test with ordered logit and probit models, and the F-statistic in the OLS model are all statistically significant at 0.1%, which validates the regression model. As the consistency of the robustness results is derived from different models, the ordered logit model is applied in Table 2 (Panel B).Table 2 Association between energy consumption expenditure and subjective well-being in high- and non-high-income countries.Full size tableWith the control variables being constant, energy consumption expenditure improves subjective well-being, including life satisfaction and happiness. The coefficients for the relationship of energy consumption with life satisfaction and with happiness are 0.018 and 0.008, respectively, and they are statistically significant at the 1% level; in other words, there is increased energy consumption for people who are satisfied with their lives and are happier. This is because electricity, water, gas, or gasoline are indispensable consumption goods in daily life. The results suggest that when policies lead to a reduction in the consumption of these goods at the household level, the life satisfaction of citizens is likely to decrease. When reducing energy consumption at the household level to reduce the emission of greenhouse gases, the conflicts of interest of individuals in these households (given that they derive life satisfaction from energy consumption) pose a challenge to policymakers; therefore, policymakers should devise strategies to improve both citizens’ living standards and environmental preservation.Referring to the criteria developed by the World Bank, the standard classification of high-income nations and non-high-income nations is as follows. Based on the 2017 gross national income (GNI) per capita, the World Bank List of Economies (June 2018) presented the following criteria for nations to be classified as high-income and non-high-income nations, respectively: a GNI per capita of $12,056 or higher, and less than $12,056. According to this standard of classification, in this study, high-income nations comprise Japan, Singapore, Chile, Australia, the United States, Germany, the United Kingdom, France, Spain, Italy, Sweden, Canada, Netherlands, Greece, Hungary, Poland, and the Czech Republic, whereas non-high-income nations comprise Thailand, Malaysia, Indonesia, Vietnam, Philippines, Mexico, Venezuela, Brazil, Colombia, South Africa, India, Myanmar, Kazakhstan, Mongolia, Egypt, Russia, China, Turkey, Romania, and Sri Lanka.Regarding the comparison of high- and non-high-income countries, energy consumption at the household level is more likely to lead to life satisfaction in non-high-income than in high-income countries. In high-income countries, the coefficients for the relationship of energy consumption with life satisfaction and with happiness are 0.010 and 0.003, respectively; these coefficients are 0.035 and 0.015, respectively, among non-high-income countries. Hence, in both high-income and non-high-income countries, an increase in energy consumption leads to an increase in life satisfaction; nonetheless, energy consumption is more crucial for households in non-high-income countries. Compared to the effect of energy consumption on satisfaction in high-income countries and non-high-income countries, individuals living in less urbanized countries appear more satisfied with energy consumption.Table 3 presents the association between life satisfaction and energy consumption expenditure at the household level in each country by estimating Eq. (2) based on the ordered logit model for each country. There is a positive relationship between energy consumption expenditure and life satisfaction in 27 out of the 37 nations. For example, the coefficient of this relationship is 0.062 in Brazil, and is statistically significant at the 1% level. An increase in energy consumption expenditure positively impacts the life satisfaction of households in Brazil, meaning that individuals with greater energy expenditure tend to be satisfied with their lives. Similar results are found in other countries: Canada, Chile, China, Egypt, France, Germany, Greece, India, Indonesia, Italy, and Japan. As life satisfaction is a proxy of well-being, energy consumption is expected to increase when households can afford more energy to obtain higher life satisfaction. These results indicate that most of the developed and developing countries analyzed face a conflict of interest in addressing individuals’ life satisfaction and environment conservation goals; these countries include China and India that are home to large populations that have a positive desire for energy consumption.Table 3 Relationship between energy expenditure and life satisfaction for each country.Full size tableHowever, the association between life satisfaction and energy consumption expenditure at the household level was non-significant across some countries. In Australia, the coefficient of this association is positive but not statistically significant; hence, an increase in energy expenditure is not completely associated with life satisfaction at the household level here. Similar results are found in the Netherlands, Hungary, Sweden, Singapore, Poland, the Czech Republic, and Colombia. In these countries, energy consumption is at an adequate level, and additional energy consumption does not lead to higher life satisfaction. It may be that households consume an adequate amount of energy with their income and energy price.Tables 4, 5, 6, and 7 display the determinant factors of household energy consumption in 37 nations by estimating the energy demand equation for each country using Eq. (3). The key energy consumption metric is the quantity of energy consumed (e.g., kWh) across the targeted households. Since price information is limited, transforming consumption expenditure into a quantity (e.g., kWh) is problematic. As explained earlier, this study adopted the energy demand equation.Table 4 Household socioeconomic and demographic determinants of household energy consumption expenditure I.Full size tableTable 5 Household socioeconomic and demographic determinants of household energy consumption expenditure II.Full size tableTable 6 Household socioeconomic and demographic determinants of household energy consumption expenditure III.Full size tableTable 7 Household socioeconomic and demographic determinants of household energy consumption expenditure IV.Full size tableThere are positive relationships between energy consumption expenditure at the household level and household income across countries. If the coefficients for household income are positive and statistically significant, this means that energy consumption expenditure at the household level would increase with an increase in household income ensuing from economic development in the country, ceteris paribus. The positive coefficients for the association between energy consumption expenditure and household income range from 0.756 (Japan) to 3.613 (the Philippines) in our sample, indicating that an additional 10,000 USD would lead to an additional energy consumption expenditure at the household level of approximately 17.3% (Japan) – 445% (Mongolia). The number is calculated using the magnitude of the coefficient/energy consumption expenditure. The results also show that homeowners tend to consume more energy than renters in Australia, Brazil, Canada, Chile, China, Colombia, Germany, India, Italy, Japan, Malaysia, Mexico, Russia, the United States, and Vietnam. This indicates that if individuals live in their own houses, the household energy consumption expenditure tends to be higher owing to the wealth effect, as energy is a normal consumption good. Overall, the wealth effect on energy consumption expenditure at the household level is increasing in our sample, and with economic development, energy consumption may increase.The following factors are confirmed to reduce energy consumption at the household level: (1) energy-curtailment behavior regarding electricity, (2) higher education, and (3) age. The energy-saving effect is confirmed in households. In Canada, the coefficient of energy-saving behaviors is -0.642, indicating that households consume 12.5% less energy when they adopt both energy curtailment behavior and non-saving groups (64.2/513). The Canadian household average energy consumption is 513 USD. Similar results are seen in Colombia, Germany, India, Indonesia, Italy, Japan, the Netherlands, Poland, Russia, Turkey, the United Kingdom, and the United States. The magnitude of the effect of energy curtailment behavior ranged from 6.4% (Russia) to 32% (India) less energy consumption expenditure. Hence, energy-saving behaviors have a favorable effect on environmentally preferable outcomes. By contrast, households in Indonesia save electricity as they tend to spend more on purchasing energy.Individuals with higher education tend to save energy in 23 out of the 37 nations. For instance, the coefficient for individuals with university-level education is -2.292 and statistically significant at the 1% level. This suggests that households with individuals who have university-level education have less energy consumption expenditure than households with individuals with junior high school or lower levels of education. Similar results are seen in Brazil, Canada, Chile, Colombia, the Czech Republic, France, Germany, Hungary, India, Indonesia, Japan, Malaysia, the Netherlands, the Philippines, Poland, Russia, Singapore, South Africa, Spain, Sweden, Turkey, the United Kingdom, and the United States. Encouraging households to engage in energy curtailment behaviors and higher educational attainment may lead to environment-friendly outcomes.Surprisingly, purchasing energy-saving household products has a limited effect on reducing energy consumption expenditure at the household level. The coefficients for purchasing energy-saving household products are negative, ranging between -0.044 and -0.763, and are statistically significant in Australia, Canada, the Czech Republic, Italy, and Kazakhstan. Hence, the purchase of these products in these five countries decreases energy expenditure from 2.9% (China) to 14% (Australia). However, the relationship between energy consumption expenditure at the household level and purchasing energy-saving household products is non-significant in the other countries. Moreover, in Poland and Turkey, households that purchase these products consume more energy than those that do not. Therefore, purchasing energy-saving household products has a limited contribution to energy saving at the household level.The findings also show that older individuals tend to have lower energy consumption. The coefficients for the age variable are negative and statistically significant in 30 countries (out of 37). The effect of age on energy consumption expenditure ranges between -0.003 and -0.148, indicating that as the average age of individuals increases by one year, their monthly energy consumption expenditure reduces from 0.3–14.8 USD. This may be because older individuals are more likely to live frugally. More

DatasetsImage acquisitionFor this study, we assembled three datasets: one for training of the RootDetector Convolutional Neural Network (Training-Set), one for a performance comparison between humans and RootDetector in segmenting roots in minirhizotron images (Comparison-Set), and one for the validation of the algorithm (Validation-Set). The Training-Set contained 129 images comprised of 17 randomly selected minirhizotron images sampled in a mesocosm experiment (see “Mesocosm sampling” Section), 47 randomly selected minirhizotron images sampled in a field study (see “Field sampling” Section) as well as the 65 minirhizotron images of soy roots published by Wang et al.15. The Comparison-Set contained 25 randomly selected minirhizotron images from the field-study which all were not part of the images included in the Training- and Validation-Sets. The Validation-Set contained 10 randomly selected minirhizotron images from the same field study, which had not been used in the Training-Set. All images were recorded with 2550 ✕ 2273 pixels at 300 dpi with a CI-600 In-Situ Root Imager (CID Bio-Science Inc., Camas, WA, USA) and stored as .tiff files to reduce compression loss. For all training and evaluation purposes we used raw, unprocessed output images from the CI-600.Mesocosm samplingThe mesocosm experiment was established in 2018 on the premises of the Institute for Botany and Landscape Ecology of the University of Greifswald (Fig. S1). It features 108 heavy duty plastic buckets of 100 l each, filled to two thirds of their height with moderately decomposed sedge fen peat. Each mesocosm contained one minirhizotron (inner diameter: 64 mm, outer diameter: 70 mm, length: 650 mm) installed at a 45°angle and capped in order to avoid penetration by light. The mesocosms were planted with varying compositions of plant species that typically occur in north-east German sedge fens (Carex rostrata, Carex acutiformis, Glyceria maxima, Equisetum fluviatile, Juncus inflexus, Mentha aquatica, Acorus calamus and Lycopus europaeus). The mesocosms were subjected to three different water table regimes: stable at soil surface level, stable at 20 cm below soil surface and fluctuating between the two levels every two weeks. The minirhizotrons were scanned weekly at two levels of soil depth (0–20 cm and 15–35 cm) between April 2019 and December 2021, resulting in roughly 9500 minirhizotron images of 216 × 196 mm. Manual quantification of root length would, based on own experience, take approximately three hours per image, resulting in approximately 28,500 h of manual processing for the complete dataset. Specimens planted were identified by author Dr. Blume-Werry, however no voucher specimen were deposited. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation.Field samplingThe field study was established as part of the Wetscapes project in 201716. The study sites were located in Mecklenburg-Vorpommern, Germany, in three of the most common wetland types of the region: alder forest, percolation fen and coastal fen (Fig. S2). For each wetland type, a pair of drained versus rewetted study sites was established. A detailed description of the study sites and the experimental setup can be found in Jurasinski et al.16. At each site, 15 minirhizotrons (same diameter as above, length: 1500 mm) were installed at 45° angle along a central boardwalk. The minirhizotrons have been scanned biweekly since April 2018, then monthly since January 2019 at two to four levels of soil depth (0–20 cm, 20–40 cm, 40–60 cm and 60–80 cm), resulting in roughly 12,000 minirhizotron images of 216 × 196 cm, i.e. an estimated 36,000 h of manual processing for the complete dataset. Permission for the study was obtained from the all field owners. Figure 1Overview of the RootDetector system. The main component is a semantic segmentation network based on the U-Net architecture. The root length is estimated by skeletonizing the segmentation output and applying the formula introduced by Kimura et al.17. During training only, a weight map puts more emphasis on fine roots.Full size imageThe CNN RootDetectorImage annotationFor the generation of training data for the CNN, human analysts manually masked all root pixels in the 74 images of the Training-Set using GIMP 2.10.12. The resulting ground truth data are binary, black-and-white images in Portable Network Graphics (.png) format, where white pixels represent root structures and black pixels represent non-root objects and soil (Fig. 2b). All training data were checked and, if required, corrected by an expert (see “Selection of participants” for definition). The Validation-Set was created in the same way but exclusively by experts.Figure 2Example of segmentation and result of skeletonization. A 1000 by 1000 pixel input image (a), the manually annotated ground truth image (b), the RootDetector estimation image (c), the combined representation image (error map, d with green indicating true positives, red indicating false positive, blue indicating false negatives), the skeletonized RootDetector estimation image (e), and the skeletonized ground truth image (f).Full size imageArchitectureRootDetector’s core consists of a Deep Neural Network (DNN) based on the U-Net image segmentation architecture[27]nd is implemented in TensorFlow and Keras frameworks18. Although U-Net was originally developed for biomedical applications, it has since been successfully applied to other domains due to its generic design.RootDetector is built up of four down-sampling blocks, four up-sampling blocks and a final output block (Fig. 1). Every block contains two 3 × 3 convolutional layers, each followed by rectified linear units (ReLU). The last output layer instead utilizes Sigmoid activation. Starting from initial 64 feature channels, this number is doubled in every down-block and the resolution is halved via 2 × 2 max-pooling. Every up-block again doubles the resolution via bilinear interpolation and a 1 × 1 convolution which halves the number of channels. Importantly, after each up-sampling step, the feature map is concatenated with the corresponding feature map from the down-sampling path. This is crucial to preserve fine spatial details.Our modifications from the original architecture include BatchNormalization19 after each convolutional layer which significantly helps to speed up the training process and zero-padding instead of cropping as suggested by Ronneberger, Fischer, & Brox20 to preserve the original image size.In addition to the root segmentation network, we trained a second network to detect foreign objects, specifically the adhesive tape that is used as a light barrier on the aboveground part of the minirhizotrons. We used the same network architecture as above and trained in a supervised fashion with the binary cross-entropy loss. During inference, the result is thresholded (predefined threshold value: 0.5) and used without post-processing.TrainingWe pre-trained RootDetector on the COCO dataset21 to generate a starting point. Although the COCO dataset contains a wide variety of image types and classes not specifically related to minirhizotron images, Majurski et al.22 showed, that for small annotation counts, transfer-learning even from unrelated datasets may improve a CNNs performance by up to 20%. We fine-tuned for our dataset with the Adam optimizer23 for 15 epochs and trained on a total of 129 images from the Training-Set (17 mesocosm images, 47 field-experiment images, 65 soy root images). To enhance the dataset size and reduce over-fitting effects, we performed a series of augmentation operations as described by Shorten & Khoshgoftaar24. In many images, relatively coarse roots ( > 3 mm) occupied a major part of the positive (white) pixel space, which might have caused RootDetector to underestimate fine root details overall. Similarly, negative space (black pixels) between tightly packed, parallel roots was often very small and might have impacted the training process to a lesser extent when compared to large areas with few or no roots (Fig. 2). To mitigate both effects, we multiplied the result of the cross-entropy loss map with a weight map which emphasizes positive–negative transitions. This weight map is generated by applying the following formula to the annotated ground truth images:$$omega left( x right) = 1 – left( {tanh left( {2tilde{x} – 1} right)} right)^{2}$$
(1)
where ω(x) is the average pixel value of the annotated weight map in a 5 × 5 neighborhood around pixel x. Ronneberger, Fischer, & Brox20 implemented a similar weight map, however with stronger emphasis on space between objects. As this requires computation of distances between two comparatively large sets of points, we adapted and simplified their formula to be computable in a single 5 × 5 convolution.For the loss function we applied a combination of cross-entropy and Dice loss 25:$${mathcal{L}} = {mathcal{L}}_{CE} + lambda {mathcal{L}}_{Dice} = – frac{1}{N}sumnolimits_{i} {wleft( {x_{i} } right)y_{i} log left( {x_{i} } right) + lambda frac{{2sumnolimits_{i} {x_{i} y_{i} } }}{{sumnolimits_{i} {x_{i}^{2} sumnolimits_{i} {y_{i}^{2} } } }}}$$
(2)

where x are the predicted pixels, y the corresponding ground truth labels, N the number of pixels in an image and λ a balancing factor which we set to 0.01. This value was derived empirically. The Dice loss is applied per-image to counteract the usually high positive-to-negative pixel imbalance. Since this may produce overly confident outputs and restrict the application of weight maps, we used a relatively low value for λ.Output and post-processingRootDetector generates two types of output. The first type of output are greyscale .png files in which white pixels represent pixels associated with root structures and black pixels represent non-root structures and soil (Fig. 2c). The advantage of .png images is their lossless ad artifact-free compression at relatively small file sizes. RootDetector further skeletonizes the output images and reduces root-structures to single-pixel representations using the skeletonize function of scikit-image v. 0.17.1 (26; Fig. 2e,f). This helps to reduce the impact of large diameter roots or root-like structures such as rhizomes in subsequent analyses and is directly comparable to estimations of root length. The second type of output is a Comma-separated values (.csv) file, with numerical values indicating the number of identified root pixels, the number of root pixels after skeletonization, the number of orthogonal and diagonal connections between pixels after skeletonization and an estimation of the physical combined length of all roots for each processed image. The latter is a metric commonly used in root research as in many species, fine roots provide most vital functions such as nutrient and water transport3. Therefore, the combined length of all roots in a given space puts an emphasis on fine roots as they typically occupy a relatively smaller fraction of the area in a 2D image compared to often much thicker coarse roots. To derive physical length estimates from skeletonized images, RootDetector counts orthogonal- and diagonal connections between pixels of skeletonized images and employs the formula proposed by Kimura et al.17 (Eq. 3).$$L = left[ {N_{d}^{2} + left( {N_{d} + N_{o} /2} right)^{2} } right]^{{1/2}} + N_{o} /2$$
(3)
where Nd is the number of diagonally connected and No the number of orthogonally connected skeleton pixels. To compute Nd we convolve the skeletonized image with two 2 × 2 binary kernels, one for top-left-to-bottom-right connections and another for bottom-left-to-top-right connections and count the number of pixels with maximum response in the convolution result. Similarly, No is computed with a 1 × 2 and a 2 × 1 convolutional kernels.Performance comparisonSelection of participantsFor the performance comparison, we selected 10 human analysts and divided them into three groups of different expertise levels in plant physiology and with the usage of digital root measuring tools. The novice group consisted of 3 ecology students (2 bachelor’s, 1 master’s) who had taken or were taking courses in plant physiology but had no prior experience with minirhizotron images or digital root measuring tools. This group represents undergraduate students producing data for a Bachelor thesis or student assistants employed to process data. The advanced group consisted of 3 ecology students (1 bachelor’s, 2 master’s) who had already taken courses in plant physiology and had at least 100 h of experience with minirhizotron images and digital root measuring tools. The expert group consisted of 4 scientists (2 PhD, 2 PhD candidates) who had extensive experience in root science and at least 250 h of experience with digital root measuring tools. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation and informed consent was obtained from all participants.Instruction and root tracingAll three groups were instructed by showing them a 60 min live demo of an expert tracing roots in minirhizotron images, during which commonly encountered challenges and pitfalls were thoroughly discussed. Additionally, all participants were provided with a previously generated, in-depth manual containing guidelines on the identification of root structures, the correct operation of the root tracing program and examples of often encountered challenges and suggested solutions. Before working on the Comparison-Set, all participants traced roots in one smaller-size sample image and received feedback from one expert.Image preparation and root tracingBecause the minirhizotron images acquired in the field covered a variety of different substrates, roots of different plant species, variance in image quality, and because tracing roots is very time consuming, we decided to maximize the number of images by tracing roots only in small sections, in order to cover the largest number of cases possible. To do this, we placed a box of 1000 × 1000 pixels (8.47 × 8.47 cm) at a random location in each of the images in the Comparison-Set and instructed participants to trace only roots within that box. Similarly, we provided RootDetector images where the parts of the image outside the rectangle were occluded. All groups used RootSnap! 1.3.2.25 (CID Bio-Science Inc., Camas, WA, USA;27), a vector based tool to manually trace roots in each of the 25 images in the comparison set. We decided on RootSnap! due to our previous good experience with the software and its’ relative ease of use. The combined length of all roots was then exported as a csv file for each person and image and compared to RootDetector’s output of the Kimura root length.ValidationWe tested the accuracy of RootDetector on a set of 10 image segments of 1000 by 1000 pixels cropped from random locations of the 10 images of the Validation-Set. These images were annotated by a human expert without knowledge of the estimations by the algorithm and were exempted from the training process. As commonly applied in binary classification, we use the F1 score as a metric to evaluate the performance RootDetector. F1 is calculated from precision (Eq. 4) and recall (Eq. 5) and represents their harmonic mean (Eq. 6). Ranging from 0 to 1, higher values indicate high classification (segmentation) performance. As one of the 10 image sections contained no roots and thus no F1 Score was calculable, it was excluded from the validation. We calculated the F1 score for each of the nine remaining image sections and averaged the values as a metric for overall segmentation performance.$$Precision;(P) = frac{{tp}}{{tp + fp}}$$
(4)
$$Recall;(R) = frac{{tp}}{{tp + fn}}$$
(5)
$$F1 = 2*frac{{P*R}}{{P + R}}$$
(6)
where P = precision, R = recall, tp = true positives; fp = false positives, fn = false negatives.Statistical analysisWe used R Version 4.1.2 (R Core Team, 2021) for all statistical analyses and R package ggplot2 Version 3.2.128 for visualizations. Pixel identification-performance comparisons were based on least-squares fit and the Pearson method. Root length estimation-performance comparisons between groups of human analysts (novice, advanced, expert) and RootDetector were based on the respective estimates of total root length plotted over the minirhizotron images in increasing order of total root length. Linear models were calculated using the lm function for each group of analysts. To determine significant differences between the groups and the algorithm, 95% CIs as well as 83% CIs were displayed and RootDetector root length outside the 95% CI were considered significantly different from the group estimate at α = 0.0529. The groups of human analysts were considered significantly different if their 83% CIs did not overlap, as the comparison of two 83% CIs approximates an alpha level of 5%30,31.This study is approved by Ethikkommission der Universitätsmedizin Greifswald, University of Greifswald, Germany. More

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