Interpolation of environmental data using deep learning and model inference

The temporal resolution of environmental data sets plays a major role in the granularity of the information that can be derived from the data. In most cases, it is required that different data sets have a common temporal resolution to enable their consistent evaluations and applications in making informed decisions. This study leverages deep learning with long short-term memory (LSTM) neural networks and model inference to enhance the temporal resolution of climate datasets, specifically temperature, and precipitation, from daily to sub-daily scales. We trained our model to learn the relationship between daily and sub-daily data, subsequently applying this knowledge to increase the resolution of a separate dataset with a coarser (daily) temporal resolution. Our findings reveal a high degree of accuracy for temperature predictions, evidenced by a correlation of 0.99 and a mean absolute error of 0.21 °C, between the actual and predicted sub-daily values. In contrast, the approach was less effective for precipitation, achieving an explained variance of only 37%, compared to 98% for temperature. Further, besides the sub-daily interpolation of the climate data sets, we adapted our approach to increase the resolution of the Normalized difference vegetation index of Landsat (from 16 d to 5 d interval) using the LSTM model pre-trained from the Sentinel 2 Normalized difference vegetation index—that exists at a relatively higher temporal resolution. The explained variance between the predicted Landsat and Sentinel 2 data is 70% with a mean absolute error of 0.03. These results suggest that our method is particularly suitable for environmental datasets with less pronounced short-term variability, offering a promising tool for improving the resolution and utility of the data.


Introduction
Environmental data such as climate and remote sensing data sets are essential for understanding the dynamics of the Earth's climate system and predicting future changes in the environment [1][2][3].However, many climate and remote sensing datasets have a low temporal resolution, typically recorded at daily or monthly intervals [4,5].The limited temporal resolution of these data sets presents significant challenges in extracting detailed insights and limits their utility for analyzing rapid, transient events [6,7].This constraint hinders a comprehensive understanding of environmental changes, especially in the context of short-term variations and extreme weather phenomena.Moreover, evaluation of the same data (variable) created from different sources or the same source but with different techniques often requires the evaluated data sets to have a common temporal resolution and coverage.Hence to improve the utility of environmental data in analyzing short-term variations, there is the need to utilize high-resolution data sets, typically sub-daily.This limited resolution of climate and remote sensing data sets results from various factors such as data collection methods, storage, and transmission limitations.Many observation networks were designed to collect data at coarser temporal resolutions, prioritizing ease of collection and resource efficiency over high-frequency measurements [8,9].Also, storage and data transmission capacities can be limited, making it impractical to collect and store large amounts of high-resolution data [9].Indeed, collecting and maintaining high-frequency data sets requires significant resources, including equipment, maintenance, and personnel, which can be cost-prohibitive for many organizations.The low temporal resolution of climate data, for example, poses significant limitations for climate analysis, such as reduced accuracy and limited process understanding [10].Coarse-resolution data can lead to inaccurate representation of climate phenomena [11,12], such as rapid weather events or diurnal temperature cycles.Low-resolution data might obscure important climate processes, like cloud formation, atmospheric circulation, and surface exchange, making it challenging to develop and rigorously validate climate models [13].
To address these limitations, various interpolation methods have been developed to estimate missing data and increase the temporal resolution of climate and remote sensing datasets [14][15][16].Traditional methods such as linear, spline, and nearest neighbor interpolation have been applied for the imputation of missing values in univariate time series [17].While these methods are computationally efficient and straightforward to implement, they have significant weaknesses.First is an oversimplification of complex climate processes, which often exhibit nonlinear behavior.Second is the limited flexibility of the techniques that make it impossible to adjust the techniques to adapt to the nature of the data considered.
Nonlinear interpolation techniques, such as artificial neural networks (ANN), support vector machines, etc, offer a more sophisticated approach to address the limitations of traditional methods.These techniques can capture complex relationships between climate variables, allowing for more accurate estimates of missing data.For example, [18] applied the long short-term memory (LSTM) neural network to predict missing temperature data.Antonić and Križan [19] applied ANN for spatiotemporal interpolation of climatic variables and found promising results.Other studies have equally applied ANN and other advanced machine-learning techniques for spatiotemporal interpolations of environmental data leading to satisfactory results [20][21][22][23][24][25][26][27][28][29][30].Also, most of the existing methods utilize linear interpolation schemes or other linear techniques such as empirical orthogonal function analysis before applying ANN in spatiotemporal predictions of environmental data [31][32][33].While promising, the performance of these hybrid methods heavily depends on the quality of the interpolation before ANN processing.For example, the study by [20] suggested that ANN can offer superior performance in interpolation/extrapolation of environmental data over traditional linear interpolation methods that can be associated with relatively more biases.Thus, we will leverage the strength of deep learning in interpolating various environmental data sets.Furthermore, most of these methods are applied as data imputation techniques to estimate missing data or interpolate data to a coarser resolution other than sub-daily.In the same paradigm, comparing the performance of the ANN interpolation for different environmental data sets (i.e.modelled climate data, observational climate data, and remote sensing data) with unique spatiotemporal characteristics has not been rigorously documented.Hence the focus of this study is to introduce a deep learning and model inference (i.e. using a trained model to make predictions on new data) approach to interpolate daily climate data to a sub-daily scale.The approach is also tested in increasing the resolution of the Normalized difference vegetation index (NDVI) from Landsat to be consistent with Sentinel 2 remote sensing data.The performance of the ANN model is compared across various data sets.
The complexity of environmental data sets, such as climate data sets is variable.For example, it is relatively easier to characterize the processes associated with sub-daily temperature compared to precipitation.The Flexibility and adaptability of ANN models often make them desirable tools in modeling the wide range of differing complex behaviors inherent in the data.As ANN models require high-quality and abundant training data to learn meaningful relationships, we combine deep LSTM and model inference to learn the relationship between high-resolution and low-resolution versions of climate model data that extends back to the 1850s, and then use the pre-trained model to predict sub-daily temperature and precipitation, respectively.The major progress in this study is (1) to introduce a novel technique combining deep learning and model inference in enhancing the temporal resolution of various environmental data sets; (2) to compare the results to other existing machine learning techniques, i.e. support vector regression; (3) and further evaluate the relative added value of the approach for different climate data sets, as well for a remote sensing data.

Data
The Max Planck Institute Earth System Model lower-resolution version [34] (MPI-ESM-LR) produces simulations with different temporal resolutions.In this study, we utilized the simulated 6 hourly and daily global temperatures and precipitation from the Coupled Model Intercomparison Project Phase 6 MPI-ESM-LR model.The horizontal resolution of the MPI-ESM-LR model is ∼200 km.The data sets were obtained from 1850 to 2014; we computed global averages for subsequent analysis.
For the remote sensing data (i.e.NDVI), we utilized Landsat 8, a satellite managed by the National Aeronautics and Space Administration and the United States Geological Survey, known for its spatial resolution of 30 m for most bands, 15 m for the panchromatic band, and 100 m for thermal bands, with a temporal resolution of approximately 16 d.We also utilized NDVI data from Sentinel-2, a mission coordinated and managed by the European Commission in partnership with the European Space Agency, European Union Member States, and European Union agencies.Sentinel-2 offers a spatial resolution of 10 m for visible and near-infrared bands, 20 m for additional near-infrared and short-wave infrared bands, and 60 m for atmospheric correction bands.Its temporal resolution is 5 d at the equator, improving at higher latitudes due to overlapping satellite coverage.Figure 1 shows the farmland in Egypt where we obtained the NDVI data.We chose this area because of the very low percentage of cloud cover in the region, which is necessary for optimal analysis from optical data sets used in this study, i.e.Landsat 8 and Sentinel-2.The NDVI data from the farmlands were averaged and used for further analysis.

Methods
A deep LSTM model, effective in capturing temporal dependencies and patterns in time-series data, was utilized for temporal interpolation of the climate data sets.LSTM models are a type of recurrent neural network specifically designed to address the challenge of learning long-term dependencies in data sequences.They are composed of units called LSTM cells, which allow the model to regulate the flow of information through three main mechanisms: input gates, output gates, and forget gates.These gates collaboratively determine which information is significant to keep, pass along, or discard, enabling LSTMs to capture long-term relationships in the data effectively.This makes LSTMs particularly useful for tasks involving sequential data such as time series forecasting.
For the climate data, our application of the LSTM involves aggregating the 6-hourly data to daily; training the LSTM model to learn the relationship between the aggregated daily data and the original 6-hourly data and using the pre-trained model to increase the resolution of the (separate) daily version of the MPI-ESM-LR model to 6-hourly.Though this might be considered an aspect of transfer learning since the deep learning model is trained and tested using high-resolution (6-hourly) data, and then applied to new coarser (daily) data to increase its resolution to sub-daily, however since the trained model is not fine-tuned, the approach better suits model inference.
Figure 2 shows the flow chart of the LSTM model and the steps followed in applying it to improve the temporal resolution of the climate model data.The first step involves pre-processing the input 6-hourly data.The input data is aggregated to daily data and the daily values are repeated/duplicated to align with 6-hourly sub-daily values.The predictor is the daily values and the predictand is the 6-hourly values.
In the second step, the data set from 1850 to 2014 is split into training, test, and validation sets.80% of the total data is used for the training set and the remaining 20% for the test set.20% of the 80% training set was used as the validation set for tuning the model hyperparameters.
The third step involves building the deep LSTM model architecture.The construction of the deep LSTM model is a pivotal step in our methodology.This model architecture begins with an LSTM layer comprising 100 neurons.This configuration was chosen based on experimental evaluations aimed at optimizing predictive accuracy on the validation set, ensuring the model effectively generalizes to unseen data.The LSTM layer in Keras [35], which we utilize, inherently incorporates the constant error carousel mechanism, a fundamental aspect of LSTM functionality.Our model employs a standard LSTM architecture, where the tanh activation function is used for the cell state, and sigmoid activation is applied to the gates.These choices are intrinsic to Keras's LSTM design.The initial LSTM layer is configured to return sequences, a crucial feature that enables the chaining of LSTM layers.This setup enhances the model's capacity to capture more complex patterns and dependencies in the data.
Following the first LSTM layer, we introduce a second LSTM layer, this time with 50 neurons.This additional layer further contributes to the model's depth and complexity and through experimentation was found to improve predicted values.The architecture concludes with a dense layer consisting of a single neuron.This layer is responsible for producing the predicted 6-hourly values, which is the primary output of our model.
In the compilation phase, we opt for the Adam optimizer [36], renowned for its efficiency in handling sparse gradients on noisy problems.The loss function employed is the Mean Squared Error (MSE), a standard choice for regression problems.Following experimentation of different hyperparameters to ensure an optimal model and reduce the risk of overfitting, the LSTM model is trained using the following parameters: a maximum of 50 epochs, a batch size of 32, and a learning rate of 0.001.To prevent overfitting, we implement early stopping with a patience of 5 epochs, monitoring the validation loss.This implies that the training stops when the model validation loss does not improve after 5 consecutive epochs.The same approach applied to the climate data was also utilized for the NDVI data, but in this case, we trained the deep LSTM to learn the relationship between 5 d and 16 d data using the Sentinel 2 data, the pre-trained model is used to increase the resolution of the Landsat data from 16 d interval to 5 d interval.
The predictions are first evaluated on the test data using several metrics such as the mean absolute error (MAE) (equation ( 1)), root mean square error (RMSE) (equation ( 2)), Pearson correlations; and hit rate (equation ( 3)), false alarm ratio (FAR) (equation ( 4)), critical success index (CSI) (equation ( 5)) for cold and warm extremes based on 5 percentile and 95 percentiles of the actual values respectively, for temperature and using the 0.1 threshold to designate hours with rain for precipitation data.The MAE measures the average magnitude of errors in a set of predictions, without considering their direction.RMSE assesses the square root of the average squared differences between predicted and actual values, emphasizing larger errors.Pearson Correlations evaluates the linear relationship between predicted and actual values, indicating how well the predictions match the actual values.Hit rate captures the proportion of correctly predicted events (e.g.temperature extremes or rain occurrences) to the total actual events.FAR measures the proportion of incorrect positive predictions (e.g.predicted but not actual extremes or rain) to the total predicted positive events.CSI assesses the accuracy of predicted events, considering both successful predictions and misses, specifically for extreme weather events.These metrics are particularly useful in evaluating how well a predictive model performs in terms of both its sensitivity to detecting events (hit rate) and its precision in minimizing false alarms (FAR), while the CSI provides a comprehensive measure considering both aspects.

MAE =
1 n where n is the number of observations.y i is the actual value and ŷi is the predicted value where n is the number of observations.y i is the actual value and ŷi is the predicted value where TP is true positives and FN is false negatives where FP is false positives The predicted values from the separate data with relatively lower resolution are also compared to the high-resolution data, using the same metrics.We also compared our results with predictions from the support vector machine regression [37] under the same data conditions.

Results and discussion
Figure 3 shows the evaluation metrics between the predicted and actual 6-hourly temperature values during the test period.An impressive correlation of ∼0.99 was achieved between the actual and predicted 6-hourly temperature values during the test period.Figure 4 shows the scatter plot between the actual and predicted values.The coefficient of determination (R 2 ) is ∼0.98.The result indicates that the predicted data sufficiently captured the sub-daily variability of the global average temperature.Our results are consistent with several other studies that have applied other ANN architectures to downscale climate variables to a finer temporal resolution [38][39][40].From figure 3, the MAE and RMSE between the predicted and actual values are 0.21 • C and 0.22 • C, respectively.Considering the extreme values, the correlation was higher for warm extremes (R = 0.71), compared to cold extremes (R = 0.63).However, considering the hit rate, the predictions were relatively better for cold extremes with a hit rate of ∼0.99, FAR of 0.03, and CSI of ∼0.96, compared to warm extremes with a hit rate of ∼0.57, FAR of 0.19, and CSI of 0.50 (figure 3).The results indicate the need for a thorough evaluation of the ANN model performance by considering several evaluation metrics and several aspects of the data.
Table 1 shows that predictions from LSTM and SVM are quite comparable.LSTM outperformed SVM considering MAE, RMSE, and correlation coefficients-but with a slim margin.However, considering the FAR, CSI, and hit rate, SVM outperformed the LSTM model (table 1).The result suggests that for temperature, while the deep LSTM showed promising results, simpler machine learning models can also be sufficient for the task.Our results are consistent with [40] which reported the good performance of SVM in predicting air temperature.However, we also acknowledge that the flexibility and depth of non-linear modeling in ANNs are generally remarkable coupled with their scalability and adaptability to different types of data and problems [41].For example, for precipitation that is relatively more complex to model, the deep LSTM outperformed SVM for all the considered metrics.However, as shown in figure 5, compared to temperature (in figure 4) the LSTM model falls short in accurately predicting 6-hourly precipitation.The coefficient of determination for precipitation is ∼0.37 as compared to ∼0.98 for temperature.Thus, the approach developed here might be insufficient for interpolating daily precipitation to sub-daily, though the concept might be further adapted.The reason for the poor performance when considering precipitation is due to its short-term variability.While several studies have shown success in predicting sub-daily precipitation using ANN with sub-daily input variables [42][43][44], it is practically challenging to interpolate daily precipitation to sub-daily values.As earlier mentioned, this difficulty arises because precipitation patterns can exhibit significant variability on shorter time scales, which are not always captured in daily  aggregates.Consequently, using daily data to predict sub-daily precipitation events is inherently complex and may not always yield precise or reliable results (figure 5).In contrast, figure 4 shows that daily temperature data can be used effectively to predict sub-daily temperature variations due to the more consistent and gradual nature of temperature changes.
In the next step, the trained LSTM model, which has been evaluated in figures 3 and 4 was further applied to the coarser temperature data set to increase its resolution from daily to 6-hourly.The predictions were evaluated against the 6-hourly resolution data set.Figure 6 shows the evaluation metrics, and it can be seen that the performance mirrors the deep learning model evaluation on the test data in figure 3. The all-value correlations between the original and predicted 6-hourly precipitation impressively reached 0.99; the hit rate and CSI for extreme cold events reached 0.99 and 0.96 respectively; and 0.56 and 0.49 for extreme warm events.For other metrics, besides correlations, our interpolation model performs well for cold extreme events compared to warm extreme events (figures 3 and 6).
Given the high compatibility in the characteristics of the high-resolution and low-resolution MPI-ESM-LR temperature data sets, including their spatial resolution and temporal coverage, our model was well-positioned to learn and interpolate temporal patterns effectively.During our rigorous pre-training and validation phases, we ensured that the LSTM model could capture the intricate temporal dependencies present in high-resolution data, thereby enabling accurate inference when applied to lower-resolution data.The high degree of accuracy in our results as shown in figures 3 and 6, marked by a correlation of 0.99 and a mean absolute error of 0.21 • C between the actual and predicted sub-daily values, indicates the efficacy of our approach.This level of precision highlights the model's capacity for accurately interpolating and enhancing the temporal resolution of the MPI-ESM-LR temperature data from daily to sub-daily scales without the need for further fine-tuning.Our methodology, backed by rigorous training and validation  processes and demonstrated through high-accuracy results, justifies the use of model inference in this context.Assuming the high-resolution and the low-resolution data sets specific to this study were less compatible, then parameter-sensitive experiments, or in other words transfer learning, will be necessary in adapting the pre-trained model to the new data set it is applied to.
Furthermore, the influence of surface morphology, vegetation coverage, longitude, and latitude on temperature is a critical aspect of climate science, as these factors significantly modulate local and regional temperature patterns.Surface morphology, which includes landforms like mountains and valleys, affects temperature through variations in elevation and slope, leading to microclimates with distinct temperature regimes.Vegetation impacts temperature by altering surface albedo, evapotranspiration rates, and providing shade, thus influencing both surface and air temperatures.Longitude affects temperature primarily through its relationship with time zones and the angle of solar radiation, while latitude is a major determinant of climatic zones, influencing temperature through the angle of the sun's rays and day length over the course of the year.
In our study, while the primary focus was on enhancing the temporal resolution of environmental data using an LSTM model, the potential impact of these geographical and topographical variables on temperature patterns is indeed significant.However, the MPI-ESM-LR model data utilized in our study primarily offers a global average perspective with a horizontal resolution of approximately 200 km.This resolution, while effective for understanding broader climatic trends and patterns, may not be sufficiently fine-grained to capture the complete variations in temperature caused by local surface morphology or vegetation cover.Nevertheless, these factors are inherently embedded to some extent in the data, as the model simulations account for various geographical and environmental variables.For a more detailed analysis that specifically isolates the impact of surface morphology, vegetation, longitude, and latitude on temperature, a higher-resolution dataset or a model specifically designed to study these relationships would be necessary.For example, [20] integrated spatial-temporal correlations from various monitoring stations to develop an ANN model ('geo-LSTM') that not only captures temporal dependencies with the LSTM component but also directly addresses spatial associations in the data.Such an analysis could provide valuable insights into how these factors interact with and influence temperature patterns at a more localized scale.In terms of our study's results, the aforementioned factors could introduce additional variability into the temperature data.This variability could impact the model's ability to accurately interpolate temperatures at a sub-daily scale, especially if these factors exhibit significant diurnal variations that are not captured at a daily resolution.Future work could involve integrating additional data layers that describe these geographical and environmental factors, allowing for a more comprehensive analysis that accounts for their influence on temperature variability.
Furthermore, to ensure the robustness of the approach developed here beyond the global average and the simulated climate model data, we trained the LSTM model using the European Centre for Medium-Range Weather Forecasts Reanalysis, 5th Generation (ERA5) [45] temperature data at a single grid box and transferred the trained model to increase the resolution of assimilated temperature from the coarser twentieth-century reanalysis (20CR) [46] at the nearest grid box.The evaluation metrics resulted in a correlation of ∼0.98 and coefficient of determination of ∼0.95 and an MAE of 1.6 • C. The results, supported by figure S1 show that the trained model from ERA5 at a given grid box can be transferred and adapted to a different temperature data set, at the nearest grid box to obtain satisfactory results.
Furthermore, we applied the same technique using deep LSTM to increase the resolution of Landsat NDVI data from 16 d intervals to 5 d intervals, based on the pre-trained model using the Sentinel 2 NVDI data.The evaluation of the LSTM model on the test NDVI data from Sentinel 2 reached a correlation of 0.96, MAE 0.00, and RMSE 0.01.However, when the pre-trained model was applied to increase the resolution of the Landsat NDVI data, the MAE and RMSE were both 0.03 and a correlation of 0.84.From figure 7, though the temporal variation of the Sentinel 2 NDVI and the predicted NDVI from Landsat are fairly consistent (based on the 0.84 correlation coefficient), there are observable discrepancies compared to the accuracy reached for temperature (cf figures 3 and 7).There are several explanations for this, Sentinel-2 and Landsat 8 have different sensor technologies.Sentinel-2's MSI (MultiSpectral Instrument) and Landsat 8's OLI (Operational Land Imager) sensors have different spectral resolutions, sensitivities, and calibration methods.These variations can lead to differences in how each satellite captures and interprets light reflected from vegetation.Others include the difference in spatiotemporal resolution, which impacts the level of details captured by each data; atmospheric conditions; differences in wavelength, data processing, and calibration among others.Besides, the interpolation is not designed to notably adjust the statistical properties of the target data to be closer to the reference higher resolution data used to train the LSTM but to increase the resolution of the target data while maintaining its original statistical characteristics (figure 7).
Our results indicate that the most accurate predictions for global average temperature were obtained using the MPI-ESM model.This high accuracy might be attributed to the fact that the datasets of different resolutions originate from the same data source, thereby reducing the uncertainties typically introduced by varying data creation methods.However, a major limitation of this study is associated with the use of model inference.Specifically, it is essential to ensure that the statistical characteristics of the data used for pre-training the deep learning model closely align with those of the target data.Such alignment is crucial for the effectiveness of the model when applied to new datasets.
Finally, our results have shown that a deep learning model can be trained to capture the relationship between daily and sub-daily data, in so far, the data does not exhibit rapid short-term variability.Further, the trained model can be transferred to increase the temporal resolution of separate data with similar characteristics as the training data.This approach is unique in the context of existing literature that first applies linear interpolation schemes to the data before further processing it with neural network models (e.g.[31][32][33]).Our method is simpler, without introducing further uncertainties from a linear interpolation, and yet efficient, as evidenced by the model performance (cf figure 6).Moreover, we thoroughly evaluated our approach using diverse data sets, with unique temporal characteristics-i.e.simulated temperature and precipitation from global climate models, assimilated temperature from reanalysis data sets, and the NDVI remote sensing data.The novel application of our approach to several environmental data sets demonstrates the extent of its utility in improving the resolution of environmental data sets.

Conclusion
In this study, we trained a deep LSTM model in conjunction with model inference for increasing the temporal resolution of simulated global average temperature and precipitation, respectively, from daily to 6-hourly data.We also applied the same approach to increasing the resolution of Landsat NDVI from 16-daily intervals to 5-daily intervals.The trained model is evaluated in a test period using higher resolution data and further transferred to increase the resolution of different coarser data sets.The results show that the approach is effective for increasing the resolution of temperature with an explained variance of ∼98% but falls short for precipitation with an explained variance of ∼37%.For increasing the resolution of the Landsat NDVI data, our approach reached an explained variance of ∼70%.Hence, we conclude that when the deep learning model is pre-trained to capture the temporal patterns of the target data, the method developed here can be applied to effectively interpolate environmental data that does not have shorter rapid temporal variations (such as precipitation) to a higher resolution while still maintaining the actual fundamental characteristics of the data.
In subsequent studies, we will expand the current analysis to include spatiotemporal interpolations of various environmental data sets, which will necessitate training an ANN model that captures both the spatial and temporal patterns of the (higher resolution) target data.

Figure 1 .
Figure 1.Location of the farmland in Shurtah al-Dakhlah in Egypt where the NDVI data was obtained.The circle-like structure in the left top panel (A) shows the irrigated farms in the Sahara Desert in Egypt where we obtained the NDVI data.The right panel top plot (B) shows the zoom-out location of our area of interest in Egypt and the bottom plot (C) shows the location of the selected region in Egypt, North Africa.

Figure 2 .
Figure 2. Flow chart followed in interpolating daily to sub-daily climate data and the LSTM model architecture.

Figure 3 .
Figure 3. Evaluation metrics for the predicted 6-hourly global average temperature during the test period.Cold extremes are defined by the 5th percentile threshold of the actual values and warm extremes are defined by the 95th percentile threshold of the actual values.

Figure 4 .
Figure 4. Scatter plot between the actual and predicted 6-hourly temperature values during the test period.

Figure 5 .
Figure 5. Scatter plot between the actual and predicted 6-hourly precipitation values during the test period.

Figure 6 .
Figure 6.Evaluation metrics for the predicted 6-hourly global average temperature using the coarser daily temperature data.Cold extremes are defined by the 5th percentile threshold of the actual values and warm extremes are defined by the 95th percentile threshold of the actual values.

Table 1 .
Evaluation metrics for the actual and predicted 6-hourly temperature values during the test period.Dash (-) implies that the metric is not calculated for the data aspect considered.