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# Short-to-medium range forecast of natural gas use in the United States residential buildings

Rohith Teja Mittakola, Philippe Ciais, Chuanlong Zhou

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Rohith Teja Mittakola, Philippe Ciais, Chuanlong Zhou. Short-to-medium range forecast of natural gas use in the United States residential buildings. Journal of Cleaner Production, 2024, 437, pp.140687. 10.1016/j.jclepro.2024.140687. hal-04412182

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# Short-to-medium range forecast of natural gas use in the United States residential buildings

Rohith T. Mittakola<fnref n="1" />,<fnref n="2" />, Philippe Ciais<fnref n="1" />, Chuanlong Zhou<fnref n="1" />,⁵

## Abstract

Natural gas is the primary fuel for residential heating in the United States and plays a critical role in the transition to zero-carbon energy. In this study, a systematic framework is developed to predict short-to-medium-range (weeks to months) natural gas consumption in U.S. homes based on an interpretable model of gas consumption defined from data at county level and seasonal temperature forecast ensembles from the European Center of Medium Range Weather Forecast. Linear-plus-plateau models were fitted utilizing pipeline delivery of gas to each county, and outdoor temperatures to predict daily, weekly, and biweekly residential gas use for 1000 individual counties in the U.S. and five larger regions. The model presented highly accurate short-range (1 week) and robust medium-range (3 months) gas consumption forecasts capabilities with an average accuracy of 80%. The highest model performances were found in Midwest and East Coast regions (up to 82% accuracy), where temperature significantly drives gas consumption. This study assesses and quantifies how temperature forecast uncertainties impact gas consumption predictions for county and regional gas consumption forecasts using numerical weather forecast ensembles. Forecasting at a fine resolution over such an extensive spatial range is important for policymakers to design well informed policies adapted to local conditions and impactful for gas savings at national scale. The discussion presents the potential of this framework in aiding energy planning, supply chain optimization, and anticipating weather-driven gas demand fluctuations.

**Keywords:** Natural Gas Consumption, Ambient Temperature, Forecasting, Uncertainty Analysis

## Abbreviations:

ACS american community survey

AIC akaike information criterion

BIC bayesian information criterion

ECMWF european center of medium range weather forecast

LCS lack of correlation weighted by the standard deviations

LTC linear-plus-plateau temperature-consumption

MMBtu metric million British thermal unit

MSE mean squared error

RRMSE relative root mean squared error

RMS root mean squared error

SB squared bias

SDSD squared difference between standard deviations

## 1. Introduction

<footnote n="1">¹ Laboratoire des Sciences du Climat et de l'Environnement, IPSL CEA CNRS UVSQ, Gif-sur-Yvette, France</footnote>

<footnote n="2">² Atos France, Technical Services, 80 Quai Voltaire, 95870 Bezons, France</footnote>

<footnote n="3">³ Corresponding Author, Email: chuanlong.zhou@lsce.ipsl.fr</footnote>
## 1.1 Background

Natural gas is an important energy source for residential heating in the United States, accounting for 42% of households' energy usage ("Use of energy in homes - U.S. Energy Information Administration (EIA)," n.d.). It plays a critical role in the U.S. as a transitional fuel to reduce the carbon footprint before zero-carbon energy according to the United Nations Sustainable Development Goals (SDGs) ("Sustainable Development Goals," n.d.) and the Paris Agreement on Climate (Bu et al., 2020). Natural gas consumption as primary heating energy in the U.S. is predominantly driven by the seasonal heating demands although other social-economic factors, such as energy structure and economic development, might contribute to the geographical variances. Strong negative correlations between seasonal gas consumption and temperature were observed in European Union countries with significantly different country-based patterns (Ciais et al., 2022; Zhou et al., 2023). The temperature-consumption relationship was also studied by Timmer and Lamb, (2007) in the Central and Eastern parts of the U.S. Studies by Cong et al., (2022) and Hilbert and Werner, (2016) focus on the concept of energy poverty, which is defined as lack of energy access due to factors like affordability. Accurately forecasting natural gas consumption has multi-faceted benefits at both national and local scales. Governments can use such forecasts to inform and adjust policies related to energy, climate change and sustainable development. A local scale county level gas use forecast for the entire country is important to optimize energy allocations, incentivize CO₂ emissions reductions, and make better decisions about infrastructure management, for instance, adjusting tariffs and encouraging individual gas savings by households, tertiary, and commercial activities. Hence, a systematic approach that can accurately predict natural gas consumption at a fine spatial-temporal scale can have a range of significant applications for consumers, energy providers, and entire nations.

## 1.2 Literature Review

### 1.2.1 Natural gas consumption forecast models

A detailed history of natural gas consumption forecasting was given by Liu et al., (2021), classified into four categories: (i) early-stage statistical models, (ii) time series models, (iii) deep learning models, and (iv) interpretable models. Early-stage statistical models like the Exponentially Weighted model (Berrisford, 1965) established relationships between temperature and gas consumption to predict daily and weekly future consumption with relatively small data size due to the difficulty in collecting real-time data and the limited computational capability. The exponentially weighted model uses a best-weighted model for current and previous temperatures. Balestra and Nerlove, (1966) used the ordinary least squares method to forecast yearly natural gas demand for the residential and commercial sectors. Many time series models have also been utilized to forecast in the energy sector, like the Moving-average model (MA) for yearly forecast in China (Xu and Wang, 2010), and Autoregressive integrated moving averages (ARIMA) for daily forecast in Spain (Conejo et al., 2005). Statistical and time series models work well on low computation time but cannot handle a large number of historical data and variables. Increased computational power allows models to scale to larger input data and improve performance. Artificial neural networks (ANN) have been used to forecast natural gas consumption in several studies like multi-layer perceptron (MLP) (A. Azadeh et al., 2013), which forecasted monthly consumption in Iran. MLP is a type of feed-forward artificial neural network that has three types of layers, namely the input layer, output layer, and hidden layer. There are examples of studies using complex ANN models like improved back propagation neural networks (Yu and Xu, 2014) to forecast daily consumption in Shanghai, adaptive-network-based fuzzy inference system (ANFIS), which combines neural networks with fuzzy inference systems (Ali Azadeh et al., 2013), to forecast yearly gas consumption in 6 Southern American countries,
and wavelet neural network which is based on wavelet transform and neural network (Zhang et al., 2018) to perform short-term forecasting evaluated on data from Australia and New York city. However, ANNs are developed as black boxes and are difficult to interpret, also they suffer from inherent model issues, such as low accuracy on long-range forecasting, slow convergence, poor generalization, and overfitting (Liu et al., 2021). Regression models can handle large amounts of data and multi-dimensional medium-term forecasting where its performance is as good as complex models such as neural networks (Tso and Yau, 2007), while being interpretable and easy to understand.

### 1.2.2 Interpretable approaches and uncertainty

Various attempts have been made to forecast natural gas consumption using interpretable approaches. Temperature is the main driver for heating consumption in households during the cold season, and it was found to be the most influential factor in gas consumption prediction by Liu et al., (2021), who conducted a comprehensive analysis of 72 published papers to identify the most influential factors in gas consumption prediction. Szoplik, (2015) leveraged temperature data in conjunction with calendar information (like day of week, month, etc.) to train a neural network for gas consumption prediction in Szczecin, Poland. Similarly, Özmen et al., (2018) predicted the daily gas consumption in Ankara, Turkey, by using piecewise polynomials or splines in combination with daily temperature data. These studies have generally a local, regional coverage and have highlighted the importance of using temperature as a significant factor in gas consumption forecasts. They found that temperature was the most influential factor in predicting gas consumption across various time scales, including hourly, daily, and weekly predictions. Seasonal weather forecasts have been used to predict energy consumption, but a detailed uncertainty analysis is missing in the literature. Recent papers like Bilici et al., (2023), and Szoplik and Muchel, (2023) also incorporated temperature as a predictor for natural gas demand forecasting. There exist studies that use weather forecasts to predict gas demand, e.g., in Great Britain (Thornton et al., 2019). Seasonal weather forecasts are also employed in the electricity demand forecast (De Felice et al., 2015) and wind energy forecast (Soret et al., 2019) but not for gas consumption in the residential sector. While these studies all leverage temperature as a factor to predict energy consumption, there is a noticeable absence of a comprehensive approach for constructing a prediction model based on seasonal weather forecasts. Alternatively, when seasonal weather forecasts are employed, there is a lack of quantification of the uncertainty inherent in seasonal weather forecasts and how it translates into consumption prediction uncertainty in different areas.

### 1.2.3 Natural gas consumption prediction in the U.S.

Natural gas production in the U.S. grew by 4% in 2022 because of lower gas prices for power production than coal and because gas is seen as a fuel with a lower carbon content for incepting an energy transition. Projections indicate that storage inventories are expected to surpass 87% capacity for the East, Midwest, and South Central regions during the winter of 2023 (“Short-Term Energy Outlook - U.S. Energy Information Administration (EIA),” n.d.). Having an accurate county-scale gas demand forecast model enables energy providers to strategically manage distribution networks to improve resource allocation and emergency preparedness. Yet, studies pertaining to the U.S. daily natural gas consumption forecast are sparse. Brown et al., (1994) used feed-forward artificial neural networks (ANN) to predict daily gas consumption for Milwaukee, Wisconsin in the U.S. Brown and Matin, (1995) improved the ANN models to two regions in Wisconsin to predict daily gas consumption. Vitullo et al., (2009) applied linear regression models and ANNs to forecast daily gas demand in 14 local distribution companies in the U.S. for the residential, commercial, and industrial sectors. Merkel et al., (2018) built a deep neural network to forecast gas consumption at 176 locations across the U.S., where they used temperature, wind speed, day of week, and historical consumption as predictors. A hybrid model including wavelet transform,
recurrent neural networks, and genetic algorithm was used to forecast hourly national gas demand in the U.S. (Su et al., 2019). Another study (Wang and Jiang, 2019) used a hybrid model by integrating ARIMA and ANNs to forecast monthly gas demand in Pennsylvania and Texas. Recent literature also includes Singh et al., (2023), which forecast annual gas consumption in the U.S. using ANN, support vector machine, and linear regression algorithms. Tong et al., (2023) used an optimized grey bernoulli model to forecast gas consumption in the entire U.S., China and Russia. Despite the growing importance of natural gas in the U.S. energy landscape, existing literature mainly concentrates on either small regional areas or provides a broad overview at the national level, leaving a significant gap in understanding the nuanced daily variations in gas consumption patterns at the county scale, yet with a national coverage.

## 1.3 Description of the Study

To provide a better understanding of natural gas consumption in the U.S. with informed policy support to meet the climate goal, a novel forecast framework is developed in this study to provide accurate short-term forecasts and robust middle-range forecasts with comprehensive uncertainty analysis. This model predicts daily natural gas consumption based on county-scale linear-plus-plateau temperature-consumption (LTC) models. A large dataset of daily pipeline gas flows to residential households and commercial buildings across 1000 counties in the U.S was compiled (“Natural gas analyst,” 2020). Second, daily average air temperature gridded fields from a global weather reanalysis (ERA5 land) (Hersbach et al., 2020) was used to build linear-plus-plateau regression models in each county for simulating daily gas consumption as a function of temperature. Third, these models were forced by temperature ensemble forecasts to predict consumption. Fourth, the predictions were evaluated by comparing predicted vs. observed consumption during a given target forecast period and for different lead times (time since the current date at which the forecast is calculated). Finally, a systematic uncertainty analysis was conducted that quantified the amount of uncertainty present in the forecast ensembles, which influenced the variability in the gas consumption forecast for daily, weekly, and biweekly intervals. This explains the effects of using weather forecast data to predict gas consumption. Also, performing uncertainty analysis at different lead times and spatial resolutions is crucial for providing policymakers and stakeholders with a comprehensive understanding of the reliability and robustness of the forecasted natural gas consumption model. Forecasting at different lead times captures the dynamic nature of natural gas consumption, allowing policymakers to anticipate changes in demand over varying time horizons. Short-term forecasts enable quick policy adjustments to meet immediate consumption needs, while medium-range forecasts provide insights for mid-term policy planning. Therefore, the systematic natural gas consumption forecast framework of this study was developed to address the following questions: i) Does LTC model outperform a naive model that would predict consumption based on the average of previous years' consumption values during the target period (2021)? ii) How do the uncertainties of the ECMWF temperature ensemble forecast affect the uncertainties of LTC predictions for natural gas consumption? and, iii) How does the model perform at different lead times and spatial resolutions?

The above-raised questions are addressed by performing a hindcast (predicting past events using historical data) evaluation of LTC model against the naive model using observed consumption (for 2021). Then, performance testing with ECMWF temperature ensemble forecasts was conducted using seasonal hindcasting (4 seasons in 2018-2019). This performance evaluation was done at three temporal resolutions: daily, weekly, and biweekly, and at two spatial resolutions: county and regional scale. How the prediction accuracy decreases with increasing lead times was also analyzed, identified the sources and causes of uncertainty, and used skill-spread diagnostics to evaluate the ensemble's ability to capture the uncertainty. Additionally, this analysis finds the major component of the error, defined as the squared difference between the observed and simulated value, by decomposing the error into three components
(Kobayashi and Salam, 2000), namely, squared bias (SB), the squared difference between standard
deviations (SDSD), and lack of correlation weighted by the standard deviations (LCS). This paper thus
provides a comprehensive analysis of the performance of a new residential gas consumption forecast
model, offering insights into the factors affecting the accuracy and reliability of the predicted data. The
forecast lead times considered in this study range from one week to 12 weeks (i.e., medium-range
forecast).

This work addressed the limitations of previous studies on gas consumption forecasts and introduced a
novel contribution by presenting a medium-range daily residential gas consumption prediction model that
relies on seasonal temperature ensemble forecasts for the United States. Firstly, an interpretable model
(linear-plus-plateau regression model) was selected to build a forecast model as it does not suffer from
the issues of complex models (like ANNs), such as overfitting and poor generalization while providing
great performance. Secondly, seasonal temperature from ECMWF was used to forecast residential
natural gas consumption as it has been established as a significant factor by several prior studies. To
better understand the robustness of the forecasts, the source of uncertainty in the model was identified
and a detailed analysis performed to quantify its effects on the final prediction at different lead times,
weekly or seasonal, which had not been done before. Thirdly, the focus of this study is on medium-range
forecasts (the next season) along with short-range forecasts (the next few weeks) for a large spatial
resolution of 1000 different counties across the U.S., to address the major gap in the literature.
Additionally, despite numerous studies in this field, there remains an opportunity to explore the broader
scope of this study in terms of spatial and temporal reach for the United States, which is a major player in
the natural gas market and where natural gas is the main heating fuel for households.

The paper is organized as follows. Section 2 presents the research methodology and data sources.
Section 3 shows the evaluation of LTC prediction model against a naive model, the seasonal hindcast
performance, and the source of uncertainties. Section 4 shows discussions, and the conclusions are
made in Section 5.

## 2. Materials and Methods

In this section, the research methodology, including data acquisition, preprocessing, and modeling is
presented. The start is to obtain daily natural gas consumption data, demographic information, and
temperature data from various sources. then piecewise linear-plus-plateau models were developed for
gas consumption forecasts, operating at daily, weekly, and biweekly intervals, and on regional scales.
Several experiments were performed by constructing a naive forecast model and also incorporating
seasonal hindcast data from ECMWF to assess LTC model performance using various metrics, including
Root Mean Squared Error (RMSE) and Relative-RMSE (RRMSE).

### 2.1 Natural Gas Data

Daily natural gas consumption data were obtained from Wood Mackenzie's "Natural Gas Analyst," a comprehensive database of gas nominations and flows ("Natural gas analyst," 2020). The dataset includes data from different gas delivery points across the U.S. called a "Citygate." A Citygate can be defined as a point or a measuring station where the gas is collected from the natural gas pipeline company and delivered to the end consumers like residential and small commercial entities ("Glossary - U.S. Energy Information Administration (EIA)," n.d.). The gas data comprises two entities: net scheduled capacity and no-notice capacity. The net scheduled capacity is the volume requested by an end-user one day before consumption. The no-notice capacity is the amount of gas delivered as needed without scheduling the gas quantity in advance to meet a sudden surge in gas demand. The total gas transported
to the distributing company or Citygate from the pipeline company is computed by aggregating the net scheduled capacity and no-notice capacity. The unit used for gas volume is the Metric Million British Thermal Unit (MMBtu). Data reported at Citygate delivery points can cover multiple locations in a given county. Location-based hourly Citygate gas data were aggregated to county-level daily values. For temperature-consumption fittings, only pre-COVID period data were used as it was assumed that the influence of the pandemic had overridden the effects of climate drivers. The Citygate delivery points covered 1000 counties (out of 3143), as not all counties in the U.S. have gas pipeline access.

## 2.2 Per Household Gas Consumption

Per-household gas consumption values was calculated using demographic data from the American Community Survey (ACS 2019) (US Census Bureau, 2021). Normalization of the consumption values was necessary as different counties have different population levels, resulting in high gas consumption variability. Consumption values were normalized by the total number of households (ACS variable B11016_001E) using gas as a heating fuel in each county. The units of consumption are MMBtu/100 households. The no-notice capacity values in the data were not reported daily but with a lag of 2 to 4 days, and tended to fluctuate considerably. To maintain the homogeneity of the data, only counties with a low proportion of the no-notice capacity (< 49%) were retained in the final aggregated consumption values. Data reported on weekends and U.S. holidays were removed.

## 2.3 Temperature

Daily gridded air temperature data collected 2 m above ground at a 25 km spatial resolution were obtained from ERA5 (Hersbach et al., 2020) on the same dates as the gas use data. The gridded data were clipped using county vector polygons, and spatially distributed temperature values across each county were averaged to obtain a time series of daily average county temperatures. Counties smaller than the ECMWF grid were resampled to a spatial resolution of 2 km using a linear interpolation technique ("Xarray.DataArray.Interp," n.d.). Temperature data were obtained for all the counties with the gas consumption data.

## 2.4 Gas consumption forecast model using temperature

An interpretable linear-plus-plateau piecewise function (with one breakpoint) was fitted to the gas consumption and temperature data (LTC models). The breakpoint is also called the critical temperature ($T_{crit}$), i.e., the temperature below which the households heat their homes. A piecewise linear function with one breakpoint can be mathematically represented as

$$f(x) = \begin{cases} m_1x + b_1 & \text{if } x < a \\ m_2x + b_2 & \text{if } x \ge a \end{cases} \quad \text{Eq(1)}$$

where, $f(x)$ represents the predicted gas consumption or the dependent variable, "x" is the temperature or the independent variable, "a" is the critical temperature or the breakpoint, "m1 and m2" are the slopes of linear relationships between temperature and gas consumption, and "b1 and b2" are the intercepts on the y-axis for these linear relationships. Piecewise regression models were built for each county using 2018 and 2019 daily consumption and temperature data. These models serve as forecast models. Temperature as an input was used to forecast the gas consumption value. The forecast is conducted across three temporal intervals: daily, weekly, and biweekly. To generate forecasts for the weekly and biweekly periods, the temperature data were aggregated on a weekly or biweekly basis and utilize it to
predict gas consumption. Additionally, the forecast is performed at two spatial scales: county and regional scales. The daily, weekly, and biweekly temperature data were aggregated for the five distinct regions (West Coast, Rocky Mountains, Gulf Coast, Midwest, and East Coast) to forecast gas use at a regional scale. Different metrics were used to analyze the performance of the forecasted gas consumption values like Root Mean Squared Error (RMSE) and Relative-RMSE (it is the square root of the ratio between the sum of the squared differences between the true values and predicted values, and the sum of the squared predicted values). Relative-RMSE or RRMSE is easier to interpret than the RMSE as its values range from 0 to 100%, where 0 is the best-performing model, and 100% is the worst performer. The accuracy of the forecast is defined as a complement to the RRMSE as a performance metric.

## 2.5 Naive forecast model

A naive forecast model which forecasts simply by using the averaged values from the previous years (2018 and 2019) was built. For e.g., to forecast the gas consumption on 1 Jan 2021, the gas consumption values from 1 Jan 2018 and 1 Jan 2019 were averaged. The naive model does not take any input to forecast. The performance of forecasts between LTC model and the naive model was compared by testing on the 2021 data. The gas consumption in the full year of 2021 was forecasted using LTC model and also the naive model. Then, the RMSE values of the two models was compared to see which has the lowest error when forecasting.

## 2.6 Seasonal hindcast

Seasonal hindcast data was collected from the European Center of Medium Range Weather Forecast (ECMWF) and Copernicus ("Copernicus climate data store," n.d.). This data comprises 51 different temperature ensembles on a daily scale. Hence, 51 ensemble predictions were made and then averaged them all to get the final gas consumption prediction using the forecast model. Different types of analysis were used to test the performance of LTC forecast model on the temperature ensemble data.

## 2.7 Mean squared error decomposition

A technique mentioned in this paper Kobayashi and Salam, (2000) was used to decompose the mean squared error (MSE) into three components, namely, squared bias (SB), the squared difference between standard deviations (SDSD), and the lack of correlation weighted by the standard deviations (LCS) such that

$$MSE = SB + SDSD + LCS \quad Eq(2)$$

# 3. Results

## 3.1 LTC prediction model compared to a naive model

Empirical parametric models of the daily gas consumption of residential buildings were built as a function of air temperature using a comprehensive database of gas pipeline nominations and flows from Wood Mackenzie's "Natural Gas Analyst" ("Natural gas analyst," 2020), and air temperature data from Copernicus ERA5 land gridded data ("Copernicus climate data store," n.d.; Hersbach et al., 2020). Fig. 1A shows the daily per-household gas consumption for the entire U.S., along with daily temperature fluctuations for 2018-2021. Data from the "Citygate" ("Glossary - U.S. Energy Information Administration (EIA)," n.d.) pipeline delivery points were used, which only includes the gas consumption data belonging to residential and commercial buildings and excludes any consumption from large power plants and large
industries. Fig. 1B shows the distribution of the "Citygate" gas pipeline locations delivering gas to households and commercial buildings around the U.S. counties, along with the different regions of the U.S. The consumption data for 1000 individual counties (which are connected to the gas pipeline network) were extracted and the per-household consumption was calculated using the U.S. census data (US Census Bureau, 2022). One model per county was built using a linear-plus-plateau function because, in most counties, this function was found to best describe the relationship between daily per-household gas consumption and temperature. The entire analysis is illustrated in the form of a flow chart (Fig. S1). The parameter values per county of gas-consumption-temperature linear-plus-plateau models were calibrated using data for 2018-19, and the models were then driven by observations of daily temperature for the year 2021. The year 2020, affected by COVID confinements, was left out (estimated the peak lockdown period from March 15, 2020, to April 24, 2020, which is shown in Fig. 1A and Fig. 1D (CDC, 2022)). Linear-plus-plateau models were found to be the best fit for gas consumption and temperature, and had the lowest AIC and BIC values compared to the other models (simple linear regression, generalized additive models, and machine learning models). The predictions were compared between LTC model and a naive model (Fig. 1D and 1E). It is clear that a naive model fails to capture the correlation between temperature and consumption (Fig. 1E).

The spatial distribution of the root mean square error (RMSE in units: MMBtu/100 households) of daily gas consumption was simulated by LTC models during the year 2021 and compared with the naive models based on observations for the same day of the year averaged during the years 2018 and 2019, which do not contain any direct temperature information (Fig. S2A). For daily consumption, LTC models outperformed the naive models in 89% of the counties and have, on average, a 23% lower RMSE than the naive models. For weekly and biweekly consumption, LTC models also outperformed the naive models in 84% and 81% of counties and showed a 24.4% and 25% lower RMSE, respectively. The performance of LTC models in 2021 depends on the quality of the fit during the calibration period, as it is important to capture the correlation patterns between gas consumption and temperature. The spatial distribution of the quality of the linear-plus-plateau fits (R²) was shown for 2021 (Fig. S2B). The median R² value was 0.62 for daily prediction, and for weekly and biweekly predictions, the values were 0.73 and 0.75, respectively. The R² of the model fit during the calibration years (2018-2019) is strongly correlated with the R² in the evaluation period (2021) (Pearson correlation coefficient was found to be 0.76 with a p-value less than the significance level of 0.05). This means that LTC model prediction is more robust in the counties with a good quality of fit during the calibration years. Also, the performance of the model improves with the decrease in the prediction frequency. The performance of LTC model was compared with a different metric (easy to interpret and provides the magnitude of the error), the median relative-RMSE (RRMSE in %), and it was found that LTC daily prediction has an RRMSE value of 32%. It is higher than the values for weekly and biweekly predictions, which are 26% and 24%, respectively (Fig. S2C). At a regional level, the mean RRMSE of the three cases (daily, weekly, and biweekly) ranks as follows: East Coast (20.9%), West Coast (22.6%), Rocky Mountains (23%), Midwest (23.7%), Gulf Coast (28.8%). East Coast had the lowest mean uncertainty, where the mean R² of the prediction model was 0.70, and the Gulf Coast, with the highest mean uncertainty, had a mean R² of 0.55 (see Fig. S3 for detailed regional uncertainty and R² comparison).

## 3.2 Seasonal hindcast using temperature ensembles

Then, the models of gas consumption were tested on the task of seasonal hindcast using temperature forecast ensembles. A higher uncertainty was expected because the quality of the temperature forecasts is lower than the reanalysis, especially for long lead times of the forecast. For this, temperature forecast data was collected from the Copernicus seasonal forecast (ECMWF) ("Copernicus climate data store," n.d.). The seasonal temperature forecast is released monthly by ECMWF at a frequency of 6 hours for
5160 lead time hours (7 months). Seasonal forecast data were collected for 2018 (Spring, Summer, and Fall) and 2018-2019 (Winter) and then the data was resampled from hourly to daily frequency to match the gas consumption data frequency. The seasonal forecast data comprises 51 past forecast ensembles that were used to predict the hindcast consumption for all four seasons: Spring (2018), Summer (2018), Fall (2018), and Winter (2018-2019). The prediction for all 51 ensembles was averaged (Fig. S1B) to get the final consumption prediction value. Fig. 2A-C shows the spatial distribution of the RRMSE values for different time-averaging periods of predictions, i.e., daily, weekly, and biweekly for the winter season, where the consumption is at the peak. The lead times range from 1 week to 12 weeks. But in the case of weekly and biweekly consumption predictions, the hindcast was performed starting with a lead time of 2 weeks (not possible to start a 1 week hindcast for biweekly and not reasonable for weekly). The histograms (Fig. 2D) show that a majority of counties have an RRMSE under 40% (for all lead times and all frequencies of prediction), which indicates good performance, with a median RRMSE only 24% higher than the model prediction done with more accurate reanalysis temperature data. In the same figure, an increase in median RRMSE was observed across all ensemble members (represented by the solid vertical straight line) as the lead time increases from daily to weekly, biweekly. This result illustrates that uncertainty of the weather forecast increases with lead times. Fig. 4A shows a gradual increase of median RRMSE for all counties as the lead time increases (an increase of 11% for daily, 6% for weekly, and 3.5% for biweekly forecast from initial lead time to final lead time). For all lead times, the RRMSE in the daily hindcast is comparatively higher than the weekly and biweekly hindcast. On average, the median RRMSE for the daily forecast is 33.1% higher than the weekly forecast and 45.8% higher than the biweekly forecast (Fig. 4A). At a regional level, the Rocky Mountains and Midwest had the lowest RRMSE for the lead times of 1 to 4 weeks in daily, weekly, and biweekly forecast (Fig. S5). The Gulf Coast had the higher RRMSE among all the regions for all three temporal interval forecasts.

### 3.3 Source of uncertainty

The percentage difference from the actual value (% of uncertainty) was computed, shown in Fig. 3A; a positive change denotes an overestimation, and a negative change denotes an underestimation by the model. The model overestimates the gas consumption for counties shown in green and underestimates the consumption for the counties shown in purple (Fig. 3). A majority of counties have underestimating models in the lower lead times: 64% for daily, 60% for weekly, and 58% for biweekly. The proportion of counties with underestimating models slightly decreased as the lead time increased. At a lead time of 12 weeks, the following are the proportions of counties where consumption was underestimated: 55% for daily, 55% for weekly, and 56% for biweekly. These counties (with underestimating models) were present in the Midwest, East Coast, and Gulf Coast regions, although the forecast was not underestimated by a significant margin (10% on average). Conversely, the forecast model tends to overestimate consumption for the West Coast and Rocky Mountain regions, and the proportion of counties where the consumption is overestimated rises with the increase in lead times. This tells us that the model is leaning more towards being an overestimating model as the input uncertainty (present in the temperature ensembles) increases.

To better understand the uncertainty of the hindcast or forecast, the mean squared error was used that can be split into different additive components (Kobayashi and Salam, 2000). Fig. 4B-D shows the decomposition of mean squared error (MSE) components for daily, weekly, and biweekly hindcasts using temperature ensembles for the five regions of the U.S. at different lead times. The three components of the decomposition are squared bias (SB), the squared difference between standard deviations (SDSD), and the lack of correlation weighted by the standard deviations (LCS) (refer to flowchart in Fig. S1D). A high SB indicates that the model tends to make consistently off-target predictions, whereas a high SDSD means that the model failed to capture the magnitude of variability present in the data. LCS talks about
the pattern of variability in the data; in other words, a high LCS value means that the model failed to capture the expected temporal covariance between consumption and temperature. The spatial distribution of the dominant component of MSE in each county was shown across the U.S. at different lead times (Fig. S4). In shorter lead times (up to 2 weeks), the uncertainty of the forecast model was dominant with the SB component, where it caused 76% of uncertainty in 53% of counties (average for the 3 cases: daily, weekly, and biweekly). Out of the 3 cases, the LCS component was noticeable in a number of counties (41%) in daily forecast (as the R² of the model predicting daily consumption was lower than weekly and biweekly forecast models; refer to Fig. S2B). As the lead time increases, the proportion of the LCS component grows in the forecast uncertainty (Fig. S4). At the lead time of 12 weeks, the LCS component was dominant in 78% of counties and caused 73% of uncertainty (average of all 3 cases). This shows that in longer lead times, the model fails to capture the correlation between temperature and gas consumption (which is expected with medium and long-range forecasting). Thus, higher LCS values were observed as the lead time increases (Fig. 4B-D and Fig. S6). The component SDSD is not significant at short lead times (<= 2 weeks) for all regions except the East Coast (Fig. S6), which indicates the presence of variability in the data for this region (R² of the model is low around the Floridian peninsula of the East Coast region in Fig. S2B, which could be the source of variability in the data). This can happen due to various reasons, such as uncertainty in the weather or other external factors affecting gas demand or supply. The Midwest has some of the lowest mean square error (MSE) components (see Fig. S6). This behavior is the result of the similar patterns in the mean square components of the temperature forecast ensemble (w.r.t observed temperature), where the Midwest had the lowest MSE components compared to other regions. Also, the Midwest has a good correlation between temperature and gas consumption (Fig. S2B).

## 3.4 Performance of the ensembles in the final prediction

The ensemble's performance was calculated to capture the uncertainty in the prediction using skill spread plots (Vautard et al., 2006) (refer to Fig. S1C). The skill is the RMSE between the actual value and each ensemble member prediction, and the spread refers to the standard deviation of the ensemble. Skill spread diagnostics evaluate an ensemble's ability to capture the uncertainty, i.e., if data is difficult to model, the spread should be larger, and if the ensemble describes the uncertainty well, the points should be on the 1:1 line. The spatial distribution of the slope of the skill spread scatter plots for different counties in four seasons: Spring, Summer, Fall, and Winter is shown in Fig. S11. The forecasts made for the spring, fall, and winter seasons have slope values close to 1 (0.5<slope<1.5) for a considerable number of counties: 48% of counties in winter, and 40%, 36%, and 27% of counties in spring, fall, and summer seasons, respectively. It shows the model's ensemble spread (variability) and skill (accuracy) are relatively consistent. In other words, the forecast is reliable if the points have a slope of 1. A few counties (13.4%) (higher numbers in the summer season (26.9%)) have relatively higher slope values (greater than 2), suggesting that the model's skill is relatively high compared to its spread. It could mean that the model is not capturing all of the sources of variability in the data. Also, the summer season has a relatively high number of counties (48.8%) with slopes less than 1. This indicates that the model's spread is larger than its skill, which could produce variable forecasts that might not be accurate. The slope values of the skill spread plots for the case of temperature forecast ensembles (w.r.t observed temperature) were checked, and a high number of counties were found to have slope values close to 1 for the winter season (83%), which is reflected in the gas prediction ensemble performance (winter season having more counties with a slope close to 1). For other seasons, 50-70% of counties have slopes closer to 1.

## 3.5 Hindcast at a regional level
The performance of LTC-regional model (similar linear-plus-plateau model fitted on aggregated regional-level data) is tested on the prediction of regional-level consumption using the temperature ensembles. The RRMSE for the prediction at different lead times is shown for the five regions: West Coast, Rocky Mountains, Gulf Coast, Midwest, and East Coast (Fig. S7). The RRMSE increases with an increase in lead time as the uncertainty in the forecast increases. This is observed more for the predictions at a daily scale where the RRMSE at a lead time of 12 weeks is the highest (18%) for daily prediction than others (12% for weekly and 10% for biweekly predictions). All regions have an RRMSE lower than 30% for all temporal scales of prediction, which indicates a better performance than county scale prediction. The percentage increase or decrease of the prediction compared to the actual value is shown in Fig. S8. The Rocky Mountains and East Coast regions have models which overestimate the predictions at all lead times. Similar to the predictions at a county scale, the regional scale prediction models tend to overestimate the consumption as the lead time increases. The dominant components (of mean squared error) for each type of prediction at different lead times is shown in Fig. S9. An increase in the dominance of the LCS component was observed as the lead times increase in most regions (similar to the county scale prediction). The LCS component increases with an increase in lead time (Fig. S10B-D) and SB is the lowest in daily predictions and highest in biweekly predictions. Finally, the RRMSE is higher for daily predictions than weekly and biweekly (Fig. S10A). Overall, the behavior of the regional-level prediction performance analysis was similar to the county-level analysis but showed a lower uncertainty.

## 4. Discussion

The seasonal natural gas consumption patterns in the U.S. varies throughout the year, with higher demand during the winter when heating is necessary. Accurately forecasting these consumption patterns can help to adjust distribution infrastructures and promote sustainable development practices such as tariffs and incentives for gas savings (Wang et al., 2021). Firstly, it is demonstrated by the results that the gas consumption vs. outdoor temperature linear-plus-plateau (LTC) interpretable model outperforms a naive model, which does not use any explicit input variables for the forecast (23-25% lower uncertainty than the naive model). Some counties (11%) had a poor performance that is less than the naive model performance in forecasting daily gas consumption values (referenced as “bad” counties elsewhere). For weekly and biweekly gas consumption predictions, this percentage of these counties was 16% and 19%, respectively. This was a result of a poor fit of the linear-plus-plateau model, where the median $R^2$ for these counties was 0.28, and they showed a median 6.4% lower RMSE than the naive model. West Coast has the highest proportion of counties (17.4%) with a poor forecast performance than a naive model compared to the other regions for daily predictions (30% for the weekly and biweekly predictions). This indicates that the naive model is a better choice in these counties. It could be a case where consumption is not highly affected by temperature fluctuations or has low seasonal variability. East Coast has the lowest proportion of “bad” counties: 7.2% for the daily forecast and 14% for the weekly forecast. In the case of biweekly predictions, the Midwest region had the lowest proportion of “bad” counties. Despite the presence of a relatively high number of "bad" counties in the weekly and biweekly prediction cases, their performance is better than that of the daily prediction in the remaining counties.

Secondly, the performance of LTC model was tested at different lead times ranging from 1 week to 12 weeks and compared the uncertainties associated with the forecast (using temperature ensembles). The accuracy of the forecast model (defined as the complement of the % of RRMSE) is in the range of 76-83% for different lead times, where the accuracy is highest for the forecast at the 1-week lead time and lowest at the 12-week lead time. In other words, the forecast uncertainty increases with the lead time. On a regional level, LTC-regional model was more accurate when predicting gas consumption in the Rocky Mountains region (77% on average for all lead times) and had relatively lower confidence when predicting in the Gulf Coast region (72% on average for all lead times).
In counties with high uncertainty in the prediction of gas consumption (RRMSE > 50%), it is found that the uncertainty mainly comes from the uncertainty in the temperature forecast ensembles from ECMWF. This result was tested by establishing a "ground truth" by computing the median value (for all counties) of uncertainty (RRMSE) when the observed temperatures (re-analysis) are used to predict gas consumption. The RRMSE value ranged from 18-22% for lead times of 1-12 weeks, respectively, for the daily gas consumption forecast. In contrast, the uncertainty ranges from 2-71% (for lead times of 1-12 weeks) when the temperature forecast ensembles were used to predict the daily gas consumption. Also, the uncertainty of temperature ensembles with respect to the observed temperature lies in the range of 25-100% (for the same lead time ranges), which is quite high. It shows that the gas forecast is sensitive to the inherent uncertainties in the temperature ensembles. This behavior was compared between counties that had high uncertainty. The counties that had a high uncertainty in the gas forecast (RRMSE > 50%) showed a higher uncertainty in the temperature forecast (RRMSE > 70%). This supports the fact that gas consumption can be mapped as a function of temperature, although the uncertainties in the temperature ensembles translate into the uncertainties in the gas forecast.

For future gas forecasts, a better temperature forecast ensemble can facilitate a more robust gas forecast model. The effect of temperature ensemble uncertainties was quantified on the gas forecast uncertainties (Fig. 5). The uncertainties of the temperature ensembles and the gas forecast are fitted using a regression line to calculate the slope. For every one-unit increase in the uncertainty of the temperature ensembles, there is a 0.55 increase in the daily gas forecast uncertainty. For the weekly and biweekly cases, there is a 0.53 and 0.51 increase in gas forecast uncertainty, respectively. At a regional scale, West Coast had the highest uncertainties related to temperature forecast ensembles (median RRMSE = 87%). A high RRMSE values was observed in the West Coast for daily, weekly, and biweekly forecasts during the beginning lead times (Fig. S12). Subsequently, the same region had the highest uncertainties in the seasonal gas consumption forecast (median RRMSE = 58%). The forecast quality of the West Coast was the highest when the reanalysis temperature values were used. The temperature ensembles have high uncertainty in the West Coast region, which subsequently hampers the performance of forecasts in that region.

Lastly, the gas prediction at a regional scale was observed to be more accurate than at a county scale. Comparing Fig. 2D and Fig. S7D, the uncertainty of the prediction at the regional scale is around 50% lower on average than the county scale prediction. In both cases, an increase in uncertainties with the lead times was observed. The uncertainties are lower for predicting at a biweekly and weekly frequency than at a daily frequency. For the lower lead times (1-2 weeks), Midwest and Gulf Coast have a relatively accurate regional gas consumption forecast (lower uncertainties) than other regions. Gulf Coast shows better performance in the regional scale forecast than in the county scale forecast (as coarser resolution data suffers less from noise and variability).

Based on LTC forecast model, several policy implications can be derived to enhance gas distribution and consumption efficiency and sustainability. The model results can be used to develop tailored distribution strategies for different regions/counties as consumption patterns are not uniform across the U.S. It can also assist in planning support programs and energy allocation for the energy impoverished. The growing demand for natural gas as a transitional fuel would add more pressure on the government and various operators and consumers to conduct detailed market impact assessments. The implementation of the forecasting model proposed in this study would enhance preparedness efforts and the adjustment of tariffs in relation to market prices and saving policies. Furthermore, it also helps in understanding the consequences of shifting towards natural gas use in relation to CO2 emissions.
5. Conclusion

This study reiterates the inverse relationship between per-household gas consumption and outdoor air temperatures and provides a systematic short-to-medium-range forecast framework by showing that temperature can be effectively used to forecast future gas consumption at different temporal and spatial resolutions. It was shown that LTC forecast model is superior to a naive forecast method that relies on historical averaging of consumption values. This analysis integrated a comprehensive uncertainty analysis by highlighting the effectiveness of using temperature ensembles in forecasting daily, weekly, and biweekly gas consumption across a large geographical span of the U.S. at a county level, and provided a detailed analysis of the uncertainties involved in gas consumption prediction. Temperature ensembles inherently possess some uncertainties, and this study quantified the impact of these uncertainties on the final forecast of gas consumption. It was found that the uncertainty in the temperature ensembles influenced about 50% of the uncertainties found in the gas consumption forecast. This shows that LTC forecast model is fairly resilient to temperature uncertainties, and it has the potential to provide an accurate medium-range gas forecast with an accuracy of 83% for a lead time of 1-2 weeks and an accuracy of 76% for the 10-12 week lead time weeks. Short-term forecasts facilitate quick policy adjustments to address immediate consumption requirements, whereas medium-range forecasts offer insights for mid-term policy planning. Overall, the study contributes a robust framework, offering valuable insights for informed policy support in meeting climate goals.
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Figures

<figure><img src="image_3.png" /><figcaption>Fig. 1 (A) Temporal fluctuations in the daily per-household gas consumption and temperature in the United States. (B) Map showing the U.S. regions considered for the regional forecast and discussion and the distribution of the Citygate pipeline gas delivery locations in the U.S. The size of the dots on the map indicates the consumption value. (C) Linear-plus-plateau function fitted based on the gas consumption and temperature data from Middlesex County, Massachusetts (2018). (D) Temporal fluctuations in the daily per-household gas consumption and temperature in Middlesex County, Massachusetts, along with LTC model predictions and naive model predictions for the year 2021. (E) Comparison of the per household gas consumption prediction using LTC model (in green) vs. a naive model (in blue) for the year 2021 in Butte County, South Dakota.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2 Spatial distribution of the relative RMSE for (A) daily, (B) weekly, and (C) biweekly seasonal hindcast at different lead times (1 week to 12 weeks) using temperature forecast ensembles. (D) Histogram of RRMSE for daily, weekly, and biweekly cases at different lead times. All RRMSE values shown in the figure are median values for Winter 2018-19.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3 Spatial distribution of percentage change in gas consumption forecast compared to the actual gas consumption for (A) daily, (B) weekly, and (C) biweekly seasonal hindcast at different lead times (1 week to 12 weeks) using temperature forecast ensembles (mean of 51 ensembles). All RRMSE values shown in the figure are median values for Winter 2018-19.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>B</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>C</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>D</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 4 (A) Line chart showing median values of the relative RMSE (RRMSE) for all counties for different lead times. (B) Bar chart showing component scores for all regions for daily case. (C) Bar chart showing component scores for all regions for weekly case. (D) Bar chart showing component scores for all regions for biweekly case. The three components are the squared bias (SB), the squared difference between standard deviations (SDSD), and the lack of correlation weighted by the standard deviations (LCS).</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 5 Comparison of the relative RMSE (RRMSE) when predicting gas consumption using temperature forecast ensembles (Y-axis) and RRMSE of observed temperature and temperature forecast ensembles (X-axis) for (A) daily, (B) weekly, and (C) biweekly predictions. Each point in the plot represents a county. Values are normalized by subtracting from the maximum RRMSE for each county (at lead time 12).</figcaption></figure>