Projecting global mean total column water vapor through 2050 using univariate and multivariate time series models

Abstract Water vapor strongly influences climate and hydroclimate extremes, and total column water vapor (TCWV) typically increases by about 6–7% per 1 K (Clausius–Clapeyron scaling). This study presents a forecasting framework that combines the seasonal autoregressive integrated moving average (SARIMA) model and long short-term memory (LSTM) networks to project global monthly mean TCWV through 2050. Historical TCWV and near-surface air temperature ( $$T_{2m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) data from ERA5 (1970–2024) were used to train both univariate and multivariate configurations, with the latter incorporating $$T_{2m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> </mml:math> to reflect its thermodynamic coupling with atmospheric moisture. Projections were conducted under multiple climate scenarios (CMIP5 and CMIP6) to assess TCWV sensitivity to future emission trajectories. Results show that the multivariate LSTM model outperforms both SARIMA and univariate LSTM baselines, achieving the lowest forecasting error (MAPE = 0.5736 %, RMSE = 0.1811 $$\hbox {kg}\, \hbox {m}-{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>kg</mml:mtext> <mml:mspace/> <mml:mtext>m</mml:mtext> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , $$R = 0.9881$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.9881</mml:mn> </mml:mrow> </mml:math> ). Under the CMIP6 SSP5− 8.5 scenario, TCWV is projected to increase from 25.63 $$\hbox {kg}\, \hbox {m}-{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>kg</mml:mtext> <mml:mspace/> <mml:mtext>m</mml:mtext> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> in 2024 to 27.08 $$\hbox {kg}\, \hbox {m}-{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>kg</mml:mtext> <mml:mspace/> <mml:mtext>m</mml:mtext> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> by 2050. In the independent test phase, the multivariate LSTM provides a slight improvement over SARIMA (RMSE: 0.1811 vs. 0.1845 kg m $$^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> ). Across the CMIP5/CMIP6 pathways considered, the projected 2050 global mean TCWV spans 25.96–27.08 kg m $$^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> , indicating higher sensitivity under stronger warming scenarios. The historical record also indicates a marked acceleration in the global TCWV trend, increasing from +0.039 kg m $$^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> decade $$^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> (1970–2000) to +0.434 kg m $$^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> decade $$^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math>