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Uncertainty reduction for precipitation prediction in North America [1]

['Dan Lou', 'Nanjing Nriet Industrial Co.', 'Ltd.', 'Nanjing', 'Wouter R. Berghuijs', 'Department Of Earth Sciences', 'Free University Amsterdam', 'Amsterdam', 'Waheed Ullah', 'Defense']

Date: 2024-06 

Large differences in projected future annual precipitation increases in North America exists across 27 CMIP6 models under four emission scenarios. These differences partly arise from weak representations of land-atmosphere interactions. Here we demonstrate an emergent constraint relationship between annual growth rates of future precipitation and growth rates of historical temperature. The original CMIP6 projections show 0.49% (SSP126), 0.98% (SSP245), 1.45% (SSP370) and 1.92% (SSP585) increases in precipitation per decade. Combining observed warming trends, the constrained results show that the best estimates of future precipitation increases are more likely to reach 0.40–0.48%, 0.83–0.93%, 1.29–1.45% and 1.70–1.87% respectively, implying an overestimated future precipitation increases across North America. The constrained results also are narrow the corresponding uncertainties (standard deviations) by 13.8–31.1%. The overestimated precipitation growth rates also reveal an overvalued annual growth rates in temperature (6.0–13.2% or 0.12–0.37°C) and in total evaporation (4.8–14.5%) by the original models’ predictions. These findings highlight the important role of temperature for accurate climate predictions, which is important as temperature from current climate models’ simulations often still have systematic errors.

Data Availability: Data can be accessed as follows: The 27 CMIP6 models’ simulated data of precipitation and temperature during 1970–2100 and of land surface runoff, total evaporation and soil water content during 2015–2100 was collected from https://esgf-node.llnl.gov/projects/cmip6/ . The 33 CMIP5 models’ simulated data of precipitation and temperature during 1970–2100 was collected from https://esgf-node.llnl.gov/projects/cmip5/ . The observed precipitation and temperature data is from datasets of HadCRUT4 ( http://www.cru.uea.ac.uk/ ), GHCN ( https://www.ncdc.noaa.gov/ghcn-monthly ), NOAA ( https://www.esrl.noaa.gov/psd/data/gridded/data.noaaglobaltemp.html ) and GISS ( https://www.esrl.noaa.gov/psd/data/gridded/data.gistemp.html ).

Copyright: © 2024 Lou et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

The key of the emergent constraint technique is to explore the mechanisms that underpin the emergent constraint relationship [ 16 ]. Thereby, we first explore the main driving factor (i.e. variable x) which dominates the large spread of predicted future annual precipitation growth rates (i.e. variable y) across the 27 CMIP6 models. The identified factor then is used to build the emergent constraint relationship with future annual precipitation growth rates across the CMIP6 models under scenarios SSP126, SSP245, SSP370 and SSP585. SSP126 represents the sustainable and “green” pathway with minimizing material resource and energy usage. SSP245 is the medium pathway that the world follows a path in which social, economic, and technological trends do not shift markedly from historical patterns. SSP370 has the high GHG emissions that a low international priority for addressing environmental concerns leads to strong environmental degradation in some regions. SSP585 has a very high GHG emissions (CO 2 emissions triple by 2075) that inequality is rising. Some regions suffer drastic environmental damage. By combing the observations, we aim to reduce the uncertainty of future annual precipitation in North America during 2015–2100. To verify the robustness of the emergent constraint relationships from CMIP6, 33 CMIP5 models under RCP45 and RCP85 are also used for cross-checking of the constraint relationship on a new model ensemble, using exactly the same constraint processes. Finally, the constrained future precipitation changes, with smaller uncertainties relative to the raw model predictions, are used to re-estimate growth rates of future temperature and evapotranspiration in North America.

In recent years, the emergent constraint technique that is based on the significant statistical relationship between simulated changes of historical climate variable X and predicted changes of future climate variable Y across an ESM ensemble has emerged [ 17 – 22 ] (See methods). This empirical relationship, combined with observed changes of climate variable X, has successfully reduced uncertainties in predicted changes of future climate variable Y (e.g., permafrost melt [ 23 , 24 ], marine primary production [ 25 ], Arctic sea-ice albedo feedback [ 26 ] and precipitation extremes [ 27 ]).

Earth System models (ESMs) are widely used to investigate past climate variations and future climate predictions in response to various radiative forcings [ 7 ]. Despite consideration of physical, chemical, and biological processes, ESMs often poorly predict the most basic quantities, such precipitation, temperature, and evaporation, as seen in a series of publications of the Fifth Phase of the Coupled Model Intercomparison Project (CMIP5) [ 8 – 10 ]. For example, the spread of future increases in global mean surface temperatures during 2081–2100 across CMIP5 models is large, ranging from 0.3°C to 1.7°C (RCP2.6), 1.1°C to 2.6°C (RCP4.5), 1.4°C to 3.1°C (RCP6.0) and 2.6°C to 4.8°C (RCP8.5) [ 11 ]. The future global mean precipitation feedbacks with temperature also exhibits substantial uncertainties (0.5–4% °C -1 ) [ 11 ]. The new generation of ESMs (CMIP6) that has higher horizontal-vertical resolutions and more comprehensive experimental designs [ 12 ], still yields considerable uncertainties in predicting the basic climate variables [ 13 – 15 ]. This inaccurate information makes planning climate mitigation and adaptation measures more challenging [ 16 ].

The climate of North America varies due to changes in latitude, and a range of geographic features (including mountains and deserts), ranging from the frost-free tropical of southernmost Florida to the perennial ice and snow of the northernmost islands of the Greenland. Generally, on the mainland, the climate of becomes warmer the further south one travels, and drier the further west, until one reaches the West Coast. The annual mean precipitation, temperature and evapotranspiration are 562 mm, -3.2°C and 342 mm, respectively. The current population of Northern America is around 0.38 billion. However, North America has experienced severe droughts in recent decades [ 1 , 2 ], which has negatively influenced agriculture, energy production, food security, forestry, drinking water, and tourism [ 3 – 5 ]. Typically, the main drivers of drought are below-average precipitation and/or above-average temperature and evaporation [ 6 ]. Thereby, accurate predictions of future precipitation, temperature and total evaporation are crucial for mitigating the climate-driven drought risks [ 4 ].

Extreme light rainfall days here are defined as the days with rainfall (including days without rainfall) lower than the long-term 10th percentile. Based on the outputs of the daily precipitation during 2015–2100 from 12 CMIP6 models, we estimated the annual extreme light rainfall days in each grid. The mean value of the annual extreme light rainfall days in all terrestrial grids is regarded as the average number of annual drought days in North America.

The higher the value of standardized coefficient of a driving factor it is, the more large the effects of this factor will be[ 36 ]. Thereby, we used the Eq 14 to estimate the relative contribution of runoff (C_R) on the future precipitation changes. Similarly, we can obtain the contributions of total evaporation (C_ET), soil water content (C_SW) and temperature (C_T).

To estimate the relative contribution of each potential driving factor (i.e., temperature, land surface runoff, soil water content and total evaporation) on the future precipitation changes, we used the multiple regression method that has been widely applied by previous studies [ 33 – 36 ]. After building the multiple regression relationships ( Eq 12 ) between future precipitation changes and the physically relevant observed driving factors, we can obtain the regression coefficient of each driving factor ( Eq 12 ). Then, the regression coefficients are used to estimate the standardized coefficient of each potential driving factor ( Eq 13 ). (12) (13) Where P, R, ET, SW and T are the precipitation, land surface runoff, total evaporation, soil water content and temperature, respectively. Ɛ is the residual error term. β 1 , β 2, β 3 and β 4 are the regression coefficient of each driving factor. Stc_R is the standardized coefficient of runoff ( Eq 13 ). Similarly, we can obtain the standardized coefficients of total evaporation (Stc_ET), soil water content (Stc_SW) and temperature (Stc_T).

The changes in precipitation (ΔP) are normally accompanied by coinciding changes in land surface runoff (ΔR), total evaporation (ΔET), soil water storage (ΔSW). These closely connected processes make up the land water cycle, which is described by Eq 11 [ 30 – 32 ]. (11) Ɛ is the other minor components in land water cycle (e.g., snow melting and human water uses).

Held and Soden [ 29 ] proposed a thermodynamic scaling where precipitation (Pre) can be approximated as a product of convective mass flux (M f ) and specific humidity (q), near the global land surface ( Eq 9 ). Thus, combining Eqs 8 and 9 , we can further obtain the Eq 10 [ 28 ]. Under a unchanged atmospheric circulation (ΔM f = 0), Eq 10 shows a linear positive relationship between precipitation and temperature, i.e. per increase in temperature will lead to 7% increase in precipitation.

The Clausius–Clapeyron relations (Eqs 7 and 8 ) indicate that the saturation specific humidity (q s ) increases by about 7% per degree of warming, i.e. α = 7% K −1 [ 28 ]. (7) (8) Where q s and T are the saturation specific humidity and the temperature, respectively. L v and R v are the latent heat of condensation at temperature T and the gas constant for water vapour (461.5 J kg −1 K −1 ), respectively. Here we assumed that Lv = 2.5 10 6 J kg −1 and the total pressure is much larger than the water vapour pressure.

For checking how significant the changes of future annual precipitation growth rates before and after applying the emergent constraint technique, we estimated the PDFs of the future annual precipitation growth rates before applying the technique ( Eq 5 ). After the constraint, the PDFs for the constrained future annual precipitation growth rates (PDF(F)) is calculated by numerically integrating PDF(F/ob) and PDF(ob) ( Eq 6 ). (5) where PDF(y/x) is the PDF around the best-fit linear regression, representing the PDF of y given x. (6) where PDF(F/ob) is the probability density for the “future climate projected variable” given the “historical observable variable”; and PDF(ob) is the observation-based PDF for “historical observable variable”.

In this study, we built the emergent constraint relationships between annual growth rates of simulated historical temperature and that of future precipitation across the CMIP6 and CMIP5 models ( S1 and S2 Tables), by using the least-squares linear regression method ( Eq 1 ). The prediction error of the regression (σ y ) is estimated by Eq 2 , following the method from Cox et al [ 21 ] and Chai et al [ 22 ]. Combining the observed temperature from four different data sets, the emergent relationship provides a tight constraint on future annual precipitation growth rates. (1) where y i (future predicted climate variable y, i.e., future annual precipitation growth rates) is the value given by x i (historical simulated climate variable x, i.e., simulated historical annual temperature growth rates); a and b are the slope and intercept values, respectively; (2) where s is used for minimizing the least-squares error, calculating by Eq 3 ; N is the number of models. σ x is the variance of x i Eq 4 ; is the mean value; (3) (4)

Results and discussion

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