[Insert Figure 3 here]
To disentangle the contribution of the various potential drivers, we applied structural equation models (SEM) to quantify the environmental controls of CH4 uptake (all factors were classified into four groups: meteorology, microbes, plant, and edaphic factors,Figs. S2 and S3 ) using the field experiment’s data (Figs. 3a, 3b, 3c, and 3d ). Our models considered how nutrient additions directly or indirectly affects CH4 uptake (Figs. 3 and S3 ). The SEM results suggest that under control (non-fertilized) conditions, the impact of meteorology on CH4 uptake was directly (β = -0.33, standardized coefficient) or indirectly mediated through microbes (β = -0.8, standardized coefficient) and plants (β = -0.21, standardized coefficient) (Fig. S3a ). N and P additions affected CH4 uptake indirectly through edaphic factors (N treatment: β = 0.5, standardized coefficient, Fig. S3b ; N+P treatment: β = 0.37, standardized coefficient, Fig. S3d ). Soil NH4+ had a direct negative effect and plant N content had a positive effect on the CH4 uptake under control conditions and in all nutrient addition treatments (Figs. 3a, 3b, 3c, and 3d ). Meanwhile, added N stimulated the accumulation of soil NH4+ (N treatment: β = 0.45), added P had a positive impact on plant P and soil P, but had no impact on soil NH4+; while the N + P treatment had a negative impact on soil NH4+ (β = -0.18). Compared to the control, the N addition strengthened the negative effect of NH4+ on CH4 uptake (β ranging from -0.57 to -0.77) (Figs. 3a and 3b ); P addition did not change the negative effect of NH4+(β = -0.57) and the positive effect of plant N (β = 0.34) (Figs. 3a and 3c ); N + P additions strengthened the suppression effect of soil NH4+ (β changing from -0.57 to -0.72) (Figs. 3a and 3d ). These results showed that CH4 uptake is highly associated with soil N and P contents in semiarid grasslands.

Global Estimation of P alleviation of N-suppressed CH4 Sink in Grasslands

We further developed an empirical model to quantify the N and P impacts on soil oxidation of atmospheric CH4 across global grasslands, using existing global datasets of soil properties and meteorology (Methods ). Two thirds of the compiled data were used for model fitting, while the remaining one third of the data was used for model validation (Fig. S7 ). The best fitting equation obtained with the stepwise regression procedure was:
FCH4 = m + a × N + b × P + c × ln(N) × ln(P) + d × ST + e × pH + f × SOC + g × BD + h × CL (2)
where FCH4 is the annual CH4 uptake rate; N is the nitrogen input in g ha-1y-1; P is the phosphorus input rate in g ha-1 y-1; ln represents the natural logarithm; ST is soil temperature (K); pH is the soil pH value; SOC is soil organic carbon content (in %); BD is bulk density (g cm-3); CL is clay content (in %); m is the incept of the function; and a, b, c, d, e, f, g, and h are coefficients. The coefficients and key parameters for the regression are listed inTable S1 . The model explained more than 37% of the variation in CH4 uptake rate across the globe (Fig. S7 ).