Table S1.
Type III sums of squares for rain-fed soybean or maize yield using AOT40
| Model parameter | Degrees of freedom | Sums of squares | F value | Bootstrapped P value† |
| Soybean | ||||
| Intercept | 1 | 42,986,422 | 381.1 | 0.002 |
| Year | 1 | 109,500,327 | 970.7 | 0.002 |
| County | 253 | 51,497,998 | 1.8 | 0.002 |
| Tmax | 1 | 6,499,272 | 57.6 | 0.002 |
| P/PET | 1 | 231,458 | 2.1 | 0.162 |
| Tmax2 | 1 | 6,299,699 | 55.8 | 0.002 |
| P/PET2 | 1 | 1,177,780 | 10.4 | 0.01 |
| AOT40 | 1 | 2,143,325 | 19.0 | 0.002 |
| Year*county | 253 | 52,214,982 | 1.8 | 0.002 |
| Tmax*P/PET | 1 | 23,408 | 0.2 | 0.65 |
| Tmax*P/PET2 | 1 | 638,221 | 5.7 | 0.022 |
| P/PET*Tmax2 | 1 | 4,135 | 0.0 | 0.83 |
| P/PET*AOT40 | 1 | 3,220,478 | 28.6 | 0.002 |
| Tmax*AOT40 | 1 | 2,635,755 | 23.4 | 0.002 |
| P/PET2*AOT40 | 1 | 2,009,716 | 17.8 | 0.002 |
| Tmax2*AOT40 | 1 | 2,725,040 | 24.2 | 0.002 |
| Residuals | 6,210 | 700,493,337 | ||
| Maize | ||||
| Intercept | 1 | 607,930,191 | 640.3 | 0.002 |
| Year | 1 | 1,945,329,640 | 2,048.9 | 0.002 |
| County | 283 | 872,112,839 | 3.2 | 0.002 |
| Tmax | 1 | 63,759,208 | 67.2 | 0.002 |
| P/PET | 1 | 14,092 | 0.01 | 0.904 |
| Tmax2 | 1 | 71,493,397 | 75.3 | 0.002 |
| P/PET2 | 1 | 10,747,972 | 11.3 | 0.002 |
| AOT40 | 1 | 52,350,097 | 55.1 | 0.002 |
| Year*county | 283 | 883,549,646 | 3.3 | 0.002 |
| Tmax*P/PET | 1 | 781,632 | 0.8 | 0.384 |
| Tmax*P/PET2 | 1 | 3,969,534 | 4.2 | 0.046 |
| P/PET*Tmax2 | 1 | 1,589,393 | 1.7 | 0.218 |
| P/PET*AOT40 | 1 | 3,172,799 | 3.3 | 0.064 |
| Tmax*AOT40 | 1 | 59,760,344 | 62.9 | 0.002 |
| P/PET2*AOT40 | 1 | 1,285,533 | 1.4 | 0.19 |
| Tmax2*AOT40 | 1 | 61,096,841 | 64.3 | 0.002 |
| Residuals | 6,932 | 6,581,707,260 |
†
Bootstrapped P values were determined by comparing the F value in the table to a null F distribution that was generated by a double bootstrap procedure that accounted for spatial correlation. Thus, the P value in the table is different from that of a standard F test.