Table 1 Posterior mean and 95% credible interval of the parameter estimates from the current model

Intercept

(\({\beta }_{r,0}\)) (Mg ha^–1 year⁻¹)

5.89

(5.55, 6.24)

16.37

(14.17, 18.77)

7.34

(5.85, 8.7)

4.46

(4.31, 4.61)

MAP effect \({(\beta }_{r,1})\)

(Mg ha^–1 year⁻¹ mm^–1)

0.0071

(0.0062, 0.0079)

−0.0032

(−0.0037, −0.0027)

0.0028

(−0.0015, 0.0080)

−0.0002

(−0.0005, 0.0001)

MAT effect \({(\beta }_{r,2})\)

(Mg ha^–1 year⁻¹ °C^–1)

-0.0386

(-0.0729, -0.0043)

−0.1429

(−0.2871, 0.0114)

0.2486

(−0.0243, 0.4443)

0.2686

(0.2514, 0.2857)

Intercept

(\({\beta }_{\mu ,0}\)) (Mg ha^–1)

393.55

(360.95, 430.72)

373.10

(182.5, 645.17)

286.30

(227.29, 369.82)

449.56

(416.6, 486.7)

MAP effect \({(\beta }_{\mu ,1})\)

(Mg ha^–1 mm^–1)

−0.2122

(−0.2693, −0.1418)

−0.1905

(−0.2621, −0.1210)

−0.1964

(−0.3613, −0.0263)

0.0874

(0.0064, 0.1745)

MAT effect \({(\beta }_{\mu ,2})\)

(Mg ha^–1 °C^–1)

19.0471

(15.3600, 22.6571)

36.9300

(5.4271, 69.0714)

8.2000

(−4.3529, 19.4900)

22.3700

(18.7143, 26.0643)

Variance of error (\(\sigma\))

0.52

(0.49,0.54)

0.44

(0.41,0.47)

0.5

(0.46,0.52)

0.52

(0.5,0.53)