No Model Trend Analysis
1 \(\text{Log}\left(Q\right)\sim trend+\ \epsilon_{t}\) linear 40-year trend in streamflow to compare with LTPMK analysis
2 \(\text{Log}\left(P\right)\sim trend+\ \epsilon_{t}\) linear 40-year trend in rainfall to compare with LTPMK analysis
3 \(\text{Log}\left(Q\right)\sim s\left(P\right)+trend+\ \epsilon_{t}\) (equation 4) linear The trend in this model relative to model 1 indicates the importance of “other processes”, while the comparison with model 2 indicates the “amplification”.
4
\(\text{Log}\left(Q\right)\sim s\left(P\right)+s(maxT,P)+trend+\ \epsilon_{t}\) (equation 6)
linear
Difference between model 3 and 4 is the effect of evapotranspiration on the trend. The remaining trend is related to changes over time in the rainfall runoff response.
5 \(\text{Log}\left(Q\right)\sim s\left(P\right)+s(maxT,P)+\ \epsilon_{t}\) (equation 7) Mann Kendall and LTPMK Check if linear trend assumption is biased.