Monthly series
Every selected equation over the full record, in millimetres per month. The reference is drawn heavier and darker.
Cumulative depth
Running total over the record. Divergence between curves is the accumulated water-balance consequence of picking one equation over another.
Mean annual cycle
Long-term mean for each calendar month. Shape disagreement here is a seasonality problem; level disagreement is a bias problem.
Departure from the reference, month by month
Mean difference in mm/month. Warm cells run wetter than the reference, cool cells run drier.
Against the reference
Each point is one month. The dashed line is 1:1; the solid line is the ordinary least-squares fit.
Residual distribution
Box and whisker of (equation − reference) per month. The box spans the interquartile range, the notch marks the median.
Taylor diagram
Radial distance is the standard deviation of the equation normalised by the reference; the angle is the correlation coefficient; the distance from the reference marker on the horizontal axis is the centred RMS difference. A perfect equation sits exactly on the reference point.
Ranking
Equations are ranked separately on each criterion, then the ranks are summed. A low total means an equation is consistently good rather than good on one metric and poor on the rest.
Skill profile
Six criteria, each rescaled so that 1.00 is the best equation in this run and 0.00 the worst. Shape matters more than size: a lopsided profile means an equation is trading one kind of error for another.
Scenario response
Change in the annual total under the perturbation set in the Scenario panel, as a percentage of each equation's own baseline. Equations that respond very differently to the same climate signal are the ones worth arguing about.
Scenario table
Baseline and perturbed annual totals, in millimetres per year.
Driver sensitivity
One-at-a-time central-difference sensitivity of the annual total. Each bar is the response to a change you can state in words, not a dimensionless coefficient. This is the physical counterpart of a feature-importance plot.
Annual totals and trend
Only calendar years with all twelve months are used. The straight line is the Theil–Sen slope, drawn solid where the Mann–Kendall test rejects the no-trend hypothesis at 95 % and dashed where it does not.
Mann–Kendall and Theil–Sen
Both tests are rank based, so neither assumes a normal distribution nor a straight-line trend. A short record will not reach significance whatever the slope; the sample size is given so you can judge that.
Climatic water balance
Mean monthly evaporative demand against mean monthly rainfall. The gap in the dry half of the year is what an irrigation scheme has to supply and what a reservoir has to carry.
Aridity and reservoir loss
The UNEP aridity index is annual rainfall divided by annual demand, and its class boundaries are the ones used in the World Atlas of Desertification. Reservoir loss applies each equation to the water surface area above; open-water methods are the physically appropriate choice for that column.
Computed values
Every month, every selected equation, in mm/month. This is the sheet the export writes.