While in J...
Vector 13:2, page 10
Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 10
The so-called ‘antecedent precipitation index’ is a measure of the wetness of a catchment. Precipitation (rainfall, snow, etc.) makes a place wetter but such water is lost from a site over time by evaporation and drainage.
is one way of trying to capture this balance fairly simply.
The idea is pretty crude engineering hydrology and the API is naturally inferior to any number based on real measurements at a site. In practice, however, daily precipitation measurements for somewhere similar are far more readily available than are comparable soil moisture measurements, especially over long historical periods. I don’t know much folklore on estimating k, but one rough physical guide is that at most places wetness fluctuates about an average, especially on time scales of the order of a year. This allows you to bracket plausible values of k.
That is just context. Like the typical reader of Vector, when reading such simple formulae, I often write down the corresponding simple programs. To me, with a brain warped by too many years of Fortran and Basic, and improved slightly by exposure to various C-like languages, what springs to mind first is something like api1. To any J or APL enthusiast, api1 looks incredibly long-winded for such a mathematically trivial problem. And indeed in the best and worst traditions of APL a program can certainly be produced in one line, as for example api2.
Yet experiments clearly show that api2 is much slower and more demanding of space, as examination of the programs suggests. Can a quicker yet concise J script be produced?
As yet more context, any one who wanted to do this could easily have 1000 daily rainfalls, and in fact I will want to do something similar for more like 40,000 values. (I’ll probably do it with totally different software, but largely for reasons irrelevant to this journal.)