Phoenix hot–dry severity

This case estimates severity and clustering in a derived, EWMA-normalized hot–dry index. It is a statistical illustration, not a calibrated drought or health-risk index.

Construct the daily severity index

The source is NOAA GHCN-Daily station USW00023183, Phoenix Airport. Quality-screened TMAX and PRCP are converted to degrees Celsius and millimetres. P30_t is the sum of the preceding 30 days including the current day; all 30 observations must be available. Input completeness determines the longest continuous run before the severity index is computed.

For each numerical day-of-year group in that retained run, compute the sample mean and standard deviation of TMAX and P30, then define:

H_t = max((TMAX_t − mean_doy(TMAX)) / sd_doy(TMAX), 0)
D_t = max((mean_doy(P30) − P30_t) / sd_doy(P30), 0)
X_t = H_t + D_t

The climatology uses the full retained period, including later observations relative to earlier dates. This is retrospective standardization. The implemented dayofyear grouping is not a leap-adjusted month/day climatology. Overlapping 30-day precipitation sums also introduce dependence into the derived index.

EWMA normalization

The second step divides the nonnegative index by its past EWMA level:

Y_t = X_t / m_t
m_t = ρ m_(t−1) + (1−ρ) X_(t−1),  ρ = 2^(−1/180)

Initialize m with the first 30 index values, then fit from the next day. The fitted sample is 1948-01-29–2025-12-31, with 28,462 consecutive days. True zero-severity days remain. Y_t is a dimensionless ratio to recent severity; only this EWMA step is past-only. It does not make the preceding climatology point-in-time, and does not establish removal of seasonality.

EVI, EI, and design-life levels

Quantity	Estimate	Conditional 95% CI
EVI ξ	0.166	[0.156, 0.176]
BB-sliding-FGLS EI θ	0.274	[0.256, 0.294]
Northrop-sliding-FGLS EI θ	0.273	[0.250, 0.298]

The lower-left panel describes extremal clustering in the constructed normalized index. Click the figure for full size.

Download numerical results and preparation settings (JSON).

The selected EVI window is 31–654 days. Design-life curves use 365.25 daily observations per year. They refer to a maximum relative index value, not a temperature, precipitation deficit, or direct hazard threshold. EI cannot be interpreted as the duration of a heatwave or drought episode.

The nominal CIs use the common FGLS/Wald settings. They omit uncertainty in the full-period climatology, EWMA scale, selected record, and fit window. A narrow conditional CI does not resolve those sources of uncertainty.

Reproduce

PYTHONPATH=scripts uv run python -m application.docs_cases --keys phoenix_hot_dry_severity

Preparation uses the tracked normalization code and the archived GHCN station input.