Why rainfall-only metrics understate drought loss
Most drought overlays in credit and insurance models still run on rainfall deficits, usually the Standardized Precipitation Index. That works when temperature is stationary. It stops working the moment atmospheric demand starts moving, because a season can deliver perfectly ordinary rainfall and still dry the soil out if evaporative demand is elevated. The 2018 northern European drought and the repeated Iberian and Californian events are the obvious cases: the rainfall anomaly alone would have told you the year was unremarkable, while yields, reservoir levels and thermal plant availability all said otherwise.
SPEI closes that gap by standardising the climatic water balance rather than the rainfall series. It keeps everything that made SPI attractive to modellers — a single standardised number, comparable across regions and seasons, available at multiple accumulation windows — and adds the demand side that determines whether a rainfall deficit actually becomes an agronomic or hydrological one.
How SPEI is constructed
The index is built in three steps. First, compute the monthly water balance as precipitation minus potential evapotranspiration. Second, aggregate that balance over the accumulation window of interest — three, six, twelve or twenty-four months. Third, fit a probability distribution to the aggregated series (a log-logistic fit is the conventional choice, because the water balance can be negative and is not bounded at zero the way precipitation is) and convert the cumulative probability to a standard normal deviate.
The result reads like a z-score. Zero is the reference-period norm, around minus one is moderate drought, minus 1.5 to minus two is severe, and below minus two is extreme. The one decision that changes your numbers more than any other is the potential-evapotranspiration method. Thornthwaite is temperature-only and cheap, but it systematically exaggerates warming-driven drying; Penman-Monteith brings in radiation, humidity and wind and is what I use whenever the reanalysis inputs are available. Document the choice, because a validator will ask, and the two methods can differ by half an index point in warm arid regions.
The reference period matters too. A SPEI computed against 1981-2010 and one computed against 1991-2020 describe the same physical season with different severity labels. For risk work, fix one baseline across the whole portfolio and state it in the model documentation rather than inheriting whatever a data provider happened to ship.
Choosing the accumulation window
The window is not a tuning parameter to be optimised freely; it should be chosen to match the physical memory of the exposure. Rain-fed arable yield tends to respond to three- and six-month SPEI aligned to the growing season, because soil moisture integrates over roughly that horizon. Hydropower revenue and reservoir-linked water utilities respond to twelve- and twenty-four-month windows, since storage carries deficits across years. Irrigation demand, flash-drought insurance and thermal-plant cooling constraints respond to one- and two-month windows.
In practice I test a small grid of windows against realised loss or yield data and pick the one with both the strongest relationship and a physical justification. If the statistically best window has no agronomic or hydrological story behind it, that is usually a sign of overfitting to a short sample.
From index to financial loss
The modelling chain runs hazard, exposure, vulnerability, loss. SPEI is the hazard layer, and it needs a damage function to become anything else. For agriculture the usual shape is a piecewise relationship between SPEI and yield loss ratio: negligible impact down to around minus 0.5, a steepening loss slope through the moderate and severe bands, and a plateau where the crop is effectively lost and further drying adds nothing. Fit that curve per crop and per region; the same index value means very different things to irrigated maize and to rain-fed wheat.
For energy portfolios the translation is usually two-stage. SPEI drives inflow or storage anomaly, storage drives generation volume, and generation volume interacts with a price path that is itself correlated with the drought — which is the part most models get wrong. Drought in a hydro-dependent market raises spot prices at the same moment it cuts your volumes, so the revenue impact is a product of two correlated terms and cannot be estimated by shocking volume alone.
Once loss ratios exist at the asset level, aggregation follows normal catastrophe practice: apply the spatial correlation implied by the index field itself, build an event set from historical and simulated SPEI surfaces, and read the portfolio loss distribution off the resulting exceedance curve. Because SPEI fields are broad and highly spatially correlated, drought diversifies far less across a region than wind or flood — a portfolio that looks geographically spread can still be effectively single-event exposed.
Parametric triggers and basis risk
SPEI is attractive for parametric agricultural cover because it is objective, published, and hard to manipulate. The cost is basis risk: the contract pays on a grid cell, the farmer loses on a field. Before setting an attachment point, quantify the correlation between the index and realised loss on the specific exposure, then look at the tail cases where the index says drought and the loss did not occur, and vice versa. That second table is what determines whether the structure is a hedge or a lottery ticket, and it belongs in the product documentation rather than in a footnote.
Validation and governance
A SPEI-based drought model earns its place through backtesting against named historical events, sensitivity analysis across the evapotranspiration method and reference period, benchmarking against vendor drought models where available, and a documented statement of limitations. The main limitations are honest and worth writing down: the index does not know about irrigation, groundwater, soil type or crop management; gridded reanalysis inputs carry their own bias in data-sparse regions; and forward-looking SPEI under climate scenarios inherits every uncertainty in the underlying climate model ensemble.
None of that disqualifies the index. It means the outputs should be presented with their uncertainty attached, reviewed on the normal model-validation cycle, and used for what they are good at — comparing relative drought exposure across a portfolio and stress testing it under scenarios — rather than as a point forecast of next season's loss.
Frequently asked questions
- What is the Standardized Precipitation Evapotranspiration Index (SPEI)?
- SPEI is a multi-scalar drought index built from the climatic water balance — precipitation minus potential evapotranspiration — standardised against a reference distribution so that values are comparable across regions and seasons. Negative values indicate drier-than-normal conditions; values below -1.5 are typically treated as severe drought.
- How does SPEI differ from SPI?
- SPI uses precipitation alone. SPEI adds the atmospheric water demand side through potential evapotranspiration, so it captures heat-driven drought that a rainfall-only index misses. In warming scenarios that difference matters: two periods with identical rainfall can carry very different loss potential once temperature is accounted for.
- Which SPEI accumulation window should a risk model use?
- Match the window to the exposure. Rain-fed crop yield responds to 3-6 month SPEI over the growing season; hydropower and reservoir storage respond to 12-24 month SPEI; short-window SPEI (1-2 months) is mostly useful for flash drought and irrigation demand spikes.
- Can SPEI be used directly as a parametric insurance trigger?
- Yes, and it is — but only with an explicit basis-risk assessment. SPEI is a gridded index, so the trigger measures the grid cell, not the insured field. Quantify the correlation between the index and realised loss before setting attachment points.
For collaboration or advisory work on drought and physical climate risk modelling with Jonas Osman Abdelghafour, write to contact@jonasosman.org.