Time Series

A time series is what imagery becomes once you stop looking at a single scene and start reading the same place across many dates. As the Digital Imagery concept describes, satellites revisit the same ground again and again, so observations accumulate into a collection ordered in time. Arranging those repeated measurements into a sequence — one value, index, or image per date — lets you ask a different class of question: not what is here, but how it is changing.

Image dates, cadence, and observation gaps

Every scene carries an acquisition date and time, and those timestamps are the backbone of any time series. How often new observations arrive is the sensor’s temporal resolution, or revisit — a property the Resolution concept develops — and it sets the finest temporal detail the record can carry. A place imaged every few days can resolve short events that a monthly revisit would step straight over.

Real records are rarely as even as the nominal revisit suggests. Clouds and sensor gaps remove many passes, while overlapping orbits and off-nadir pointing add observations with different viewing geometry, so the series that reaches analysis is irregularly spaced, with clusters of dates and long gaps between them. This unevenness matters because a signal can only be followed if it is sampled often enough: variation faster than the effective sampling interval is missed entirely or, worse, aliased into a false slower pattern. Knowing the true cadence of valid observations — not just the satellite’s design revisit — is the first thing to establish before trusting any temporal claim.

Seasonal cycles, trends, and abrupt events

A temporal signal usually mixes several kinds of behavior, and separating them is much of what interpretation means. The most common is a periodic seasonal cycle: vegetation greening and senescing through the year, snow arriving and melting, water levels rising and falling. Overlaid on that periodicity there may be a gradual trend — a slow, directional drift across several years, such as steady vegetation gain or long-term drying — that is only visible once the record is long enough to see past the seasonal swing. And punctuating both are abrupt events: a fire, a flood, a harvest, a clearing, which appear as a sharp step or spike between two dates.

These three components make different demands on the record. Resolving a trend needs a long enough span that the underlying drift outweighs year-to-year variability; catching an abrupt event needs dense enough sampling that a usable observation falls close to both sides of it. A record that is long but sparse can describe trends while missing every short event, and a dense but short record can catch events while saying nothing about slow change. Matching the record’s length and density to the phenomenon is the design decision behind any time-series analysis.

Separating the components in practice usually means fitting a model to the series — a smooth seasonal curve built from harmonic (sine and cosine) terms, or a sequence of straight-line segments — which also bridges the gaps between clear observations. The continuous monitoring methods described under Change Detection are built on fits of this kind.

Composites, windows, and summary statistics

Because raw observations are irregular and noisy, they are often reduced into a smaller number of cleaner, evenly spaced layers. A composite collapses all the valid observations within a temporal window — a month, a season, a year — into one representative image by choosing a per-pixel summary, computed independently for each pixel from whatever clear dates it had. The summaries fall into two kinds. A per-band statistic such as the median builds a spectrum that no single date actually observed, while selecting one whole observation — the date with the highest vegetation index, say — keeps that pixel’s bands consistent with one another. This is why compositing tolerates the gaps: a pixel clouded on one date can still contribute from another within the same window.

Compositing and summarizing trade temporal detail for consistency. A wider window yields cleaner, more gap-free layers but blurs anything that changes faster than the window; a narrower window preserves timing but lets noise and missing dates through. The choice of statistic carries its own assumptions — a median suppresses outliers including residual cloud, whereas a maximum-value composite of a vegetation index favors the greenest, clearest observation but can latch onto an anomalous spike from residual noise. Clear-pixel composites in particular depend on first removing contaminated observations, which is the work of the Cloud Masking concept.

Consistency and the sources of temporal noise

A time series is only meaningful if a change in the numbers reflects a change on the ground rather than a change in how the ground was observed. Several effects can inject apparent change that is really an artifact. Undetected cloud, haze, and shadow are the largest, dropping or lifting values on individual dates. Differences between sensors — even nominally matching bands respond slightly differently — introduce steps when a record is stitched across instruments. And varying viewing and illumination geometry, as the sun angle shifts through the year and the sensor views from different angles, changes measured brightness without any change in the surface — the directional behavior of reflectance known as the bidirectional reflectance distribution function, or BRDF.

The conditions that keep dates comparable — calibrated values, a well-registered common grid, and screening for cloud — are set out under Change Detection; for a series the added hazard is that they must hold across every date, not just two.

Interpreting a temporal signal with domain context

A plotted curve does not interpret itself. Deciding whether a dip is a normal dry-season trough or a genuine disturbance, or whether a rising trend is recovery or encroachment, requires domain knowledge of what the surface should do: the expected phenology of the land cover, the local climate, the management calendar. The same shape means different things in a deciduous forest, an irrigated field, and a wetland. This is where a time series stops being a sequence of numbers and becomes evidence about a process.

That interpretation is also what Change Detection builds on when it turns a departure in the signal into a checked claim about what changed. Read with its uncertainty and its context in view — the cadence that set what could be seen, the compositing that shaped it, the noise that was controlled for — a time series turns a stack of dated images into an account of how a place behaves through time.