temperaturesare

Temperaturesare is a conceptual metric used in climate informatics to summarize the state of ambient temperatures over a region by aggregating measurements from a network of sensors into a single scalar value. It is designed to reflect not only average temperature but also the spatial distribution of readings, through a weighted aggregation that can emphasize certain locations or land-use types.

Construction and calculation

In discrete form, temperaturesare at time t is defined as temperaturesare(t) = sum over i of w_i T_i(t), where T_i(t) is the temperature reading from sensor i at time t and w_i are nonnegative weights with sum w_i = 1. The weights can be chosen to reflect sensor density, area coverage, population exposure, land use, or urban morphology. In a continuous formulation, temperaturesare(t) = ∫∫_A T(x,y,t) w(x,y) dx dy, with w(x,y) ≥ 0 and ∫∫ w dx dy = 1, where A is the region of interest and w(x,y) encodes the relative influence of each location.

Interpretation and use

Temperaturesare is a descriptive statistic intended to facilitate regional comparison, trend analysis, and decision support. It can be computed at varying timescales (hourly, daily, weekly) and extended to spatiotemporal analyses by considering temperaturesare(t) across multiple time points. It is not a fundamental physical quantity but a convenience metric akin to a weighted regional mean that may improve representativeness when sensor networks are uneven.

Limitations

The value of temperaturesare depends on the chosen weights and sensor layout, and can obscure local extremes or microclimates. It should be used alongside other statistics such as variance, min/max, and quantiles to capture distributional information and potential biases.

See also

Mean temperature, spatial averaging, gridded temperature data, urban heat island, heat index.