Two independent analyses are performed for 2 m temperature and 2 m relative humidity. The method used is a two-dimensional univariate statistical interpolation. In a first step, the background field (6 h or 12 h forecast) is interpolated horizontally to the observation locations using a bilinear interpolation scheme and background increments

are estimated at each observation location

.

The analysis increments

at each model grid-point

are then expressed as a linear combination of the first-guess increments (up to

values) :

(12.1)

where

are optimum weights given (in matrix form) by :

(12.2)

The column vector

(dimension

) represents the background error covariance between the observation

and the model grid-point

. The

matrix

describes the error covariances of background fields between pairs of observations. The horizontal correlation coefficients (structure functions) of

and

are assumed to have the following form:

(12.3)

where

is the horizontal separation between points

and

the e-folding distance taken to 300 km (hard coded in subroutine OIINC).

Therefore :

(12.4)

with

the standard deviation of background errors.

The covariance matrix of observation errors

is set to

where

is the standard deviation of observation errors and

the identity matrix.

The standard deviations of background and observation errors are set respectively to 1.5 K and 2 K for temperature and 5% and 10% for relative humidity. The number of observations closest to a given grid point that are considered to solve (12.1) is

(scanned within a radius of 1000 km). The analysis is performed over land and ocean but only land (ocean) observations are used for model land (ocean) grid points.

12.2.2 Quality controls

Gross quality checks are first applied to the observations such as

and

where

is the dewpoint temperature. Redundant observations are also removed by keeping only the closest (and more recent) to the analysis time.

Observation points that differ by more than 300 m from the model orography are rejected.

For each datum a check is applied based on statistical interpolation methodology. An observation is rejected if it satisfies :

(12.5)

where

has been set to 3, both for temperature and humidity analyses.

The number of used observations every 6 hours varies between 4000 and 6000 corresponding to around 40% of the available observations.

The final relative humidity analysis is bounded between 2% and 100%. The final MARS archived product is dew-point temperature that uses the 2 m temperature analysis

to perform the conversion :

(12.6)

with

(12.7)

12.2.3 Technical aspects

The technical aspects are similar to the snow analysis (see Chapter 11) expect for the computation of the analysis increments obtained from the subroutine OIUPD instead of SUCSNW (Cressman interpolation).

Subroutine OISET selects the