Sustratos no pulidos: proceso con doble lift-off

Two different approaches can in general be applied to compare satellite measurements to in-situ datasets for validation purposes. On the one hand, the observational data may be interpolated to match those originating from the satellite. On the other hand, one can approach the problem by means of finding those satellite recordings, which are closest in time (concurrent) and space (co-located) to the respective in-situ data. As the latter method, amongst others, does not only save computational energy, but also avoids smoothing of extremes (which are essential in the validation procedure), this so-called ’nearest neighbour’ approach is chosen within this work and termed collocation as of now.

Due to the satellites’ rapid propagation (6.58 km/s), the probability of applied SSM/I instruments to traverse RV Polarstern simultaneously to an hourly in-situ measurement remains very low. To nevertheless allow for matching HOAPS- to ship- (and ERA-) based records, the nearest neighbour attempt permits small spatial and temporal shifts between both data sources, respectively.

The question remains as to how the thresholds of these shifts should be specified. A too strict strategy (i.e. too small shifts) would reduce the available match-ups in a needless manner. A too generous approach, to the contrary, would concede collocated pairs, the underlying data of which may not be physically meaningful. The problem is further complicated, as only one research vessel is available, which propagates simultaneously in time and space. The latter inhibits the separate deriva- tion of temporal and spatial shifts at the same instant.

The issues addressed above are solved by initially calculating temporal decorrelation timescales Γ (see Eq. 22) of the in-situ dataset, which serve as a basis for deriving the spatial decorrelation timescales Υ subsequently.

Assuming the discrete time series of hourly ship observations, X, to be generated by a stationary process, its autocorrelation solely depends on the time lag τ = t2− t1, where t1and t2 correspond to

arbitrary times. Accordingly, the autocovariance function is defined as

the normalization (by σ2) of which leads to the autocorrelation function (ACF)

ρ(τ ) = R(τ )

R(0) =

R(τ )

σ2 , (21)

where t = 0, ±1, ±2, ... and µ represents the expected value of X.

The largest permitted temporal shift between ship- and HOAPS-based records is defined by Γ, which can be expressed as follows:

Γ =

Z ∞

0

ρ(τ )dτ. (22)

Definitions of Γ vary in literature; here, it is defined as the time lag after which a reduction of ρ to its e-folding value30 _{has occurred. Depending on the geophysical parameter and the climate zone, Γ}

exhibits a considerable spread (Strehz et al. (2009)). As mid-latitudinal regions are characterized by frequent passages of frontal zones, associated with strong gradients in wind speed, specific humidity, and consequently also LHF, respective decorrelation time scales are expected to be small compared to (sub-)tropical regions.

Fig. 3.2: ρ(τ ) of several geophysical bulk parameters (thin, dashed lines), on which the latent heat flux (thick, dashed line) depends on. All ACFs represent arithmetic means composed of 23 subseries between 40◦-60◦ N/S each of which are 24 hours long. A rather constant, relatively high ship speed underlies these subseries, allowing for an estimation of Υ later on. qsat,seaequals to qsin the text. The black horizontal line indicates

the e-folding value. Its intersection with the individual ρ(τ ) contours allows for deriving the respective parameter-dependent Γ. Compare text for interpretation.

To avoid too generous colloca- tion requirements, Eqs. 20-22 are applied to 24-hour sub time se- ries obtained in the mid-latitudes between 40◦ − 60◦ _{N/S (compare}

Fig. 3.2). For reasons of sim- plicity, the outcome of Γ is ap- plied to data within all latitudinal

bands. As only ≈ 22% of all

measurements performed on RV Po- larstern between 1995-1997 were obtained equatorwards of 40◦ N/S and owing to a general large data availability, this assumption is justi- fied.

Fig. 3.2 illustrates ship-based ρ(τ ) for several bulk input param- eters (thin, dashed contours), on which LHF (thick, dashed contour)

depends. All ρ(τ ) fall off in an exponential manner, indicating a first-order Markov process (Tren- berth(1985)). As can be seen, ρ(τ ) associated with LHF falls below 1/e for Γ = 4 hours, owing to

fairly large Γ of qaand qs(SST) and concurrent smallest Γ associated with absolute wind speeds ~u.

In order to circumvent large collocation biases owing to an overestimation of the decorrelation time scale, the latter is defined to be Γ = 3 hours for all displayed parameters in Fig. 3.2, following the absolute wind speed possessing the least temporal persistency of all.

Given Γ, Υ may be derived via simple velocity considerations. As the mean speed ~vp of RV Po-

larsternduring the sub time series shown in Fig. 3.2 is given by 22 km/h, Υ = Γ · ~vp = 66 km. Υ is

rounded down to 60 km, bearing in mind that covered distances within three hours may be less during non-transit cruises.

Having set Γ = 3 hours and Υ = 60 km allows for collocating ship- (and consequently also ERA- ) to HOAPS-based geophysical parameters (compare Table 4) following the nearest neighbour ap- proach in a final step. Match-ups exceeding Γ and Υ are exclusively omitted.