Decorrelation scales for Arctic Ocean hydrography – Part I: Amerasian Basin

Any use of observational data for data assimilation requires adequate information of their representativeness in space and time. This is particularly important for sparse, non-synoptic data, which comprise the bulk of oceanic in situ observations in the Arctic. To quantify spatial and temporal scales of temperature and salinity variations, we estimate the autocorrelation function and associated decorrelation scales for the Amerasian Basin of the Arctic Ocean. For this purpose, we compile historical measurements from 1980 to 2015. Assuming spatial and temporal homogeneity of the decorrelation scale in the basin interior (abyssal plain area), we calculate autocorrelations as a function of spatial distance and temporal lag. The examination of the functional form of autocorrelation in each depth range reveals that the autocorrelation is well described by a Gaussian function in space and time. We derive decorrelation scales of 150–200 km in space and 100–300 days in time. These scales are directly applicable to quantify the representation error, which is essential for use of ocean in situ measurements in data assimilation. We also describe how the estimated autocorrelation function and decorrelation scale should be applied for cost function calculation in a data assimilation system.

Decorrelation scales for Arctic Ocean Hydrography. Part I: Amerasian Basin

Abstract. Any use of observational data for data assimilation requires adequate information of their representativeness in space and time. This is particularly important for sparse, non-synoptic data, which comprise the bulk of oceanic in-situ observations in the Arctic. To quantify spatial and temporal scales of temperature and salinity variations, we estimate the autocorrelation function and associated decorrelation scales for the Amerasian Basin of the Arctic Ocean. For this purpose, we compile historical measurements from 1980 to 2015. Assuming spatial and temporal homogeneity of the decorrelation scale in the basin interior (abyssal plain area), we calculate autocorrelations as a function of spatial distance and temporal lag. The examination of the functional form of autocorrelation in each depth range reveals that the autocorrelation is well described by a Gaussian function in space and time. We derive decorrelation scales of 150~200 km in space and 100~300 days in time. These scales are directly applicable to quantify the representation error, which is essential for use of ocean in-situ measurements in data assimilation. We also describe how the estimated autocorrelation function and decorrelation scale should be applied for cost function calculation in a data assimilation system.

Creation of a Gridded Dataset for the Southern Ocean with a Topographic Constraint Scheme

This study investigated a method for creating a climatological dataset with improved reproducibility and reliability for the Southern Ocean. Despite sparse observational sampling, the Southern Ocean has a dominant physical characteristic of a strong topographic constraint formed under weak stratification and strong Coriolis effect. To increase the fidelity of gridded data, the topographic constraint is incorporated into the interpolation method, the weighting function of which includes a contribution from bottom depth differences and horizontal distances. Spatial variability of physical properties was also analyzed to estimate a realistic decorrelation scale for horizontal distance and bottom depth differences using hydrographic datasets. A new gridded dataset, the topographic constraint incorporated (TCI), was then developed for temperature, salinity, and dissolved oxygen, using the newly derived weighting function and decorrelation scales. The root-mean-square (RMS) of the difference between the interpolated values and the neighboring observed values (RMS difference) was compared among available gridded datasets. That the RMS differences are smaller for the TCI than for the previous datasets by 12%–21% and 8%–20% for potential temperature and salinity, respectively, demonstrates the effectiveness of incorporating the topographic constraint and realistic decorrelation scales. Furthermore, a comparison of decorrelation scales and an analysis of interpolation error suggests that the decorrelation scales adopted in previous gridded datasets are 2 times or more larger than realistic scales and that the overestimation would increase the interpolation error. The interpolation method proposed in this study can be applied to other high-latitude oceans, which are weakly stratified but undersampled.

A Study on the Scale Dependence of the Predictability of Precipitation Patterns

A methodology is proposed to investigate the scale dependence of the predictability of precipitation patterns at the mesoscale. By applying it to two or more precipitation fields, either modeled or observed, a decorrelation scale can be defined such that all scales smaller than are fully decorrelated. For precipitation forecasts from a radar data–assimilating storm-scale ensemble forecasting (SSEF) system, is found to increase with lead time, reaching 300 km after 30 h. That is, for , the ensemble members are fully decorrelated. Hence, there is no predictability of the model state for these scales. For , the ensemble members are correlated, indicating some predictability by the ensemble. When applied to characterize the ability to predict precipitation as compared to radar observations by numerical weather prediction (NWP) as well as by Lagrangian persistence and Eulerian persistence, increases with lead time for most forecasting methods, while it is constant (300 km) for non–radar data–assimilating NWP. Comparing the different forecasting models, it is found that they are similar in the 0–6-h range and that none of them exhibit any predictive ability at meso-γ and meso-β scales after the first 2 h. On the other hand, the radar data–assimilating ensemble exhibits predictability of the model state at these scales, thus causing a systematic difference between corresponding to the ensemble and corresponding to model and radar. This suggests that either the ensemble does not have sufficient spread at these scales or that the forecasts suffer from biases.

Covariance Localization with the Diffusion-Based Correlation Models

Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.

Drift in Salinity Data from Argo Profiling Floats in the Sea of Japan*

In drift analysis of salinity sensors, one major problem is the difficulty in delineating sensor drift from water mass changes. In the present study, a new method is proposed for finding sensor drift that is free from water mass changes. The efficiency of this new method in finding out possible drift in the Argo salinity is demonstrated in the Sea of Japan (SOJ) by using the “near-linear” subsurface salinity structure of the SOJ. The new method is based on the time–space decorrelation scale. The salinity difference between two neighboring observations within the time–space decorrelation scale (SALD) is used to find out possible drift. Neighboring observations within the time–space decorrelation scale are referred to as matchups. The SALD derived from matchups between Argo floats and shipboard CTD observations from the SOJ shows linear drift. Although all four selected floats (5 yr completed) from the SOJ show linear drift (<0.001 PSS yr−1), the drift alone is not so significant to affect the objective of the Argo program in understanding climate variability. In the SOJ, SALD identified salinity error other than drift in good quality data that are flagged by the Argo delayed-mode quality control (ADMQC) method. Therefore, SALD could be used as an effective additional tool in the Argo data quality control. To examine the applicability of SALD in open ocean regions, in addition to confined basins such as SOJ, SALD was applied successfully to detect salinity error in Argo data from the subtropical North Pacific (SNP).

The Impact of Assimilating Atmospheric Infrared Sounder Observation on the Forecast of Typhoon Tracks

This work assesses the effects of assimilating atmospheric infrared sounder (AIRS) observations on typhoon prediction using the three-dimensional variational data assimilation (3DVAR) and forecasting system of the weather research and forecasting (WRF) model. Two major parameters in the data assimilation scheme, the spatial decorrelation scale and the magnitude of the covariance matrix of the background error, are varied in forecast experiments for the track of typhoon Sinlaku over the Western Pacific. The results show that within a wide parameter range, the inclusion of the AIRS observation improves the prediction. Outside this range, notably when the decorrelation scale of the background error is set to a large value, forcing the assimilation of AIRS data leads to degradation of the forecast. This illustrates how the impact of satellite data on the forecast depends on the adjustable parameters for data assimilation. The parameter-sweeping framework is potentially useful for improving operational typhoon prediction.

Physical response of the coastal ocean to Hurricane Isabel near landfall

Hurricane Isabel made landfall near Drum Inlet, North Carolina on 18 September 2003. In nearby Onslow Bay an array of 5 moorings captured the response of the coastal ocean to the passage of the storm by measuring currents, surface waves, bottom pressure, temperature and salinity. Temperatures across the continental shelf decreased by 1–3°C, consistent with a surface heat flux estimate of 750 W/m2. Salinity decreased at most mooring locations. A calculation at one of the moorings estimates rainfall of 11 cm and a net addition of fresh water at the surface of 8 cm. The low-pass current field shows a shelf-wide movement of water, first to the southwest, with an abrupt reversal to the northeast along the shelf after landfall. Close analysis of this reversal shows it to be a disturbance propagating offshore at a speed somewhat less than the local shallow water wave speed. The high-pass current field at one of the moorings shows a significant increase in kinetic energy at periods between 10 min and 2 h during the approach of the storm. This high-pass flow is isotropic and has a short (<5 m) vertical decorrelation scale. It appears to be closely associated with the winds, Finally we examined the surface wave field at one of the moorings. It shows the swell energy peaking well before the winds waves. At the height of the storm, as the winds rotated rapidly in the cyclonic sense, the wind wave direction rotated as well, with a lag of 45–90°.

Solar flux dependence of coherence scales in scintillation patterns produced by ESF irregularities

The coherence scale length, defined as the 50% decorrelation scale length along the magnetic east-west direction, in the ground scintillation pattern obtained at a dip equatorial location, due to scattering of VHF radio waves by equatorial spread F (ESF) irregularities, is calculated, using amplitude scintillation data recorded by two spaced receivers. The average east-west drift of the ground scintillation pattern, during the pre- and post-midnight periods, also calculated from the same observations, shows an almost linear increase with 10.7-cm solar flux. In the present paper the variability of the drift is automatically taken into account in the calculation of the coherence scale length of the ground scintillation pattern. For weak scintillations, the coherence scale depends on the Fresnel scale, which varies with the height of the irregularity layer, and also on the spectral index of the irregularity power spectrum. It is found that for weak scintillations, the coherence scales are much better organized according to the 10.7-cm solar flux, during the pre-midnight period, than during the post-midnight period, with a general trend of coherence scale length increasing with 10.7-cm solar flux except for cases with F 10.7-cm solar flux <100. This indicates that, during the initial phase of ESF irregularity development, the irregularity spectrum does not have much variability while further evolution of the spatial structure in ESF irregularities is controlled by factors other than the solar flux.