Sampling errors in satellite-derived infrared sea-surface temperatures. Part I: Global and regional MODIS fields

Highlights

• Sampling errors in MODIS Terra SSTs are quantified.

• Large errors are found in the high latitudes.

• Small errors are within ± 30° latitude, except in the TIW region.

• Atmosphere–ocean interactions cause dynamically distributed sampling errors.

• MODIS cloud mask for SSTs has imperfections around Antarctica.

Abstract

Long time series of accurate Sea Surface Temperatures (SSTs) are needed to resolve subtle signals that may be indicative of a changing climate. Motivated by the stringent requirements on SST accuracy required for Climate Data Records (CDR) we quantify sampling errors in satellite SSTs. Infrared sensors, including the Moderate Resolution Imaging Spectroradiometer (MODIS), have sampling errors caused by incomplete coverage primarily due to clouds and inter-swath gaps (gaps between successive swaths/orbits). Unlike retrieval errors, the sampling errors are introduced when calculating mean values and in generating gap-free SST fields. We generate MODIS-sampled SST fields by superimposing MODIS cloud masks on top of the Multi-scale Ultrahigh Resolution (MUR) SST field for the same day. Based on the MODIS-sampled fields, we calculate sampling errors at different temporal and spatial resolutions to examine the impacts at different scales. Our results indicate that sampling errors are significant, more so in the high latitudes, especially the Arctic. The 30°N–30°S zonal band is found to have the smallest errors; a notable exception is the persistent negative errors found in the Tropical Instability Wave area, where the mesoscale ocean–atmosphere interaction leads to a more frequently satellite sampling above the cold sections of the wave area. The global mean sampling error is generally positive and increases approximately exponentially with missing data fraction at a fixed averaging interval, while error variability is mainly controlled by SST variability. Areas with persistent cloud cover have large sampling errors in temporally averaged SSTs. We conclude that the sampling error can be an important or even dominant component of the error budget of mean and gap-free SST fields. Climate data generation and interpretation of satellite-derived SST CDRs and their application must be conducted with due regard to the sampling error.

Introduction

Global Sea Surface Temperature (SST) is an essential climate variable (ECV, listed by the Global Climate Observing System) that can be used to assess climate change. In order to resolve the subtle signals that maybe indicative of a changing climate, long time-series of accurate, spatially and temporally averaged SSTs are needed. Specifically, an SST Climate Data Record (CDR) (National Research Council, 2004) requires an absolute temperature uncertainty of 0.1 K and stability of 0.04 K per decade (Ohring, Wielicki, Spencer, Emery, & Datla, 2005). Such stringent requirements are intended to enable the detection of the likely regional or global signals of 0.2 K per decade. Hence, the correct quantification of errors and uncertainties in observed SSTs has become a critical need.

Among all the SST observing methods, satellites provide the most consistent global coverage. Infrared (IR) sensors in particular provide measurements of a fine resolution as well as having a long history. Therefore, for generating SST CDRs from satellite measurements (Minnett & Corlett, 2012), IR measured SSTs are a potentially valuable source. The Moderate Resolution Imaging Spectroradiometer (MODIS (Esaias et al., 1998)) on board the NASA Earth Observing System satellites Terra and Aqua obtain SST retrievals in a 2330 km swath. SST is derived from MODIS measurements of top-of-atmosphere radiances in mid- and thermal-IR bands (centered at wavelengths of 3.7, 3.9, 4.0, 11 and 12 μm), at which the atmosphere is relatively transparent to the transmission of surface IR emission. The comparison with independent measurements from shipboard spectroradiometers (Minnett et al., 2001) confirms that the derived SSTs from MODIS generally have mean biases < 0.1 K and scatter < 0.5 K (Minnett, 2010).

However, in a general satellite data processing flow, errors from different sources are produced at each of the successive data levels (Level 0 (digitized detector output) to Level 4 (bias corrected, geo-located, gridded, and gap-free SSTs in lat/lon coordinates) and accumulate toward higher levels, as discussed by the Interim Sea Surface Temperature Science Team White Paper (ISSTST, 2010). As with other satellite measurements, the MODIS SST accuracy refers to the retrieval error produced at Level 2 (derived SSTs at pixel bases), but Level 3 (binned, gridded and averaged Level 2 values) and Level 4 fields are extensively used in climate and modeling studies, mainly because of the desirable features of being “gridded and gap-free”. Another important error in Level 4 fields, independent of the retrieval error, is the sampling error caused by incomplete coverage of satellite measurements, and this is the focus of this paper.

There are two main reasons for this incomplete coverage. First, for any IR sensors such as MODIS, the presence of clouds causes gaps in the sampling, or ‘undersampling’, of SSTs. Cloudy pixels rejected by many currently used SST cloud masks constitute up to 90% of the total pixels sampled. Instead of being random, clouds around the globe form geographical patterns where some regions are prone to cloudiness while others are not. Some regions are even found with cloud-SST relations due to physical (e.g. Ramanathan and Collins (1991)) and dynamical mechanisms (e.g. Xie (2004) and Klein (1997)). Second, gaps between successive swaths of some sensors also lead to sampling errors. Sensors with narrower swaths are subject to a larger gap than others. The relatively broad swath of MODIS indicates that a scan gap of 432.8 km exists at the equator every 98.8 min. This gap narrows as it extends to the mid-latitudes of 32.3° poleward of which there is overlap of successive swaths. Consequently, these two factors become the fundamental issues in generating gap-free SST fields and lead to sampling errors.

In early studies, incomplete sampling issues were highlighted to ascertain the sampling errors of averaged climate data (Parker, 1984, Trenberth, 1984a, Trenberth, 1984b, Wigley et al., 1984). Recent sampling error studies for climatic time–space grid box averages of in-situ measured Surface Air Temperature (SAT) (Parker and Horton, 2005, Shen et al., 2007) and SST (Brohan, Kennedy, Harris, Tett, & Jones, 2006) are based on the quantification framework proposed by Jones, Osborn, and Briffa (1997) (referred to here as J97). In J97, the sampling error was expressed as the additional variance contributing to the grid box long-term temporal variance due to spatially incomplete sampling. Certain assumptions were made about the data statistics (e.g., homogeneity and stationarity) and the data spatial correlation curve. The sampling uncertainty was calculated by estimating averaged variance of stations and the inter-correlation between stations in the grid box. The SST data were mostly from ship and buoy observations and control run outputs from models. Morrissey and Greene (2009) developed a more general quantification framework by including temporally-insufficient sampling associated with ship measurements, assuming observations are randomly distributed. Kennedy, Rayner, Smith, Parker, and Saunby (2011) updated the work of J97 by applying an isotropic correlation decay function in both time and space. These previous works relied on the assumption made for the spatial or temporal inter-correlation curves within a grid box; additionally, the in-situ SSTs were used. Most recently, Hearty et al. (2014) quantified sampling biases in climatologies of atmospheric temperature and water vapor by comparing two MERRA (Modern Era Retrospective-Analysis for Research Applications; Rienecker et al. (2011)) climatologies sampled separately by the time and quality components of AIRS (Atmospheric Infrared Sounder) (Aumann et al., 2003) with a MERRA climatology sampled like a climate model, assuming that the MERRA data represents the real atmospheric state.

The sampling error of IR SSTs remains to be determined. Therefore, this paper will initiate the sampling error quantification for satellite IR SSTs. Furthermore, IR SSTs have different sampling structures (not random) and known sources of the sampling error (i.e., clouds and inter-swath gaps). The aforementioned statistical assumptions may not be necessary nor appropriate for determining sampling error magnitudes, and they may smooth sampling error variations which in fact can give information on how the errors are generated and whether they can be reduced. In this study, we calculate the MODIS sampling errors without presuming SST spatial or temporal correlations. Instead, we assume that a reasonable Level 4 field can be the reference, or ‘true’ field to help quantify the impact of the under-sampling in IR fields. For the purpose of this work, we calculate the difference between the sampled fields and the corresponding gap-free reference fields as an ‘error’ instead of ‘uncertainty’ because of our assumption about the reference fields. The merit of this approach is that we can suggest possible causes and impacts that can be physical and predictable, instead of just statistical, which can further help develop solutions or predictions of the sampling error. We show the sampling errors found in monthly IR SST fields are large at O(1 K), especially in regions sensitive to climate change, and have geographical distributions due to natural and artificial causes. We conclude that sampling errors can be an important or even dominant component in the error budget of Level 4 SSTs, compared with the typical magnitudes of retrieval error (< 0.5 K). Hence, climate data generation and interpretation of satellite-derived SST CDRs and their application must be conducted with due regard to the sampling error.