Sampling errors in satellite-derived infrared sea-surface temperatures. Part I: Global and regional MODIS fields
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.
Section snippets
Data and methods
We used masks from the thermal IR daytime and mid-IR nighttime Level 3 fields of Terra MODIS SSTs. These data are globally gridded fields at 4 km spatial resolution and were generated from the MODIS Collection 6 retrievals, which is the most recent reprocessing of the MODIS SST. Global day and night cloud masks (i.e., quality mask, referred to as cloud mask in this paper, with flags = 0 indicating the best quality) were derived by considering quality flags > 1 as missing data primarily due to cloud
Sampling error quantification framework
Let SST0ref represent the reference data at a base resolution R0 of 0.04°and 1 day (1d), which is the Level 4 field, MUR. Then, for a grid box centered at location i and time j, the averaged reference field iswhere the averaging for space and time is denoted in a new resolution size R. R is selected as every combination of spatial resolutions of 0.04° (4 km, here after as ‘4 k’), 0.12° (12 k), 0.25°, 0.5°, 1°, 2.5°, and 5° and temporal resolutions of 1
Sampling error annual mean characteristics
Annual means of the sampling error are estimated by averaging over the full time period at a certain resolution R, and are shown in Fig. 2. Generally for these three cases, global sampling errors are prevalently within ± 0.5 K. Regions where fronts and upwelling occur have some values at about ± 1.0 K. Extreme values of ± 1.0 K to ± 6.0 K only occur in the Hudson Bay and other seasonally open water regions at high latitudes. The error pattern varies with resolution. In the [4 k, mon] map, positive errors
Discussion
We analyzed the effects of daily MODIS SST cloud masks of 4 months to characterize the resulting sampling errors. Note that because the MODIS swath width is insufficient to provide overlap of successive swaths equatorward of 32.3° latitude, the resulting, systematic gaps in the SST fields are included in this analysis with the missing data that result from the presence of clouds. The annual mean sampling error magnitude might fluctuate around the values we calculated for the 4 sample months.
Summary and conclusions
Motivated by the demanding accuracy of SSTs required for the SST CDR generation, we quantified the sampling errors of MODIS SSTs. We found that the MODIS monthly sampling error, using MUR SSTs as reference fields, is up to O(1 K), which far exceeds the error threshold needed for climate research and monitoring. Although the high latitudes are measured the most frequently by satellites, the largest sampling error (> 5 K) is found in the Arctic, which is believed to be the most vulnerable to climate
Acknowledgments
The initial stages of this research were supported by a grant from the NASA Physical Oceanography Program (NNX11AF26G) and then by a NASA Graduate Fellowship to Y. Liu (NNX14AL28H). This work has benefited from discussions with colleagues at RSMAS, including R. H. Evans, S. Walsh, K.A. Kilpatrick, D. Putrasahan, P. Zuidema and A. Adebiyi.
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