Download Hourly Temperature Data
Shanae Maerz
Conceptual diagram for filling missing temperature data. Spatial methods rely on interpolation between available stations at a given time. Temporal methods interpolate within the time series at a given location. Spatiotemporal methods make use of both spatial and temporal correlations to fill the missing period.
Locations of five hourly near-surface air temperature datasets used in this study. The maps are as follows: (a) American River, CA; (b) eastern Pyrenees, France; (c) Yosemite, CA; (d) northern Cascades, WA; and (e) Loch Vale, CO. Shading indicates topography and shows that each dataset is located in an area of large elevation range and terrain complexity. The SNOTEL dataset station locations are shown in Fig. 2 of Raleigh and Lundquist (2012).
Distributions of physical characteristics [(a) vertical distance, (b) horizontal distance, and (c) correlation as in Fig. 6] from the Monte Carlo simulations for the different datasets. On the y axis of each subplot is the fraction of the total runs falling within the 10 bins on the x axis. The Yosemite dataset had the greatest average vertical distance between stations, the American River dataset had the greatest average horizontal distance, and the northern Cascades dataset had the lowest average correlation.
Hourly RMSE from filling a version of the American River dataset in which two target sites existed only for one training year, while other permanent stations maintained coverage throughout the 3-yr period. In this case, the gap is the two prediction years in which the target stations were not present. The number of permanent stations was varied and is plotted along the x axis. The EOF, hourly lapse rate, and long-term lapse rate methods were applied to estimate the missing periods.
Method with the lowest RMSE (C) in at least two of the five datasets, plotted over a range of number of stations and gap lengths. Methods that had the lowest RMSE with statistical significance in at least three datasets are indicated by an symbol. Cases in which two methods both showed the lowest RMSE in at least two datasets are indicated by the labels.
Missing data are a common problem in meteorological and hydrologic observational datasets. Instruments may break, or data transmission may be interrupted. A meteorological phenomenon of interest (i.e., precipitation, snow, or ice) may even cause the temporary failure to record observations. Erroneous or unreasonable values may also be recorded and must be removed during data processing.
Missing data are also unacceptable if the observations are to be used as the meteorological forcing data of a numerical model. For example, distributed hydrological models require that inputs be both temporally and spatially complete (Wigmosta et al. 1994; Daly et al. 2000), which may necessitate both filling of missing data and spatial distribution via objective analysis (Liston and Elder 2006). In this type of application, techniques must be chosen to fill in missing data. While spatial interpolation via objective analysis to estimate missing data is common (e.g., Eischeid et al. 2000), there are many other methods for filling near-surface air temperature data.
Broadly, filling of missing temperature data is similar to the techniques of interpolation, extrapolation, and forecasting, in that available observations are used as predictors of missing data. Much effort has been devoted to interpolating temperature fields across the land surface at a given time. Techniques for spatial interpolation of air temperature include inverse-distance weighting (Daly et al. 2000) and thin-plate splines (Pape et al. 2009), as well as kriging (Tobin et al. 2011; Garen et al. 1994) and multiple regressions (Stahl et al. 2006). In particular, the well-established relationship between temperature and elevation, described by the lapse rate, allows for distribution of temperature across complex terrain, provided that the lapse rate can be accurately estimated (Minder et al. 2010; Rolland 2003; Daly et al. 2002; Dodson and Marks 1997). However, filling with an observed local lapse rate requires the presence of multiple observing stations, which is not always the case in the context of hydrologic modeling at the basin scale.
The entire spatial and temporal correlation structure of a dataset can be described using empirical orthogonal functions (EOFs) (Von Storch and Zwiers 1999). EOFs are generated from a singular value decomposition of the dataset matrix, and they represent its dominant patterns of spatial and temporal variation (Preisendorfer 1988). The dataset can be represented as a linear orthogonal sum of the products of the spatial EOFs and their temporal weights at each time. Because the leading EOFs contain the bulk of the variance, they are more likely to represent broadscale patterns, while the latter EOFs likely represent local-scale patterns and instrument noise.
Because singular value decomposition cannot operate on matrices with missing data, Beckers and Rixen (2003) developed a method that iteratively estimates both the missing data and the complete EOFs. Filling is carried out by first inserting mean values in place of the missing data, then using a truncated series of EOFs to iteratively improve the estimates until convergence. The truncated series employs the leading EOFs to estimate missing data using the spatially and temporally coherent patterns while neglecting the local-scale noise associated with the subsequent EOFs. The EOF reconstruction approach has been used in oceanography, but EOF-based filling of missing data has not been widely applied to meteorological datasets such as air temperature.
To test the methods, we used five hourly near-surface air temperature datasets. Each set had between 19 and 63 stations and spanned at least 1 year, and all were located in areas of complex terrain. The largest was the National Oceanic and Atmospheric Administration (NOAA) Hydrometeorological Testbed (HMT) (Ralph et al. 2005) in the American River basin in the Sierra Nevada of California. The additional datasets were located in the French Pyrenees, the Yosemite region of the Sierra Nevada, the northern Cascades of Washington State, and the Colorado Rocky Mountains.
Five datasets of hourly near-surface air temperature were used as a basis for testing the skill of the filling methods. One was made up of previously unpublished distributed temperature data from the NOAA HMT-West watershed, the northern fork of the American River (basin size 885 km2). This area is located on the western slope of the Sierra Nevada, approximately along the I-80 corridor between Sacramento and Lake Tahoe. The other four datasets were from the eastern Pyrenees on the border of Spain and France (Pepin and Kidd 2006), Yosemite National Park, also in the Sierra Nevada of California (Lundquist et al. 2003), North Cascades National Park in Washington State (Minder et al. 2010), and Loch Vale in Rocky Mountain National Park, Colorado (Lundquist et al. 2008). We considered an additional dataset of mean daily temperatures from the Snowpack Telemetry (SNOTEL) network in Washington State and Oregon (Serreze et al. 1999; data subset from Raleigh and Lundquist 2012), where the stations were much less spatially dense. Figure 2 displays the location of the datasets. Table 1 lists the characteristics of each dataset, including the number of stations, period of record, and completeness after quality control.
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