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A refined index of model performance: a rejoinder

Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology , forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance ( d r ) that they purport to be superior to other methods. Their refined index ranges from − 1.0 to 1.0 to resemble a correlation coefficient, but it is merely a linear rescaling of our modified coefficient of efficiency ( E 1 ) over the positive portion of the domain of d r . We disagree with Willmott et al. ( 2012 ) that d r provides a better interpretation; rather, E 1 is more easily interpreted such that a value of E 1 = 1.0 indicates a perfect model (no errors) while E 1 = 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of E 1 (and, for that matter, d r < 0.5) indicate a substantially flawed model as they simply describe a ‘level of inefficacy’ for a model that is worse than the comparison baseline. Moreover, while d r is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency ( E or E 2 ) and its modified form ( E 1 ) are superior and preferable to many other statistics, including d r , because of intuitive interpretability and because these indices have a fundamental meaning at zero. We also expand on the discussion begun by Garrick et al. [Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall-runoff models. Journal of Hydrology 36 : 375-381.] and continued by Legates and McCabe [Legates DR, McCabe GJ. 1999. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resources Research 35 (1): 233-241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value? Hydrological Processes 21 : 2075-2080. DOI: 10.1002/hyp.6825.]. This important discussion focuses on the appropriate baseline comparison to use, and why the observed mean often may be an inadequate choice for model evaluation and development.

International Journal of Climatology

Assessing recovery and change in West Africa's rainfall regime from a 161-year record

The Sahel region is known for the multi-decadal occurrence of severe drought that commenced in the late 1960s. A still open question is whether or not the region's rainfall has returned to “normal.” This paper provides a compelling answer to that question by examining the longest and most comprehensive gauge series for the region ever published. It extends from 1854 to 2014 and is based on 602 gauge records. A comparative series for the Guinea Coast region to the south is also presented, as the two regions collectively provide insight into the long-term variability of the West African monsoon. In contrast to many previous studies, here the question of recovery and regime change is not restricted to the core of the Sahelian rainy season (July–September), but is separately discussed also for the coastal phase (April–May), transition phase (June), Sahelian phase (July–September) and the second transition phase (October–November) of the West African monsoon. These analyses suggest that full recovery from the droughts of the 1970s and 1980s has not occurred that a major change in the rainfall regime occurred around 1968 and that since that time large-scale teleconnections have also changed markedly. The shift post-1968 is evident in all phases of the monsoon except the coastal phase, in which a change to drier conditions occurred a decade later. Overall, recovery has been greater in the east than in the west, creating a change in the climatological east–west rainfall gradient. The drier post-1968 conditions appear to be associated with a general weakening of the intensity of the West African monsoon and only a small southwards displacement of the rainfall maximum. These changes have strong implications for the future of this region and for seasonal prediction.

International Journal of Climatology

The Forecast Interpretation Tool—a Monte Carlo technique for blending climatic distributions with probabilistic forecasts

Probabilistic forecasts are produced from a variety of outlets to help predict rainfall, and other meteorological events, for periods of 1 month or more. Such forecasts are expressed as probabilities of a rainfall event, e.g. being in the upper, middle, or lower third of the relevant distribution of rainfall in the region. The impact of these forecasts on the expectation for the event is not always clear or easily conveyed. This article proposes a technique based on Monte Carlo simulation for adjusting existing climatologic statistical parameters to match forecast information, resulting in new parameters defining the probability of events for the forecast interval. The resulting parameters are shown to approximate the forecasts with reasonable accuracy. To show the value of the technique as an application for seasonal rainfall, it is used with consensus forecast developed for the Greater Horn of Africa for the 2009 March-April-May season. An alternative, analytical approach is also proposed, and discussed in comparison to the first simulation-based technique.

International Journal of Climatology

Changing station coverage impacts temperature trends in the Upper Colorado River Basin

Over the Upper Colorado River Basin (UCRB), temperatures in widely used gridded data products do not warm as much as mean temperatures from a stable set of U.S. Historical Climatology Network (USHCN) stations, located at generally lower elevations, in most months of the year. This is contrary to expectations of elevation-dependent warming, which suggests that warming increases with elevation. These findings could reflect 1) a genuine absence of elevation-dependent warming in the region, 2) systematic non-climatic influences on either the USHCN stations or high elevation stations, including known inhomogeneities related to changes in the time of observation and instrumentation, or 3) suppression of an elevation-dependent warming signal introduced by changes in the station network. While we cannot categorically dismiss the first two possibilities, we show here that over portions of the 20th century, gridded temperatures warm less than USHCN temperatures and the difference cannot be explained by accounting for known inhomogeneities. These analyses suggest that changing station coverage in the UCRB has influenced trends in gridded temperature estimates that incorporate changing suites of stations over time. Specifically, increases in the number of high-elevation stations in the UCRB may have led to an underestimation of elevation-dependent warming, particularly during the spring and summer. This phenomenon is unlikely limited to this specific basin, and may be present in other high-elevation watersheds across the western U.S.

Upper Colorado River Basin

Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States

Spatial climate data sets of 1971–2000 mean monthly precipitation and minimum and maximum temperature were developed for the conterminous United States. These 30‐arcsec (∼800‐m) grids are the official spatial climate data sets of the U.S. Department of Agriculture. The PRISM (Parameter‐elevation Relationships on Independent Slopes Model) interpolation method was used to develop data sets that reflected, as closely as possible, the current state of knowledge of spatial climate patterns in the United States. PRISM calculates a climate–elevation regression for each digital elevation model (DEM) grid cell, and stations entering the regression are assigned weights based primarily on the physiographic similarity of the station to the grid cell. Factors considered are location, elevation, coastal proximity, topographic facet orientation, vertical atmospheric layer, topographic position, and orographic effectiveness of the terrain. Surface stations used in the analysis numbered nearly 13 000 for precipitation and 10 000 for temperature. Station data were spatially quality controlled, and short‐period‐of‐record averages adjusted to better reflect the 1971–2000 period. PRISM interpolation uncertainties were estimated with cross‐validation (C‐V) mean absolute error (MAE) and the 70% prediction interval of the climate–elevation regression function. The two measures were not well correlated at the point level, but were similar when averaged over large regions. The PRISM data set was compared with the WorldClim and Daymet spatial climate data sets. The comparison demonstrated that using a relatively dense station data set and the physiographically sensitive PRISM interpolation process resulted in substantially improved climate grids over those of WorldClim and Daymet. The improvement varied, however, depending on the complexity of the region. Mountainous and coastal areas of the western United States, characterized by sparse data coverage, large elevation gradients, rain shadows, inversions, cold air drainage, and coastal effects, showed the greatest improvement. The PRISM data set benefited from a peer review procedure that incorporated local knowledge and data into the development process.

International Journal of Climatology

Midwestern streamflow, precipitation, and atmospheric vorticity influenced by Pacific sea-surface temperatures and total solar-irradiance variations

A solar effect on streamflow in the Midwestern United States is described and supported in a six-step physical connection between total solar irradiance (TSI), tropical sea-surface temperatures (SSTs), extratropical SSTs, jet-stream vorticity, surface-layer vorticity, precipitation, and streamflow. Variations in the correlations among the individual steps indicate that the solar/hydroclimatic mechanism is complex and has a time element (lag) that may not be constant. Correct phasing, supported by consistent spectral peaks between 0.092 and 0.096 cycles per year in all data sets within the mechanism is strong evidence for its existence. A significant correlation exists between total solar irradiance and the 3-year moving average of annual streamflow for Iowa (R = 0.67) and for the Mississippi River at St Louis, Missouri (R = 0.60), during the period 1950-2000. Published in 2005 by John Wiley & Sons, Ltd.

International Journal of Climatology

Multidecadal climate variability of global lands and oceans

Principal components analysis (PCA) and singular value decomposition (SVD) are used to identify the primary modes of decadal and multidecadal variability in annual global Palmer Drought Severity Index (PDSI) values and sea-surface temperature (SSTs). The PDSI and SST data for 1925-2003 were detrended and smoothed (with a 10-year moving average) to isolate the decadal and multidecadal variability. The first two principal components (PCs) of the PDSI PCA explained almost 38% of the decadal and multidecadal variance in the detrended and smoothed global annual PDSI data. The first two PCs of detrended and smoothed global annual SSTs explained nearly 56% of the decadal variability in global SSTs. The PDSI PCs and the SST PCs are directly correlated in a pairwise fashion. The first PDSI and SST PCs reflect variability of the detrended and smoothed annual Pacific Decadal Oscillation (PDO), as well as detrended and smoothed annual Indian Ocean SSTs. The second set of PCs is strongly associated with the Atlantic Multidecadal Oscillation (AMO). The SVD analysis of the cross-covariance of the PDSI and SST data confirmed the close link between the PDSI and SST modes of decadal and multidecadal variation and provided a verification of the PCA results. These findings indicate that the major modes of multidecadal variations in SSTs and land-surface climate conditions are highly interrelated through a small number of spatially complex but slowly varying teleconnections. Therefore, these relations may be adaptable to providing improved baseline conditions for seasonal climate forecasting. Published in 2006 by John Wiley & Sons, Ltd.

International Journal of Climatology

Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications

Evaluating a range of scenarios that accurately reflect precipitation variability is critical for water resource applications. Inputs to these applications can be provided using location- and interval-specific probability distributions. These distributions make it possible to estimate the likelihood of rainfall being within a specified range. In this paper, we demonstrate the feasibility of fitting cell-by-cell probability distributions to grids of monthly interpolated, continent-wide data. Future work will then detail applications of these grids to improved satellite-remote sensing of drought and interpretations of probabilistic climate outlook forum forecasts. The gamma distribution is well suited to these applications because it is fairly familiar to African scientists, and capable of representing a variety of distribution shapes. This study tests the goodness-of-fit using the Kolmogorov&ndash;Smirnov (KS) test, and compares these results against another distribution commonly used in rainfall events, the Weibull. The gamma distribution is suitable for roughly 98% of the locations over all months. The techniques and results presented in this study provide a foundation for use of the gamma distribution to generate drivers for various rain-related models. These models are used as decision support tools for the management of water and agricultural resources as well as food reserves by providing decision makers with ways to evaluate the likelihood of various rainfall accumulations and assess different scenarios in Africa.

International Journal of Climatology

Trends and spatial distribution of annual and seasonal rainfall in Ethiopia

As a country whose economy is heavily dependent on low-productivity rainfed agriculture, rainfall trends are often cited as one of the more important factors in explaining various socio-economic problems such as food insecurity. Therefore, in order to help policymakers and developers make more informed decisions, this study investigated the temporal dynamics of rainfall and its spatial distribution within Ethiopia. Changes in rainfall were examined using data from 134 stations in 13 watersheds between 1960 and 2002. The variability and trends in seasonal and annual rainfall were analysed at the watershed scale with data (1) from all available years, and (2) excluding years that lacked observations from at least 25% of the gauges. Similar analyses were also performed at the gauge, regional, and national levels. By regressing annual watershed rainfall on time, results from the one-sample t -test show no significant changes in rainfall for any of the watersheds examined. However, in our regressions of seasonal rainfall averages against time, we found a significant decline in June to September rainfall (i.e. Kiremt) for the Baro-Akobo, Omo-Ghibe, Rift Valley, and Southern Blue Nile watersheds located in the southwestern and central parts of Ethiopia. While the gauge level analysis showed that certain gauge stations experienced recent changes in rainfall, these trends are not necessarily reflected at the watershed or regional levels.

International Journal of Climatology

Millennial precipitation reconstruction for the Jemez Mountains, New Mexico, reveals changing drought signal

Drought is a recurring phenomenon in the American Southwest. Since the frequency and severity of hydrologic droughts and other hydroclimatic events are of critical importance to the ecology and rapidly growing human population of this region, knowledge of long-term natural hydroclimatic variability is valuable for resource managers and policy-makers. An October–June precipitation reconstruction for the period AD 824–2007 was developed from multi-century tree-ring records of Pseudotsuga menziesii (Douglas-fir), Pinus strobiformis (Southwestern white pine) and Pinus ponderosa (Ponderosa pine) for the Jemez Mountains in Northern New Mexico. Calibration and verification statistics for the period 1896–2007 show a high level of skill, and account for a significant portion of the observed variance (>50%) irrespective of which period is used to develop or verify the regression model. Split-sample validation supports our use of a reconstruction model based on the full period of reliable observational data (1896–2007). A recent segment of the reconstruction (2000–2006) emerges as the driest 7-year period sensed by the trees in the entire record. That this period was only moderately dry in precipitation anomaly likely indicates accentuated stress from other factors, such as warmer temperatures. Correlation field maps of actual and reconstructed October–June total precipitation, sea surface temperatures and 500-mb geopotential heights show characteristics that are similar to those indicative of El Niño–Southern Oscillation patterns, particularly with regard to ocean and atmospheric conditions in the equatorial and north Pacific. Our 1184-year reconstruction of hydroclimatic variability provides long-term perspective on current and 20th century wet and dry events in Northern New Mexico, is useful to guide expectations of future variability, aids sustainable water management, provides scenarios for drought planning and as inputs for hydrologic models under a broader range of conditions than those provided by historical climate records.

New Mexico

General circulation model simulations of winter and summer sea-level pressures over North America

Temporal variability of synoptic-scale circulation is a dominant factor in regional temporal climate variations. In the midlatitudes, temporal variability of synoptic-scale circulation has been found to be related to temporal variations in regional air temperature and precipitation. General circulation model (GCM) simulations of long-term changes in synoptic-scale circulation may be useful in assessing the effects of climate change on regional air temperature and precipitation. Atmospheric pressure is an important component of synoptic-scale circulation. In this paper, observed sea-level pressures were used to evaluate winter and summer sea-level pressures over North America simulated by the Goddard Institute for Space Studies (GISS) and the Geophysical Fluid Dynamics Laboratory (GFDL) general circulation models. The objective of the study is to determine how similar the spatial and temporal distributions of GCM-simulated daily sea-level pressures over North America are to observed distributions. Overall, both models are better at reproducing observed within-season variance of winter and summer sea-level pressures than they are at simulating the magnitude of mean winter and summer sea-level pressures. Results indicate that winter sea-level pressures are better simulated by the GISS model than by the GFDL model. The GFDL model simulates anomalously high winter sea-level pressures over north-eastern North America. In summer, the GISS model underestimates sea-level pressures, whereas the GFDL model overestimates sea-level pressures over most of North America. Kolmogorov-Smirnov tests indicate that much of the error in model simulations can be attributed to differences between simulated and observed means. Comparisons of spatial correlation matrices of observed and simulated sea-level pressures indicate that GCMs simulate spatial variability of sea-level pressures that is similar to observed. These results suggest that GCMs are able to simulate major components of synoptic-scale circulation over North America, especially for winter.

International Journal of Climatology

Relations between winter precipitation and atmospheric circulation simulated by the Geophysical Fluid Dynamics Laboratory general circulation model

General circulation model (GCM) simulations of atmospheric circulation are more reliable than GCM simulations of temperature and precipitation. In this study, temporal correlations between 700 hPa height anomalies simulated winter precipitation at eight locations in the conterminous United States are compared with corresponding correlations in observations. The objectives are to 1) characterize the relations between atmospheric circulation and winter precipitation simulated by the GFDL, GCM for selected locations in the conterminous USA, ii) determine whether these relations are similar to those found in observations of the actual climate system, and iii) determine if GFDL-simulated precipitation is forced by the same circulation patterns as in the real atmosphere. -from Authors

International Journal of Climatology

Influences of the El Niño Southern Oscillation and the Pacific Decadal Oscillation on the timing of the North American spring

Detrended, modelled first leaf dates for 856 sites across North America for the period 1900–2008 are used to examine how the El Niño Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) separately and together might influence the timing of spring. Although spring (mean March through April) ENSO and PDO signals are apparent in first leaf dates, the signals are not statistically significant (at a 95% confidence level (p < 0.05)) for most sites. The most significant ENSO/PDO signal in first leaf dates occurs for El Niño and positive PDO conditions. An analysis of the spatial distributions of first leaf dates for separate and combined ENSO/PDO conditions features a northwest–southeast dipole that is significantly (at p < 0.05) different than the distributions for neutral conditions. The nature of the teleconnection between Pacific SST's and first leaf dates is evident in comparable composites for detrended sea level pressure (SLP) in the spring months. During positive ENSO/PDO, there is an anomalous flow of warm air from the southwestern US into the northwestern US and an anomalous northeasterly flow of cold air from polar regions into the eastern and southeastern US. These flow patterns are reversed during negative ENSO/PDO. Although the magnitudes of first leaf date departures are not necessarily significantly related to ENSO and PDO, the spatial patterns of departures are significantly related to ENSO and PDO. These significant relations and the long-lived persistence of SSTs provide a potential tool for forecasting the tendencies for first leaf dates to be early or late.

International Journal of Climatology

Climatic trends over Ethiopia: regional signals and drivers

This study analyses observed and projected climatic trends over Ethiopia, through analysis of temperature and rainfall records and related meteorological fields. The observed datasets include gridded station records and reanalysis products; while projected trends are analysed from coupled model simulations drawn from the IPCC 4th Assessment. Upward trends in air temperature of + 0.03 °C year −1 and downward trends in rainfall of − 0.4 mm month −1 year −1 have been observed over Ethiopia's southwestern region in the period 1948-2006. These trends are projected to continue to 2050 according to the Geophysical Fluid Dynamics Lab model using the A1B scenario. Large scale forcing derives from the West Indian Ocean where significant warming and increased rainfall are found. Anticyclonic circulations have strengthened over northern and southern Africa, limiting moisture transport from the Gulf of Guinea and Congo. Changes in the regional Walker and Hadley circulations modulate the observed and projected climatic trends. Comparing past and future patterns, the key features spread westward from Ethiopia across the Sahel and serve as an early warning of potential impacts.

International Journal of Climatology

Spring onset variations and trends in the continental United States: past and regional assessment using temperature-based indices

Phenological data are simple yet sensitive indicators of climate change impacts on ecosystems, but observations have not been made routinely or extensively enough to evaluate spatial and temporal patterns across most continents, including North America. As an alternative, many studies use weather-based algorithms to simulate specific phenological responses. Spring Indices (SI) are a set of complex phenological models that have been successfully applied to evaluate variations and trends in the onset of spring across the Northern Hemisphere’s temperate regions. To date, SI models have been limited by only producing output in locations where both the plants’ chilling and warmth requirements are met. Here, we develop an extended form of the SI (abbreviated SI-x) that expands their application into the subtropics by ignoring chilling requirements while still retaining the utility and accuracy of the original SI (now abbreviated SI-o). The validity of the new indices is tested, and regional SI anomalies are explored across the data-rich continental United States. SI-x variations from 1900 to 2010 show an abrupt and sustained delay in spring onset of about 4–8 d (around 1958) in parts of the Southeast and southern Great Plains, and a comparable advance of 4–8 d (around 1984) in parts of the northern Great Plains and the West. Atmospheric circulation anomalies, linked to large-scale modes of variability, exert modest but significant roles in the timing of spring onset across the United States on interannual and longer timescales. The SI-x are promising metrics for tracking spring onset variations and trends in mid-latitudes, relating them to relevant ecological, hydrological, and socioeconomic phenomena, and exploring connections between atmospheric drivers and seasonal timing.

International Journal of Climatology

Comparison of elevation and remote sensing derived products as auxiliary data for climate surface interpolation

Climate models may be limited in their inferential use if they cannot be locally validated or do not account for spatial uncertainty. Much of the focus has gone into determining which interpolation method is best suited for creating gridded climate surfaces, which often a covariate such as elevation (Digital Elevation Model, DEM) is used to improve the interpolation accuracy. One key area where little research has addressed is in determining which covariate best improves the accuracy in the interpolation. In this study, a comprehensive evaluation was carried out in determining which covariates were most suitable for interpolating climatic variables (e.g. precipitation, mean temperature, minimum temperature, and maximum temperature). We compiled data for each climate variable from 1950 to 1999 from approximately 500 weather stations across the Western United States (32° to 49° latitude and −124.7° to −112.9° longitude). In addition, we examined the uncertainty of the interpolated climate surface. Specifically, Thin Plate Spline (TPS) was used as the interpolation method since it is one of the most popular interpolation techniques to generate climate surfaces. We considered several covariates, including DEM, slope, distance to coast (Euclidean distance), aspect, solar potential, radar, and two Normalized Difference Vegetation Index (NDVI) products derived from Advanced Very High Resolution Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS). A tenfold cross-validation was applied to determine the uncertainty of the interpolation based on each covariate. In general, the leading covariate for precipitation was radar, while DEM was the leading covariate for maximum, mean, and minimum temperatures. A comparison to other products such as PRISM and WorldClim showed strong agreement across large geographic areas but climate surfaces generated in this study (ClimSurf) had greater variability at high elevation regions, such as in the Sierra Nevada Mountains.

International Journal of Climatology

Climate change and water resources in a tropical island system: Propagation of uncertainty from statistically downscaled climate models to hydrologic models

Many tropical islands have limited water resources with historically increasing demand, all potentially affected by a changing climate. The effects of climate change on island hydrology are difficult to model due to steep local precipitation gradients and sparse data. This work uses 10 statistically downscaled general circulation models (GCMs) under two greenhouse gas emission scenarios to evaluate the uncertainty propagated from GCMs in projecting the effects of climate change on water resources in a tropical island system. The assessment is conducted using a previously configured hydrologic model, the Precipitation Runoff Modelling System (PRMS) for Puerto Rico. Projected climate data and their modelled hydrologic variables versus historical measurements and their modelled hydrologic variables are found to have empirical distribution functions that are statistically different with less than 1 year of daily data aggregation. Thus, only annual averages of the projected hydrologic variables are employed as completely bias‐corrected model outputs. The magnitude of the projected total flow decreases in the four regions covering Puerto Rico, but with a large range of uncertainty depending on the makeup of the GCM ensemble. The multi‐model mean projected total flow decreases by 49–88% of historical amounts from the 1960s to the 2090s for the high emissions scenarios and by 39–79% for the low emissions scenarios. Subsurface flow contributions decreased the least and groundwater flow contributions decreased the most across the island. At locations critical to water supply for human use, projected streamflow is shown to decrease substantially below projected withdrawals by 2099.

Puerto Rico

Variability of runoff-based drought conditions in the conterminous United States

In this study, a monthly water-balance model is used to simulate monthly runoff for 2109 hydrologic units (HUs) in the conterminous United States (CONUS) for water-years 1901 through 2014. The monthly runoff time series for each HU were smoothed with a 3-month moving average, and then the 3-month moving-average runoff values were converted to percentiles. For each HU, a drought was considered to occur when the HU runoff percentile dropped to the 20th percentile or lower. A drought was considered to end when the HU runoff percentile exceeded the 20th percentile. After identifying drought events for each HU, the frequency and length of drought events were examined. Results indicated that (1) the longest mean drought lengths occur in the eastern CONUS and parts of the Rocky Mountain region and the northwestern CONUS, (2) the frequency of drought is highest in the southwestern and central CONUS, and lowest in the eastern CONUS, the Rocky Mountain region, and the northwestern CONUS, (3) droughts have occurred during all months of the year and there does not appear to be a seasonal pattern to drought occurrence, (4) the variability of precipitation appears to have been the principal climatic factor determining drought, and (5) for most of the CONUS, drought frequency appears to have decreased during the 1901 through 2014 period.

International Journal of Climatology