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P. Philip and B. Yu

Abstract

Rainfall in the southwest of Western Australia (SWWA) has decreased significantly over recent decades. Previous studies documented this decrease in terms of the change in rainfall depth or decrease in the frequency of rainfall events for selected sites. Although rainfall volume is of vital importance to determine water resources availability for a given region, no study has yet been undertaken to examine the change in rainfall volume in SWWA. The aim of this study is to examine the spatiotemporal changes in rainfall volume and to attribute this change to the changes in wet area and rainfall depth. Gridded daily rainfall data at 0.05° resolution for the period from 1911 to 2018 were used for an area of 265 952 km2 in SWWA. For the whole region and most zones, rainfall volume decreased, which was mostly due to a decrease in the wet area, despite an increase in the mean rain depth. In the regions near the coast with mean annual rainfall ≥ 600 mm, 84% of the decrease in rainfall volume could be attributed to a decrease in the wet area, whereas the decrease in rainfall depth only played a minor role. The regions near the coast with a higher number of rain days showed a decreasing trend in wet area, and the regions farther inland with a lower number of rain days showed an increasing trend in wet area. On the coast, the rate of decrease in rainfall has been reduced, and heavy rainfall, in fact, has increased over the past 30 years, although there was no concurrent change in the southern annular mode (SAM). This suggests that the relationship between SAM and rainfall could have changed and that other climate drivers could also be responsible for the recent rainfall trend and variations in the coastal regions of SWWA.

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PHILIP P. CALVERT Ph. D

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Philip S. Brown Jr. and Joseph P. Pandolfo

Abstract

The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.

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Philip S. Brown Jr. and Joseph P. Pandolfo

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A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.

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Philip S. Brown Jr. and Joseph P. Pandolfo

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A procedure is given here that allows two finite-difference schemes having dissimilar time-differencing operators (say, a horizontal advection-diffusion scheme and a vertical diffusion scheme) to be merged into a single equation at the cost of increasing storage requirements through the introduction of an additional time level. lie accuracy and stability of the combined scheme are investigated.

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Philip D. Hammer, Francisco P. J. Valero, and Stefan Kinne

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Infrared radiance measurements were acquired from a narrow-field nadir-viewing radiometer based on the NASA ER-2 aircraft during a coincident Landsat 5 overpass on 28 October 1986 as part of the FIRE Cirrus IFO in the vicinity of Lake Michigan. The spectral bandpasses are 9.90–10.87 μm for the ER-2–based radiometer and 10.40–12.50 μm for the Landsat thematic mapper band. After adjusting for spatial and temporal differences, a comparative study using data from these two instruments is undertaken in order to retrieve cirrus cloud ice-crystal sizes and optical depths. Retrieval is achieved by analysis of measurement correlations between the two spectral bands and comparison to multistream radiative transfer model calculations. The results indicate that the equivalent sphere radii of the cirrus ice crystals were typically less than 30 μm. Such particles were too small to be measured by the available in situ instrumentation. Cloud optical depths at a reference wavelength of 11.4 µm ranged from 0.3 to 2.0 for this case study. Supplemental results in support of this study are described using radiation measurements from the King Air aircraft, which was also in near coincidence with the Landsat overpass.

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Philip S. Brown Jr., Joseph P. Pandolfo, and Anthony R. Hansen

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Average statistics for periods of large positive 500 mb height anomalies are compared to statistics for all other situations using NMC data for the 15 Januaries from 1963 to 1977. The 500 mb heights and geostrophic streamfunctions are represented as surface spherical harmonics, and energy and enstrophy spectra along with nonlinear wave-wave interaction statistics are computed.

Differences in 500 mb geopotential height variance, kinetic energy and enstrophy spectra occur between large positive anomaly events and other days in the two-dimensional spectral index band from roughly n=6 to n=9, where n is the degree of the associated Legendre function. The same index band experiences a reversal of both the usual kinetic energy and enstrophy cascades during large positive anomaly events. That is, the 6≤n≤9 band gains energy and enstrophy from wave-wave interactions during the anomaly events and loses energy and enstrophy by the same process at other times. The source of this energy and enstrophy is higher index (smaller two-dimensional scale) waves. The indication is that the Atlantic cases are more Subject to this cascade reversal than are Pacific events.

Our results suggest that the smaller scale, transient eddies may play a regime-dependent role in interactions with atmospheric circulation modes on the scale of the persistent anomalies. When interacting with larger-scale features, the role of smaller-scale transients may not always be dissipative.

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Gabriele C. Hegerl, Philip D. Jones, and Tim P. Barnett

Abstract

The effect of sampling error in surface air temperature observations is assessed for detection and attribution of an anthropogenic signal. This error arises because grid-box values are based on varying densities of station and marine data. An estimate of sampling error is included in the application of an optimal detection and attribution method based on June–August trends over 50 yr. The detection and attribution method is applied using both the full spatial pattern of observed trends and spatial patterns from which the global mean warming has been subtracted.

Including the effect of sampling error is found to increase the uncertainty in estimates of the greenhouse gas–plus–sulfate aerosol signal from observations by less than 2%–6% for recent trend patterns (1949–98), and 3%–8% for signal estimates from observations in the first half of the twentieth century. Random instrumental error shows even smaller effects. However, the effects of systematic instrumental errors, such as changes in measurement practices or urbanization, cannot be estimated at present. The detection and attribution results for recent 50-yr summer trends are very similar between the case including and the case disregarding the global mean. However, results based on observations from the first half of the twentieth century yield high signal amplitudes with global mean and low ones without, suggesting little pattern agreement for that warming with the anthropogenic climate change signal.

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Philip W. Mote, Alan F. Hamlet, Martyn P. Clark, and Dennis P. Lettenmaier

In western North America, snow provides crucial storage of winter precipitation, effectively transferring water from the relatively wet winter season to the typically dry summers. Manual and telemetered measurements of spring snowpack, corroborated by a physically based hydrologic model, are examined here for climate-driven fluctuations and trends during the period of 1916–2002. Much of the mountain West has experienced declines in spring snowpack, especially since midcentury, despite increases in winter precipitation in many places. Analysis and modeling show that climatic trends are the dominant factor, not changes in land use, forest canopy, or other factors. The largest decreases have occurred where winter temperatures are mild, especially in the Cascade Mountains and northern California. In most mountain ranges, relative declines grow from minimal at ridgetop to substantial at snow line. Taken together, these results emphasize that the West's snow resources are already declining as earth's climate warms.

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Alan F. Hamlet, Philip W. Mote, Martyn P. Clark, and Dennis P. Lettenmaier

Abstract

A physically based hydrology model is used to produce time series for the period 1916–2003 of evapotranspiration (ET), runoff, and soil moisture (SM) over the western United States from which long-term trends are evaluated. The results show that trends in ET in spring and summer are determined primarily by trends in precipitation and snowmelt that determine water availability. From April to June, ET trends are mostly positive due primarily to earlier snowmelt and earlier emergence of snow-free ground, and secondarily to increasing trends in spring precipitation. From July to September trends in ET are more strongly influenced by precipitation trends, with the exception of areas (most notably California) that receive little summer precipitation and have experienced large changes in snowmelt timing. Trends in the seasonal timing of ET are modest, but during the period 1947–2003 when temperature trends are large, they reflect a shift of ET from midsummer to early summer and late spring. As in other studies, it is found that runoff is occurring earlier in spring, a trend that is related primarily to increasing temperature, and is most apparent during 1947–2003. Trends in the annual runoff ratio, a variable critical to western water management, are determined primarily by trends in cool season precipitation, rather than changes in the timing of runoff or ET. It was found that the signature of temperature-related trends in runoff and SM is strongly keyed to mean midwinter [December–February (DJF)] temperatures. Areas with warmer winter temperatures show increasing trends in the runoff fraction as early as February, and colder areas as late as June. Trends toward earlier spring SM recharge are apparent and increasing trends in SM on 1 April are evident over much of the region. The 1 July SM trends are less affected by snowmelt changes and are controlled more by precipitation trends.

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