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Gerald R. North
,
Thomas L. Bell
,
Robert F. Cahalan
, and
Fanthune J. Moeng

Abstract

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is “close” to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

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Kyung-Sup Shin
,
Gerald R. North
,
Yoo-Shin Ahn
, and
Phillip A. Arkin

Abstract

A statistical analysis of time series of area-averaged rainfall over the oceans has been conducted around the diurnal time scale. The results of our analysis can be applied directly to the problem of establishing the magnitude of expected errors to be incurred in the estimation of monthly area-averaged rain rates from low orbiting satellites. Such statistics as the mean, standard deviation, integral time scale of background red noise and spectral analyses were performed oil time series of the GOES Precipitation Index (GPI) taken at 3-hour intervals during the period spanning 19 December 1987 to 31 March 1988 over the central and eastern tropical Pacific. The analyses have been conducted on 2.5°×2.5° and 5°×5° grid boxes, separately.

The ratio of standard deviation to mean for area-averaged rain rate in the Pacific ITCZ is very regular and similar to that in GATE. Analysis of the area-averaged rainfall in the SPCZ shows a longer autocorrelation time scale than that in the ITCZ. The SPCZ exhibits significant power at the diurnal and semidiurnal frequencies, but the ITCZ shows only a marginally significant diurnal cycle in our data. The rainfall characteristics in the Pacific ITCZ appear to be similar to those in the Atlantic ITCZ in both autocorrelation time scale and diurnal variation. The mechanism driving convection in the ITCZ is suggested to be different from that in the SPCZ. The study shows that rainfall measurements by a sun-synchroneous satellite visiting a spot twice per day will include a bias due to the existence of the semidiurnal cycle in the SPCZ ranging from 5 to 10 percentage points. The bias in the ITCZ may be of the order of 5 percentage points.

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David A. Short
,
Gerald R. North
,
T. Dale Bess
, and
G. Louis Smith

Abstract

Empirical studies of total outgoing infrared radiation IR and surface temperature T have shown them to be well correlated for large time and space scales. An analysis of one year of Nimbus-6 data shows that the simple form IR = A + BT (with A = 204 W m−2, B = 1.93 W m−2K−1) explains 90% of the area-weighted variance in the annual mean and annual cycle of the zonally averaged IR field. The geographical distribution of the annual cycle in IR shows a large amplitude over the continental interiors, as is found in the observed temperature field, and the ratio of the large amplitudes (Blocal ) is approximately 2 W m−2K−1. This helps to explain our recent success in modeling the geographical distribution of the annual cycle in T with a two-dimensional, time-dependent energy balance climate model (EBCM) which makes use of the A + BT rule. The parameterization works well in regions where the thermal inertia is small and the annual cycles of T and IR are large and in phase. Those regions where Blocal differs markedly from 2 W m−2K−1 are where the IR is strongly affected by the cloudiness of seasonal precipitation regimes. This effect is especially evident over the tropical oceans where the parameterization fails; but that is where the thermal inertia is large, the seasonal cycle in T is small, and even large errors in the radiative cooling approximation will have little impact on seasonal cycle simulations by simple climate models.

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Charles E. Graves
,
Juan B. Valdés
,
Samuel S. P. Shen
, and
Gerald R. North

Abstract

The spatial and temporal characteristics of rainfall over Oklahoma and Kansas are analyzed in this paper using the raingage data collected during the Preliminary Regional Experiment for STORM-Central (PRESTORM). The autocorrelation function and the spectrum are obtained directly from both processing the raingage data and using a theoretical stochastic model of space–time precipitation. This theoretical model serves as an intermediate step to obtain more information from the raingage records. The spectra obtained are then compared with those obtained from oceanic precipitation in the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE) and with that obtained from analyzing raingage records in east Texas. Finally, the spectra are used to evaluate the sampling errors that are due to the spatial gaps in measurements. The sampling error is expressed as an integral over the product of the spectral density of the stochastic rain field and a filter function. This filter function solely depends on the space–time configuration of the measurement instruments. The values of the analytical and numerical results on the sampling error are obtained for ground, spaceborne, and combined sensors of precipitation for several aggregation levels in space and time and alternative spacing and visiting times. It was found that sampling errors of land precipitation are higher than those reported for ocean precipitation.

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William T. Hyde
,
Thomas J. Crowley
,
Kwang-Yul Kim
, and
Gerald R. North

Abstract

The Sensitivity of a linear two dimensional Energy Balance Model (EBM) to altered surface albedo and insolation over the last 18 000 years is compared to simulators made with the NCAR Community Climate Model (CCM). The two-dimensional EBM is a more general form of that described in North et al. and allows for regionally varying albedos of ice sheets and sea ice. It is shown that the EBM's hemispherically averaged land and sea seasonal temperature departures agree excellently with the CCM's in the Northern Hemisphere. In the Southern Hemisphere the seasonal comparisons are legs favorable, although the annual-averaged oceanic temperature departures at glacial maximum agree to within 0.3°C. Since the CCM used prescribed SSTs (from CLIMAP), whereas the ERMs are calculated, our results suggest that the hemispherically averaged glacial- interglacial SST change estimated by CLIMAP is consistent with the altered energy balance requirements of the earth-atmosphere system. Results also suggest that on the largest scales the seasonal temperature field at the earth's surface may be linearly dependent on change in orbital forcing and surface albedo. We conclude that the EBM performs well enough to justify its use as an exploratory tool for investigating the effect of altered boundary conditions on the earth/s annual temperature cycle.

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Gerald R. North
,
Kwang-Y. Kim
,
Samuel S. P. Shen
, and
James W. Hardin

Abstract

This paper considers the construction of a linear smoothing filter for estimation of the forced part of a change in a climatological field such as the surface temperature. The filter is optimal in the sense that it suppresses the natural variability or “noise” relative to the forced part or “signal” to the maximum extent possible. The technique is adapted from standard signal processing theory. The present treatment takes into account the spatial as well as the temporal variability of both the signal and the noise. In this paper we take the signal's waveform in space-time to be a given deterministic field in space and lime. Formulation of the expression for the minimum mean-squared error for the problem together with a no-bias constraint leads to an integral equation whose solution is the filter. The problem can be solved analytically in terms of the space-time empirical orthogonal function basis set and its eigenvalue spectrum for the natural fluctuations and the projection amplitudes of the signal onto these eigenfunctions. The optimal filter does not depend on the strength of the assumed waveform used in its construction. A lesser mean-square error in estimating the signal occurs when the space-time spectral characteristics of the signal and the noise are highly dissimilar; for example, if the signal is concentrated in a very narrow spectral band and the noise in a very broad band. A few pedagogical exercises suggest that these techniques might be useful in practical situations.

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Gerald R. North
,
Kuor-Jier Joseph Yip
,
Lai-Yung Leung
, and
Robert M. Chervin

Abstract

The concept of “forced” and “free” variations of large-scale surface temperature is examined by analyzing several long runs of the Community Climate Model (CCMO) with idealized boundary conditions and forcing. 1) The planet is all land with uniform sea-level topography and fixed soil moisture. 2) The planetary surface and prescribed ozone are reflection symmetric across the equator and there is no generation of snow. 3) The obliquity is set to zero so that the climate is for a perpetual equinox solar insolation (i.e., sun fixed over the equator). After examining some relevant aspects of the undisturbed climate (surface temperature field) such as temporal and spatial autocorrelations and the corresponding spectra, two types of changes in external forcing are imposed to study the model response: 1) sinusoidal changes of the solar constant (5%, 10%, 90%, and 40% amplitudes) at periods of 15 and 30 days (the latter is the autocorrelation time for the global average surface temperature) and 20% at 60 days and 2) insertion of steady heat sources (points and zonal bands) of variable strength at the surface. Then the temporal spectra of large scales for the periodically forced climate and the ensemble-averaged influence functions are examined for the point source disturbed climates. In each class of experiments the response of ensemble-averaged amplitudes was found to be proportional to the amplitude of the forcing. These results suggest that the lowest moments of the surface temperature field have a particularly simple dependence on forcing. Furthermore, the apparent finiteness of the variance spectrum at low frequencies suggests that estimates of long-term statistics are stable in this type of atmospheric general circulation model.

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Bo Li
,
Aditya Murthi
,
Kenneth P. Bowman
,
Gerald R. North
,
Marc G. Genton
, and
Michael Sherman

Abstract

The Taylor hypothesis (TH) as applied to rainfall is a proposition about the space–time covariance structure of the rainfall field. Specifically, it supposes that if a spatiotemporal precipitation field with a stationary covariance Cov(r, τ) in both space r and time τ moves with a constant velocity v, then the temporal covariance at time lag τ is equal to the spatial covariance at space lag r = vτ that is, Cov(0, τ) = Cov(vτ, 0). Qualitatively this means that the field evolves slowly in time relative to the advective time scale, which is often referred to as the frozen field hypothesis. Of specific interest is whether there is a cutoff or decorrelation time scale for which the TH holds for a given mean flow velocity v. In this study, the validity of the TH is tested for precipitation fields using high-resolution gridded Next Generation Weather Radar (NEXRAD) reflectivity data produced by the WSI Corporation by employing two different statistical approaches. The first method is based on rigorous hypothesis testing, while the second is based on a simple correlation analysis, which neglects possible dependencies between the correlation estimates. Radar reflectivity values are used from the southeastern United States with an approximate horizontal resolution of 4 km × 4 km and a temporal resolution of 15 min. During the 4-day period from 2 to 5 May 2002, substantial precipitation occurs in the region of interest, and the motion of the precipitation systems is approximately uniform. The results of both statistical methods suggest that the TH might hold for the shortest space and time scales resolved by the data (4 km and 15 min) but that it does not hold for longer periods or larger spatial scales. Also, the simple correlation analysis tends to overestimate the statistical significance through failing to account for correlations between the covariance estimates.

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Libin Yan
,
Xiaodong Liu
,
Ping Yang
,
Zhi-Yong Yin
, and
Gerald R. North

Abstract

The regional coupled climate–chemistry/aerosol model (RegCM3) is used to investigate the difference in the spatial distribution of aerosol optical depth (AOD) between a strong summer monsoon year (SSMY; July 2003) and a weak summer monsoon year (WSMY; July 2002) under the actual- and same-emission scenarios. It is shown that the intensity of the Asian summer monsoon is primarily responsible for the AOD spatial distribution anomaly in midsummer over East Asia. Specifically, the AOD over southern China, upwind of the Asian summer monsoon, is greater in WSMY than in SSMY, but the opposite is observed for the AOD downwind over northern China and the Korean Peninsula. The AOD spatial distribution patterns simulated on the basis of the actual emission inventories for the SSMY and WSMY do not substantially differ from their counterparts that are based on the same emission inventory, confirming that the monsoon circulation, rather than local emissions or dry and wet deposition processes, is the predominant factor determining the regional AOD distribution. These modeling results are consistent with the analyses based on the Moderate Resolution Imaging Spectroradiometer (MODIS) products, NCAR–Department of Energy wind fields, and air parcel movements according to the 7-day trajectories of air parcels determined by the Hybrid Single-Particle Lagrangian Integrated Trajectory model.

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Xiaodong Liu
,
Libin Yan
,
Ping Yang
,
Zhi-Yong Yin
, and
Gerald R. North

Abstract

The spatial and temporal variations of aerosol loading over eastern Asia specified in terms of the aerosol optical depth (AOD) at the 550-nm wavelength during July are examined in conjunction with the intensity of the Indian summer monsoon. AOD derived from Moderate Resolution Imaging Spectroradiometer (MODIS) observations, gridded reanalyses, and ground-based measurements are used in the analysis. Two contrasting years, 2002 and 2003, which represent weak and active Indian summer monsoon events, respectively, are selected for the study, with a focus on an eastern Asian southern subregion (SR; 23°–32°N, 105°–120°E) and an eastern Asian northern subregion (NR; 35°–44°N, 115°–130°E). It is shown that the interannual variation of July mean wind intensity is a major factor in regulating the midsummer spatial pattern of aerosols over eastern Asia when the Indian monsoon index is anomalously large. The AOD anomalies in the NR and SR are positive and negative, respectively, during an active monsoon year, whereas the opposite is observed during a weak monsoon year. The variation patterns of less cloudy-day visibility, observed at four meteorological stations in the SR and NR subregions, also show spatial–temporal aerosol variability evident in the MODIS AOD data. Relative to the case of a weak monsoon year, meridional winds and convection are stronger and more clouds and precipitation are observed in the NR subregion during the active monsoon year. The opposite pattern is observed in the SR subregion. The spatial–temporal variation pattern of aerosols over eastern Asia illustrates the nonnegligible role of transport and dispersal mechanisms associated with the Indian summer monsoon in the region.

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