Sampling uncertainties in surface radiation budget calculations in RADAGAST

In the Radiative Atmospheric Divergence Using ARM Mobile Facility GERB and AMMA Stations (RADAGAST) project we calculate the divergence of radiative flux across the atmosphere by comparing fluxes measured at each end of an atmospheric column above Niamey, in the African Sahel region. The combination of broadband flux measurements from geostationary orbit and the deployment for over 12 months of a comprehensive suite of active and passive instrumentation at the surface eliminates a number of sampling issues that could otherwise affect divergence calculations of this sort. However, one sampling issue that challenges the project is the fact that the surface flux data are essentially measurements made at a point, while the top-of-atmosphere values are taken over a solid angle that corresponds to an area at the surface of some 2500 km2. Variability of cloud cover and aerosol loading in the atmosphere mean that the downwelling fluxes, even when averaged over a day, will not be an exact match to the area-averaged value over that larger area, although we might expect that it is an unbiased estimate thereof. The heterogeneity of the surface, for example, fixed variations in albedo, further means that there is a likely systematic difference in the corresponding upwelling fluxes. In this paper we characterize and quantify this spatial sampling problem. We bound the root-mean-square error in the downwelling fluxes by exploiting a second set of surface flux measurements from a site that was run in parallel with the main deployment. The differences in the two sets of fluxes lead us to an upper bound to the sampling uncertainty, and their correlation leads to another which is probably optimistic as it requires certain other conditions to be met. For the upwelling fluxes we use data products from a number of satellite instruments to characterize the relevant heterogeneities and so estimate the systematic effects that arise from the flux measurements having to be taken at a single point. The sampling uncertainties vary with the season, being higher during the monsoon period. We find that the sampling errors for the daily average flux are small for the shortwave irradiance, generally less than 5 W m−2, under relatively clear skies, but these increase to about 10 W m−2 during the monsoon. For the upwelling fluxes, again taking daily averages, systematic errors are of order 10 W m−2 as a result of albedo variability. The uncertainty on the longwave component of the surface radiation budget is smaller than that on the shortwave component, in all conditions, but a bias of 4 W m−2 is calculated to exist in the surface leaving longwave flux.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Observational constraints on atmospheric and oceanic cross-equatorial heat transports: revisiting the precipitation asymmetry problem in climate models

Satellite based top-of-atmosphere (TOA) and surface radiation budget observations are combined with mass corrected vertically integrated atmospheric energy divergence and tendency from reanalysis to infer the regional distribution of the TOA, atmospheric and surface energy budget terms over the globe. Hemispheric contrasts in the energy budget terms are used to determine the radiative and combined sensible and latent heat contributions to the cross-equatorial heat transports in the atmosphere (AHT_EQ) and ocean (OHT_EQ). The contrast in net atmospheric radiation implies an AHT_EQ from the northern hemisphere (NH) to the southern hemisphere (SH) (0.75 PW), while the hemispheric difference in sensible and latent heat implies an AHT_EQ in the opposite direction (0.51 PW), resulting in a net NH to SH AHT_EQ (0.24 PW). At the surface, the hemispheric contrast in the radiative component (0.95 PW) dominates, implying a 0.44 PW SH to NH OHT_EQ. Coupled model intercomparison project phase 5 (CMIP5) models with excessive net downward surface radiation and surface-to-atmosphere sensible and latent heat transport in the SH relative to the NH exhibit anomalous northward AHT_EQ and overestimate SH tropical precipitation. The hemispheric bias in net surface radiative flux is due to too much longwave surface radiative cooling in the NH tropics in both clear and all-sky conditions and excessive shortwave surface radiation in the SH subtropics and extratropics due to an underestimation in reflection by clouds.

Large contribution of supercooled liquid clouds to the solar radiation budget of the Southern Ocean

The Southern Ocean is a critical region for global climate, yet large cloud and solar radiation biases over the Southern Ocean are a long-standing problem in climate models and are poorly understood, leading to biases in simulated sea surface temperatures. This study shows that supercooled liquid clouds are central to understanding and simulating the Southern Ocean environment. A combination of satellite observational data and detailed radiative transfer calculations is used to quantify the impact of cloud phase and cloud vertical structure on the reflected solar radiation in the Southern Hemisphere summer. It is found that clouds with supercooled liquid tops dominate the population of liquid clouds. The observations show that clouds with supercooled liquid tops contribute between 27% and 38% to the total reflected solar radiation between 40° and 70°S, and climate models are found to poorly simulate these clouds. The results quantify the importance of supercooled liquid clouds in the Southern Ocean environment and highlight the need to improve understanding of the physical processes that control these clouds in order to improve their simulation in numerical models. This is not only important for improving the simulation of present-day climate and climate variability, but also relevant for increasing confidence in climate feedback processes and future climate projections.

Improved simulation of water vapour and clear-sky radiation using 24 hour forecasts from ERA40

Monthly mean water vapour and clear-sky radiation extracted from the European Centre for Medium Range Weather Forecasts 40-year reanalysis (ERA40) forecasts are assessed using satellite observations and additional reanalysis data. There is a marked improvement in the interannual variability of column-integrated water vapour (CWV) over the oceans when using the 24-hour forecasts compared with the standard 6-hour forecasts products. The spatial distribution of CWV are well simulated by the 6-hour forecasts; using the 24-hour forecasts does not degrade this simulation substantially and in many cases improves on the quality. There is also an improved simulation of clear-sky radiation from the 24-hour forecasts compared with the 6-hour forecasts based on comparison with satellite observations and empirical estimates. Further work is required to assess the quality of water vapour simulation by reanalyses over land regions. Over the oceans, it is recommended that 24-hour forecasts of CWV and clear-sky radiation are used in preference to the standard 6-hour forecast products from ERA40

Observations of the diurnal cycle of outgoing longwave radiation from the Geostationary Earth Radiation Budget instrument

The Geostationary Earth Radiation Budget instrument on Meteosat-8, located over Africa, provides unprecedented temporal sampling (~17 minutes) of the broadband emitted thermal and reflected solar radiances. We analyse the diurnal cycle of the outgoing longwave radiation (OLR) fluxes derived from the thermal radiances for July 2006. Principal component (PC) analysis separates the signals of the surface temperature response to solar heating and of the development of convective clouds. The first two PCs explain most of the OLR variations: PC1 (surface heating) explains 82.3% of the total variance and PC2 (cloud development) explains 12.8% of the variance. Convection is initiated preferentially over mountainous regions and the cloud then advects downstream in the ambient flow. Diurnal variations are much weaker over the oceans, but a coherent signal over the Gulf of Guinea suggests that the cloudiness is modulated by the diurnally varying contrast between the Gulf and the adjacent land mass.

Evaluation of the Met Office global forecast model using Geostationary Earth Radiation Budget (GERB) data

Simulations of the top-of-atmosphere radiative-energy budget from the Met Office global numerical weather-prediction model are evaluated using new data from the Geostationary Earth Radiation Budget (GERB) instrument on board the Meteosat-8 satellite. Systematic discrepancies between the model simulations and GERB measurements greater than 20 Wm-2 in outgoing long-wave radiation (OLR) and greater than 60 Wm-2 in reflected short-wave radiation (RSR) are identified over the period April-September 2006 using 12 UTC data. Convective cloud over equatorial Africa is spatially less organized and less reflective than in the GERB data. This bias depends strongly on convective-cloud cover, which is highly sensitive to changes in the model convective parametrization. Underestimates in model OLR over the Gulf of Guinea coincide with unrealistic southerly cloud outflow from convective centres to the north. Large overestimates in model RSR over the subtropical ocean, greater than 50 Wm-2 at 12 UTC, are explained by unrealistic radiative properties of low-level cloud relating to overestimation of cloud liquid water compared with independent satellite measurements. The results of this analysis contribute to the development and improvement of parametrizations in the global forecast model.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Modeled and observed atmospheric radiation balance during the West African dry season: role of mineral dust, biomass burning aerosol, and surface albedo

The global radiation balance of the atmosphere is still poorly observed, particularly at the surface. We investigate the observed radiation balance at (1) the surface using the ARM Mobile Facility in Niamey, Niger, and (2) the top of the atmosphere (TOA) over West Africa using data from the Geostationary Earth Radiation Budget (GERB) instrument on board Meteosat-8. Observed radiative fluxes are compared with predictions from the global numerical weather prediction (NWP) version of the Met Office Unified Model (MetUM). The evaluation points to major shortcomings in the NWP model's radiative fluxes during the dry season (December 2005 to April 2006) arising from (1) a lack of absorbing aerosol in the model (mineral dust and biomass burning aerosol) and (2) a poor specification of the surface albedo. A case study of the major Saharan dust outbreak of 6–12 March 2006 is used to evaluate a parameterization of mineral dust for use in the NWP models. The model shows good predictability of the large-scale flow out to 4–5 days with the dust parameterization providing reasonable dust uplift, spatial distribution, and temporal evolution for this strongly forced dust event. The direct radiative impact of the dust reduces net downward shortwave (SW) flux at the surface (TOA) by a maximum of 200 W m−2 (150 W m−2), with a SW heating of the atmospheric column. The impacts of dust on terrestrial radiation are smaller. Comparisons of TOA (surface) radiation balance with GERB (ARM) show the “dusty” forecasts reduce biases in the radiative fluxes and improve surface temperatures and vertical thermodynamic structure.

Tripleclouds: an efficient method for representing horizontal cloud inhomogeneity in 1D radiation schemes by using three regions at each height

Radiation schemes in general circulation models currently make a number of simplifications when accounting for clouds, one of the most important being the removal of horizontal inhomogeneity. A new scheme is presented that attempts to account for the neglected inhomogeneity by using two regions of cloud in each vertical level of the model as opposed to one. One of these regions is used to represent the optically thinner cloud in the level, and the other represents the optically thicker cloud. So, along with the clear-sky region, the scheme has three regions in each model level and is referred to as “Tripleclouds.” In addition, the scheme has the capability to represent arbitrary vertical overlap between the three regions in pairs of adjacent levels. This scheme is implemented in the Edwards–Slingo radiation code and tested on 250 h of data from 12 different days. The data are derived from cloud retrievals using radar, lidar, and a microwave radiometer at Chilbolton, southern United Kingdom. When the data are grouped into periods equivalent in size to general circulation model grid boxes, the shortwave plane-parallel albedo bias is found to be 8%, while the corresponding bias is found to be less than 1% using Tripleclouds. Similar results are found for the longwave biases. Tripleclouds is then compared to a more conventional method of accounting for inhomogeneity that multiplies optical depths by a constant scaling factor, and Tripleclouds is seen to improve on this method both in terms of top-of-atmosphere radiative flux biases and internal heating rates.

Examination of Relationships between Clear-Sky Longwave Radiation and Aspects of the Atmospheric Hydrological Cycle in Climate Models, Reanalyses, and Observations

Relationships between clear-sky longwave radiation and aspects of the atmospheric hydrological cycle are quantified in models, reanalyses, and observations over the period 1980-2000. The robust sensitivity of clear-sky surface net longwave radiation (SNLc) to column-integrated water vapor (CWV) of 1-1.5 Wm(-2) mm(-1) combined with the positive relationship between CWV and surface temperature (T-s) explains substantial increases in clear-sky longwave radiative cooling of the atmosphere (Q(LWc)) to the surface over the period. Clear-sky outgoing longwave radiation (OLRc) is highly sensitive to changes in aerosol and greenhouse gas concentrations in addition to temperature and humidity. Over tropical ocean regions of mean descent, Q(LWc) increases with T-s at similar to 3.5-5.5 W m(-2) K-1 for reanalyses, estimates derived from satellite data, and models without volcanic forcing included. Increased Q(LWc) with warming across the tropical oceans helps to explain model ensemble mean increases in precipitation of 0.1-0.15 mm day(-1) K-1, which are primarily determined by ascent regions where precipitation increases at the rate expected from the Clausius-Clapeyron equation. The implications for future projections in the atmospheric hydrological cycle are discussed