General Circulation Model Grid Research Articles

Convective Momentum Transport and Its Impact on the Madden‐Julian Oscillation in E3SM‐MMF

AbstractConvective momentum transport (CMT) is the process of vertical redistribution of horizontal momentum by small‐scale turbulent flows from moist convection. Traditional general circulation models (GCMs) and their multiscale modeling framework (MMF) versions poorly represent CMT due to insufficient information of subgrid‐scale flows at each GCM grid. Here the explicit scalar momentum transport (ESMT) scheme for representing CMT is implemented in the Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) with embedded 2‐D cloud‐resolving models (CRMs), and verified against E3SM‐MMF simulations with 3‐D CRMs and observations. The results show that representing CMT by ESMT helps reduce climatological mean precipitation model bias over the western Pacific and the ITCZ regions, which is attributed to the weakened mean easterlies over the Pacific. Also, CMT from simulations with 2‐D and 3‐D CRMs impose a similar impact on Kelvin waves by reducing their variability and slowing down their phase speed, but opposite impacts on the Madden‐Julian Oscillation (MJO) variability. The ESMT scheme readily captures the climatological mean spatial patterns of the zonal and meridional components of CMT and their variability across multiple time scales, but shows some differences in estimating its magnitude. CMT mainly affects the MJO by decelerating its winds in the free troposphere, but accelerates its near‐surface winds. This study serves as a prototype for implementing CMT scheme in the MMF simulations, highlighting its crucial role in reducing model bias in mean state and spatiotemporal variability.

Statistically Steady State Large‐Eddy Simulations Forced by an Idealized GCM: 1. Forcing Framework and Simulation Characteristics

AbstractUsing large‐eddy simulations (LES) systematically has the potential to inform parameterizations of subgrid‐scale processes in general circulation models (GCMs), such as turbulence, convection, and clouds. Here we show how LES can be run to simulate grid columns of GCMs to generate LES across a cross section of dynamical regimes. The LES setup approximately replicates the thermodynamic and water budgets in GCM grid columns. Resolved horizontal and vertical transports of heat and water and large‐scale pressure gradients from the GCM are prescribed as forcing in the LES. The LES are forced with prescribed surface temperatures, but atmospheric temperature and moisture are free to adjust, reducing the imprinting of GCM fields on the LES. In both the GCM and LES, radiative transfer is treated in a unified but idealized manner (semigray atmosphere without water vapor feedback or cloud radiative effects). We show that the LES in this setup reaches statistically steady states without nudging to thermodynamic GCM profiles. The steady states provide training data for developing GCM parameterizations. The same LES setup also provides a good basis for studying the cloud response to global warming.

Determination of General Circulation Model Grid Resolution to Improve Accuracy of Rainfall Prediction in West Java

Determination of General Circulation Model Grid Resolution to Improve Accuracy of Rainfall Prediction in West Java

A downscaling-disaggregation approach for developing IDF curves in arid regions.

Over the past decades, urbanization in Arabian Gulf region expands in flood-prone areas at an unprecedented rate. Chronic water stress and potential changes in extreme rainfall attributed to climate change therefore pose unique challenges in planning and designing water management infrastructures. The objective of this study is to develop a framework to integrate climate change variations into intensity-duration-frequency (IDF) curves in Oman. A two-stage downscaling-disaggregation method was applied with rainfall at Tawi-Atair station in Dhofar region. Potential variations of extreme rainfall in future were examined by eight scenarios composed with two general circulation models (GCMs), two representative concentration pathways (RCPs), and two future periods (2040-2059 and 2080-2099). A stochastic weather generator model was used to downscale rainfall output from GCM grid scale to local scale. Downscaled daily data were then disaggregated to hourly and 5-min series by using K-nearest neighbor (K-NN) technique. Annual maximum rainfall extracted from eight future scenarios and also from present climate (baseline period) was used to develop rainfall intensity-frequency relationships for eight durations range from 5min to 24h. Results of the K-NN analysis indicate that the optimum window size of 57days and 181h is suitable for hourly and 5-min disaggregation models, respectively. Results also predict that the effects of climate change on the rainfall intensity will be more significant on storms with shorter durations and higher return periods. Moving towards the end of the twenty-first century, the return period of extreme rainfall events is likely to decrease due to intensified rainfall events.

Forced gravity waves and the tropospheric response to convection

We present theoretical work directed toward improving our understanding of the mesoscale influence of deep convection on its tropospheric environment through forced gravity waves. From the linear, hydrostatic, non‐rotating, incompressible equations, we find a two‐dimensional analytical solution to prescribed heating in a stratified atmosphere, which is upwardly radiating from the troposphere when the domain lid is sufficiently high. We interrogate the spatial and temporal sensitivity of both the vertical velocity and potential temperature to different heating functions, considering both the near‐field and remote responses to steady and pulsed heating. We find that the mesoscale tropospheric response to convection is significantly dependent on the upward radiation characteristics of the gravity waves, which are in turn dependent upon the temporal and spatial structure of the source, and the assumed stratification. We find a 50% reduction in tropospherically averaged vertical velocity when moving from a trapped (i.e. low lid) to upwardly radiating (i.e. high lid) solution but, even with maximal upward radiation, we still observe significant tropospheric vertical velocities in the far‐field 4 h after heating ends. We quantify the errors associated with coarsening a 10 km‐wide heating to a 100 km grid (in the way a general circulation model (GCM) would), observing a 20% reduction in vertical velocity. The implications of these results for the parametrization of convection in low‐resolution numerical models are quantified, and it is shown that the smoothing of heating over a grid box leads to significant in‐grid‐box tendencies, due to the erroneous rate of transfer of compensating subsidence to neighbouring regions. Further, we explore a simple time‐dependent heating parametrization that minimizes error in a parent GCM grid box, albeit at the expense of increased error in the neighbourhood.

Land–Ocean Shifts in Tropical Precipitation Linked to Surface Temperature and Humidity Change

A compositing scheme that predicts changes in tropical precipitation under climate change from changes in near-surface relative humidity (RH) and temperature is presented. As shown by earlier work, regions of high tropical precipitation in general circulation models (GCMs) are associated with high near-surface RH and temperature. Under climate change, it is found that high precipitation continues to be associated with the highest surface RH and temperatures in most CMIP5 GCMs, meaning that it is the “rank” of a given GCM grid box with respect to others that determines how much precipitation falls rather than the absolute value of surface temperature or RH change, consistent with the weak temperature gradient approximation. Further, it is demonstrated that the majority of CMIP5 GCMs are close to a threshold near which reductions in land RH produce large reductions in the RH ranking of some land regions, causing reductions in precipitation over land, particularly South America, and compensating increases over ocean. Recent work on predicting future changes in specific humidity allows the prediction of the qualitative sense of precipitation change in some GCMs when land surface humidity changes are unknown. However, the magnitudes of predicted changes are too small. Further study, perhaps into the role of radiative and land–atmosphere feedbacks, is necessary.

Precipitation change assessment over upper Bagmati river basin using regional bias corrected GCM data

Climate change impacts on precipitation pattern have been assessed over upper Bagmati river basin, Nepal. General circulation model (GCM) projections, which are widely used to assess climate change impacts, consist of significant biases due to oversimplification of the global climate system. Bias in daily GCM precipitation was corrected at grid cell scale using regional quantile-based bias correction technique. In this technique, bias correction pattern is established by comparing GCM grid data with nearby observation station data. Concepts of homogeneous precipitation regions were used to transfer statistical characteristics of nearby observation stations to ungauged cells. Calibration and validation of the regional bias correction technique was performed over 1979-2003. Comparative precipitation change assessments were carried out at annual, monthly and daily time scales considering bias corrected precipitation data of 1979-2003 and 2075-2099 periods respectively.

Precipitation change assessment over upper Bagmati river basin using regional bias corrected GCM data

Climate change impacts on precipitation pattern have been assessed over upper Bagmati river basin, Nepal. General circulation model (GCM) projections, which are widely used to assess climate change impacts, consist of significant biases due to oversimplification of the global climate system. Bias in daily GCM precipitation was corrected at grid cell scale using regional quantile-based bias correction technique. In this technique, bias correction pattern is established by comparing GCM grid data with nearby observation station data. Concepts of homogeneous precipitation regions were used to transfer statistical characteristics of nearby observation stations to ungauged cells. Calibration and validation of the regional bias correction technique was performed over 1979-2003. Comparative precipitation change assessments were carried out at annual, monthly and daily time scales considering bias corrected precipitation data of 1979-2003 and 2075-2099 periods respectively.

OBLIMAP 2.0: a fast climate model–ice sheet model coupler including online embeddable mapping routines

Abstract. This paper accompanies the second OBLIMAP open-source release. The package is developed to map climate fields between a general circulation model (GCM) and an ice sheet model (ISM) in both directions by using optimal aligned oblique projections, which minimize distortions. The curvature of the surfaces of the GCM and ISM grid differ, both grids may be irregularly spaced and the ratio of the grids is allowed to differ largely. OBLIMAP's stand-alone version is able to map data sets that differ in various aspects on the same ISM grid. Each grid may either coincide with the surface of a sphere, an ellipsoid or a flat plane, while the grid types might differ. Re-projection of, for example, ISM data sets is also facilitated. This is demonstrated by relevant applications concerning the major ice caps. As the stand-alone version also applies to the reverse mapping direction, it can be used as an offline coupler. Furthermore, OBLIMAP 2.0 is an embeddable GCM–ISM coupler, suited for high-frequency online coupled experiments. A new fast scan method is presented for structured grids as an alternative for the former time-consuming grid search strategy, realising a performance gain of several orders of magnitude and enabling the mapping of high-resolution data sets with a much larger number of grid nodes. Further, a highly flexible masked mapping option is added. The limitation of the fast scan method with respect to unstructured and adaptive grids is discussed together with a possible future parallel Message Passing Interface (MPI) implementation.

Development and Evaluation of Statistical Downscaling Models for Monthly Precipitation

Abstract Several statistical downscaling models have been developed in the past couple of decades to assess the hydrologic impacts of climate change by projecting the station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs). This paper presents and compares different statistical downscaling models that use multiple linear regression (MLR), positive coefficient regression (PCR), stepwise regression (SR), and support vector machine (SVM) techniques for estimating monthly rainfall amounts in the state of Florida. Mean sea level pressure, air temperature, geopotential height, specific humidity, U wind, and V wind are used as the explanatory variables/predictors in the downscaling models. Data for these variables are obtained from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis dataset and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled Global Climate Model, version 3 (CGCM3) GCM simulations. The principal component analysis (PCA) and fuzzy c-means clustering method (FCM) are used as part of downscaling model to reduce the dimensionality of the dataset and identify the clusters in the data, respectively. Evaluation of the performances of the models using different error and statistical measures indicates that the SVM-based model performed better than all the other models in reproducing most monthly rainfall statistics at 18 sites. Output from the third-generation CGCM3 GCM for the A1B scenario was used for future projections. For the projection period 2001–10, MLR was used to relate variables at the GCM and NCEP grid scales. Use of MLR in linking the predictor variables at the GCM and NCEP grid scales yielded better reproduction of monthly rainfall statistics at most of the stations (12 out of 18) compared to those by spatial interpolation technique used in earlier studies.

Modeling the moist‐convective atmosphere with a Quasi‐3‐D Multiscale Modeling Framework (Q3D MMF)

The Q3D MMF (Quasi‐Three‐Dimensional Multiscale Modeling Framework) is a new generation of MMF that replaces the conventional subgrid‐scale parameterizations in general circulation models (GCMs) with explicit simulations of cloud and associated processes by cloud‐resolving models (CRMs). In the Q3D MMF, 3‐D CRMs are applied to the channel domains that extend over GCM grid cells. To avoid “double counting” of the large‐scale effects, only the eddy effects simulated by the CRMs are implemented into the GCM as far as the transports are concerned, while the total effects are implemented for diabatic processes. The CRMs recognize the large‐scale horizontal inhomogeneity through the lateral boundary conditions obtained from the GCM through interpolation. To maintain compatibility between the GCM and CRMs, the averages of CRM variables over the GCM grid spacing are relaxed to the corresponding GCM variables with the advective time scale. To evaluate the Q3D MMF, a transition from a wave to strong vortices is simulated in an idealized horizontal domain. Comparison with a fully 3‐D benchmark simulation shows that the Q3D MMF successfully predicts the evolution of the vortices. It also captures important statistics such as the domain‐averaged surface precipitation rate, turbulent fluxes and subgrid‐scale (co)variances. From tests with 3‐D and 2‐D CRMs, respectively, it is concluded that the ability to recognize large‐scale inhomogeneities is primarily responsible for the successful performance of the Q3D MMF. It is also demonstrated that the use of two perpendicular sets of CRMs has positive impacts on the simulation.

Monte Carlo-based subgrid parameterization of vertical velocity and stratiform cloud microphysics in ECHAM5.5-HAM2

Abstract. A new method for parameterizing the subgrid variations of vertical velocity and cloud droplet number concentration (CDNC) is presented for general circulation models (GCMs). These parameterizations build on top of existing parameterizations that create stochastic subgrid cloud columns inside the GCM grid cells, which can be employed by the Monte Carlo independent column approximation approach for radiative transfer. The new model version adds a description for vertical velocity in individual subgrid columns, which can be used to compute cloud activation and the subgrid distribution of the number of cloud droplets explicitly. Autoconversion is also treated explicitly in the subcolumn space. This provides a consistent way of simulating the cloud radiative effects with two-moment cloud microphysical properties defined at subgrid scale. The primary impact of the new parameterizations is to decrease the CDNC over polluted continents, while over the oceans the impact is smaller. Moreover, the lower CDNC induces a stronger autoconversion of cloud water to rain. The strongest reduction in CDNC and cloud water content over the continental areas promotes weaker shortwave cloud radiative effects (SW CREs) even after retuning the model. However, compared to the reference simulation, a slightly stronger SW CRE is seen e.g. over mid-latitude oceans, where CDNC remains similar to the reference simulation, and the in-cloud liquid water content is slightly increased after retuning the model.

Gravity wave momentum flux generation close to mid-latitude Andes in mesoscale simulations of late 20th and 21st centuries

Adequate representations of diverse dynamical processes in general circulation models (GCM) are necessary to obtain reliable simulations of the present and the future. The parameterization of orographic gravity wave drag (GWD) is one of the critical components of GCM. It is therefore convenient to evaluate whether standard orographic GWD parameterizations are appropriate. One alternative is to study the generation of gravity waves (GW) with horizontal resolutions that are higher than those used in current GCM simulations. Here we assess the seasonal pattern of topographic GW momentum flux (GWMF) generation for the late 20th and 21st centuries in a downscaling using the Rossby Centre regional atmospheric model under the Intergovernmental Panel on Climate Change A1B emission conditions. We focus on one of the world’s strongest extra-tropical GW zones, the Andes Mountains at mid-latitudes in the Southern Hemisphere. The presence of two GCM sub-grid scale structures locally contributing to GWMF (one positive and one negative) is found to the East of the mountains. For the late 21st century the strength of these structures during the GW high season increases around 23% with respect to the late 20th century, but the GWMF average over GCM grid cell scales remains negative and nearly constant around −0.015 Pa. This constitutes a steady significant contribution during GW high season, which is not related to the GWMF released by individual sporadic strong GW events. This characteristic agrees with the fact that no statistically significant variation in GWMF at source level has been observed in recent GCM simulations of atmospheric change induced by increases in greenhouse gases.

Aerosol indirect effects in a multi-scale aerosol-climate model PNNL-MMF

Abstract. Much of the large uncertainty in estimates of anthropogenic aerosol effects on climate arises from the multi-scale nature of the interactions between aerosols, clouds and dynamics, which are difficult to represent in conventional general circulation models (GCMs). In this study, we use a multi-scale aerosol-climate model that treats aerosols and clouds across multiple scales to study aerosol indirect effects. This multi-scale aerosol-climate model is an extension of a multi-scale modeling framework (MMF) model that embeds a cloud-resolving model (CRM) within each vertical column of a GCM grid. The extension allows a more physically-based treatment of aerosol-cloud interactions in both stratiform and convective clouds on the global scale in a computationally feasible way. Simulated model fields, including liquid water path (LWP), ice water path, cloud fraction, shortwave and longwave cloud forcing, precipitation, water vapor, and cloud droplet number concentration are in reasonable agreement with observations. The new model performs quantitatively similar to the previous version of the MMF model in terms of simulated cloud fraction and precipitation. The simulated change in shortwave cloud forcing from anthropogenic aerosols is −0.77 W m−2, which is less than half of that (−1.79 W m−2) calculated by the host GCM (NCAR CAM5) with traditional cloud parameterizations and is also at the low end of the estimates of other conventional global aerosol-climate models. The smaller forcing in the MMF model is attributed to a smaller (3.9 %) increase in LWP from preindustrial conditions (PI) to present day (PD) compared with 15.6 % increase in LWP in stratiform clouds in CAM5. The difference is caused by a much smaller response in LWP to a given perturbation in cloud condensation nuclei (CCN) concentrations from PI to PD in the MMF (about one-third of that in CAM5), and, to a lesser extent, by a smaller relative increase in CCN concentrations from PI to PD in the MMF (about 26 % smaller than that in CAM5). The smaller relative increase in CCN concentrations in the MMF is caused in part by a smaller increase in aerosol lifetime from PI to PD in the MMF, a positive feedback in aerosol indirect effects induced by cloud lifetime effects from aerosols. The smaller response in LWP to anthropogenic aerosols in the MMF model is consistent with observations and with high resolution model studies, which may indicate that aerosol indirect effects simulated in conventional global climate models are overestimated and point to the need to use global high resolution models, such as MMF models or global CRMs, to study aerosol indirect effects. The simulated total anthropogenic aerosol effect in the MMF is −1.05 W m−2, which is close to the Murphy et al. (2009) inverse estimate of −1.1±0.4 W m−2 (1σ) based on the examination of the Earth's energy balance. Further improvements in the representation of ice nucleation and low clouds in MMF are needed to refine the aerosol indirect effect estimate.

Implied Ocean Heat Transports in the Standard and Superparameterized Community Atmospheric Models

Abstract Implied ocean heat transport (To) based on net surface energy budgets is computed for two versions of the Community Atmospheric Model (CAM, version 3.0) general circulation model (GCM). The first version is the standard CAM with parameterized convection. The second is the multiscale modeling framework (MMF), in which parameterized convection is replaced with a two-dimensional cloud-resolving model in each GCM grid column. Although global-mean net surface energy totals are similar for both models, differences in the geographic distributions of the component errors lead to distinctly different To for each model, with CAM’s To generally agreeing with observationally based To estimates, and the MMF’s To producing northward transport at all latitudes north of ∼50°S. Analysis of component error sources in the To calculation identifies needed improvements in the MMF. Net surface shortwave radiation and latent heat fluxes over the oceans are the primary causes of To errors in the MMF. Surface shortwave radiation biases in the MMF are associated with liquid and/or ice water content biases in tropical and extratropical convection and a deficit of marine stratocumulus clouds. It is expected that tropical ice water contents in the MMF can be made more realistic via improvements to the cloud microphysics parameterization. MMF marine stratocumulus clouds are overly sensitive to low-level relative humidity and form only with nearly saturated conditions and a shallow boundary layer. Latent heat flux errors in the MMF are amplifications of those found in the CAM and are concentrated in the trade wind regime and the Asian monsoon region and the adjacent western Pacific Ocean. Potential improvements to To are estimated by replacing either simulated net surface shortwave or latent heat fluxes with those from observations and recomputing To. When observed shortwave fluxes are used, both CAM and MMF produce greatly improved To curves for both hemispheres. When To is computed using observed latent heat fluxes, CAM To degrades slightly and MMF To improves, especially in the sign of Southern Hemisphere transport.

А review of modern methods for spacial detailing of meteorological fields

Рассматриваются современные методы повышения детализации метеорологических полей с недостаточным пространственным разрешением. Кратко приводятся основные достоинства и недостатки статистических, физических и динамико-статистических методов. Большее внимание уделяется динамическим методам, основанным на интегрировании численных моделей атмосферы с высоким пространственным разрешением. Анализируются различные способы использования данных с грубым разрешением для коррекции состояния численной модели при подобном интегрировании. Кратко рассматривается методология циклического инкрементного усвоения данных, пригодная для повышения детализации метеорологических полей.

Mapping technique of climate fields between GCM's and ice models

Abstract. Here, we present a mapping method OBLIMAP, which projects and interpolates fields like surface temperature, surface mass balance, and surface height between a geographical based coordinate system of a General Circulation Model (GCM) and a rectangular based Ice Model (IM). We derive an oblique stereographic projection and its inverse, which holds for any area at the Earth's surface, and which can be combined with two different interpolation methods. The first one is suited to interpolate the projected fields of a coarse GCM grid on a fine meshed IM grid. The second one is appropriate for the opposite case. Both grids are allowed to be arbitrary and irregularly spaced. Therefore the OBLIMAP technique is suitable for any GCM-IM combination. After a first scan of the GCM grid coordinates and the specification of the IM grid, fast mapping of various fields is possible. To and fro (GCM-IM-GCM) mapping tests with the Climate Community System Model (CCSM) at T42 resolution (~313 km) and the Regional Atmospheric Climate Model (RACMO) at ~11 km and ~55 km, show average temperature differences of less than 0.1 K with small standard deviations. OBLIMAP, available at GMD, is an accurate, robust and well-documented mapping method for coupling an IM with a GCM or to map state of the art initial and forcing fields available at geographical coordinates to any local IM grid with an optimal centered oblique projection. Currently, the oblique stereographic and the oblique Lambert azimuthal equal-area projections for both the sphere and the ellipsoid are implemented in OBLIMAP.

Investigation of Regional and Seasonal Variations in Marine Boundary Layer Cloud Properties from MODIS Observations

Abstract To aid in understanding the role that marine boundary layer (MBL) clouds play in climate and assist in improving their representations in general circulation models (GCMs), their long-term microphysical and macroscale characteristics are quantified using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard the National Aeronautics and Space Administration’s (NASA’s) Terra satellite. Six years of MODIS pixel-level cloud products are used from oceanic study regions off the west coasts of California, Peru, the Canary Islands, Angola, and Australia where these cloud types are common. Characterizations are given for their organization (macroscale structure), the associated microphysical properties, and the seasonal dependencies of their variations for scales consistent with the size of a GCM grid box (300 km × 300 km). MBL mesoscale structure is quantified using effective cloud diameter CD, which is introduced here as a simplified measure of bulk cloud organization; it is straightforward to compute and provides descriptive information beyond that offered by cloud fraction. The interrelationships of these characteristics are explored while considering the influences of the MBL state, such as the occurrence of drizzle. Several commonalities emerge for the five study regions. MBL clouds contain the best natural examples of plane-parallel clouds, but overcast clouds occur in only about 25% of the scenes, which emphasizes the importance of representing broken MBL cloud fields in climate models (that are subgrid scale). During the peak months of cloud occurrence, mesoscale organization (larger CD) increases such that the fractions of scenes characterized as “overcast” and “clumped” increase at the expense of the “scattered” scenes. Cloud liquid water path and visible optical depth usually trend strongly with CD, with the largest values occurring for scenes that are drizzling. However, considerable interregional differences exist in these trends, suggesting that different regression functionalities exist for each region. For peak versus off-peak months, the fraction of drizzling scenes (as a function of CD) are similar for California and Angola, which suggests that a single probability distribution function might be used for their drizzle occurrence in climate models. The patterns are strikingly opposite for Peru and Australia; thus, the contrasts among regions may offer a test bed for model simulations of MBL drizzle occurrence.

Tripleclouds: An Efficient Method for Representing Horizontal Cloud Inhomogeneity in 1D Radiation Schemes by Using Three Regions at Each Height

Abstract 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.

A numerical approach to calculating soil wetness and evapotranspiration over large grid areas

Soil wetness is typically highly variable in space over the length scales of general circulation model grid areas (∼100 km), and the stress functions relating the surface evapotranspiration rate to local‐scale (∼1–100 m) soil wetness are very nonlinear. These two factors give rise to significant inaccuracies whenever a single grid area average soil wetness value is inserted into a stress function to calculate the evapotranspiration rate for a large grid area. A numerical method is presented to mitigate this problem. The distribution of soil wetness within a grid area is represented by binning, and a numerical integration of the stress function over this binned distribution provides a spatially integrated wetness stress term for the whole grid area, which permits calculation of grid area fluxes in a single operation. The method is very accurate when 10 or more bins are used. It can deal realistically with spatially variable precipitation, conserves moisture exactly, strongly reduces any oscillations, and allows for precise modification of the soil wetness distribution after every time step.