Moisture Balance Model Research Articles

Medium Term Climate Change Effects on Millet Yields in Gulu District, Northern Uganda

Climate change is expected to adversely affect crop yields and livelihoods of agro-dependent societies, especially in Sub-Saharan Africa. However, there remain gaps on the effects of expected regional climatic changes on key food security crops. This study assessed the projected climatic conditions and expected changes in millet yields for Paicho Sub County (S/C) in Gulu District up to the year 2033 using a cross sectional study design. To determine future climatic conditions, PRECIS (Providing Regional Climates for Impact Studies) model was used based on projected conditions at a 50 km spatial resolution while millet yields were modelled using Penman Grindley soil moisture balance model. PRECIS projected changes for 2033 reveal a strong and significant decrease in rainfall (p< 0.05). This is likely to decrease millet yields by 2.6% below the average current yields of 1.8 tons per hectare per year under business-as-usual scenario. The finding indicates a need for improved millet varieties that can survive under changed climatic conditions

Estimating internal moisture generation rates in recently constructed, occupied homes in the southeastern United States

Internal moisture generation (IMG), or moisture generated by building occupants via activities such as respiration, cooking, bathing, and cleaning, is a critical input required for design, analysis, and simulation of building enclosure and HVAC systems. Based on previously published values, ASHRAE Standard 160-2021 provides guidance for estimating IMG rates for moisture control design analysis, which is based on occupied home datasets collected in the 1980s and 1990s. Residential energy use simulation software also utilizes estimates for IMG for energy rating, energy analysis, and code compliance calculations, as specified in ANSI/RESNET/ICC Standard 301. Data quantifying IMG rates in newer homes are useful in determining the continued relevance of current design and simulation guidance, and whether the guidance represents conditions found in new housing stock. ASHRAE Research Project 1844, conducted by the Florida Solar Energy Center (FSEC), a research institute of the University of Central Florida, estimated IMG rates in newer occupied homes built since 2013 in the southeastern United States using a moisture balance model approach. The project obtained occupied home data in cooperation with a U.S. Department of Energy Building America research project to characterize indoor air quality (IAQ) in newer U.S. homes, along with presence, functionality, and occupant use of control measures. Full-scale laboratory homes operating with known IMG rates were used to validate a moisture balance model and quantify the accuracy of estimates obtained when the model is applied to data from occupied homes with unknown IMG rates.

Integrated Hydrogeological Modelling for Sustainable Management of the Brindisi Plain Aquifer (Southern Italy)

Nowadays, changes in precipitation patterns together with the increasing water demand impose a sustainable management where the budget between water availability and demand is positively closed. A parsimonious hydrogeological modelling approach coupled with a soil water balance is developed and applied in order to quantify the hydrological and hydrogeological dynamics in a semi-arid region of the Mediterranean basin. In particular, the present work focuses on the hydrogeological dynamics of the catchment areas of Siedi, Foggia di Rau, Pigonati, and the Palmarini channels located in the Brindisi Plain, Southern Italy. In the last decades, in the Brindisi Plain the anthropization processes as well as the industrial and agricultural development have generated an intensive exploitation of both shallow and deep groundwater resources as well as their qualitative deterioration. A dry hydrologic year (2019–2020) caused a recharge deficit, resulting in a lowering of the groundwater level of the shallow aquifer compared to the expected seasonal value. The results evidence a sensitive natural system, where the variability of the rainfall regime combined with water withdrawal leads to a system that is very vulnerable to climate change impacts, such as the presence of erratic rainfall patterns affecting aquifer recharge. This study represents the first approach to couple a soil moisture balance model and groundwater flow model to assess the impact of changes in rainfall patterns on groundwater recharge for the Brindisi Plain aquifer. The developed integrated hydrogeological model can be applied to other sites with similar hydrogeological features and represents an important tool in order to evaluate the effectiveness of cost-effective sustainable actions for the management of the groundwater resources with respect to land-use practices and socio-economic aspects.

Drought onset and propagation into soil moisture and grassland vegetation responses during the 2012–2019 major drought in Southern California

Abstract. Despite clear signals of regional impacts of the recent severe drought in California, e.g., within Californian Central Valley groundwater storage and Sierra Nevada forests, our understanding of how this drought affected soil moisture and vegetation responses in lowland grasslands is limited. In order to better understand the resulting vulnerability of these landscapes to fire and ecosystem degradation, we aimed to generalize drought-induced changes in subsurface soil moisture and to explore its effects within grassland ecosystems of Southern California. We used a high-resolution in situ dataset of climate and soil moisture from two grassland sites (coastal and inland), alongside greenness (Normalized Difference Vegetation Index) data from Landsat imagery, to explore drought dynamics in environments with similar precipitation but contrasting evaporative demand over the period 2008–2019. We show that negative impacts of prolonged precipitation deficits on vegetation at the coastal site were buffered by fog and moderate temperatures. During the drought, the Santa Barbara region experienced an early onset of the dry season in mid-March instead of April, resulting in premature senescence of grasses by mid-April. We developed a parsimonious soil moisture balance model that captures dynamic vegetation–evapotranspiration feedbacks and analyzed the links between climate, soil moisture, and vegetation greenness over several years of simulated drought conditions, exploring the impacts of plausible climate change scenarios that reflect changes to precipitation amounts, their seasonal distribution, and evaporative demand. The redistribution of precipitation over a shortened rainy season highlighted a strong coupling of evapotranspiration to incoming precipitation at the coastal site, while the lower water-holding capacity of soils at the inland site resulted in additional drainage occurring under this scenario. The loss of spring rains due to a shortening of the rainy season also revealed a greater impact on the inland site, suggesting less resilience to low moisture at a time when plant development is about to start. The results also suggest that the coastal site would suffer disproportionally from extended dry periods, effectively driving these areas into more extreme drought than previously seen. These sensitivities suggest potential future increases in the risk of wildfires under climate change, as well as increased grassland ecosystem vulnerability.

Modeling the influence of the Earth rotation axis position on the global climate variations

This study presents the results of numerical experiments to determine the Earth’s climate when its rotation axis is displaced without changing the axis tilt to the ecliptic plane. There is some evidence of the possibility of this shift in the past. The calculations were carried out using a hydrodynamic three-dimensional global climate model, including blocks of atmosphere, thermohaline large-scale ocean circulation and sea ice. Numerical experiments demonstrate a significant temperature changes throughout the world. A large area of Antarctica warmed up to temperatures above 15 ° C. This is reason of intense melting of glaciers for a long time. Significant warming of the Arctic Ocean will lead to sea ice melting in the Arctic. Strong changes in temperature and ice cover lead to significant changes in horizontal ocean circulation. A procedure is proposed for calculating wind speed in atmosphere energy - moisture balance model. It is based on the geostrophic approach, taking into account the thermal component of the wind, and introducing the mechanism of friction on the underlying surface. A technique has been developed for the formation of the necessary maps and the relationships between them when turning the Earth rotation axis or using new cartographic data.

Irrigation and crop water requirement estimation for oil palms using soil moisture balance model in Peninsular Malaysia

This study presents the irrigation and crop water estimation in a Malaysian oil palm plantation for effective irrigation water management during water years 2013 and 2014. The study area was divided into four plots: 2000, 2002, 2006 and 2010, indicating years of peat swamp forest conversion to oil palm plantation. Hydrologic Engineering Centre-Hydrologic Modeling System (HEC-HMS) and Soil moisture balance hydrologic models were used to model the rainfall-runoff in the basin. Statistical analysis using coefficient of determination (R2) and Nash–Sutcliffe efficiency coefficient (NSE) were used to evaluate the performance and correlation of the two hydrologic models. The result showed that R2 and NSE were 0.94 and 0.90 respectively for calibration and 0.92 and 0.54 respectively, for monthly validation. This showed that the models performed well for simulation of the peatland hydrology. With the modelling of rainfall-runoff satisfied, the irrigation demand of the study plots was determined using the same soil moisture balance model. The irrigation demand ranged from 0.893 to 1.6 million cubic meters (MCM) in 2010 and 2000 study plots respectively. Irrigation demand is observed to be site specific which depends on the soil moisture deficit, readily available water in the oil palm root zone and oil palm rooting depth. Estimation of a future oil palm water requirement using the soil moisture balance model would be recommended for further studies for use as an advisory manual for the oil palm managers to enhance adequate water resources planning for oil palm productivity.

Dynamics and Variability of the Spring Dry Season in the United States Southwest as Observed in AmeriFlux and NLDAS-2 Data

Abstract The spring dry season occurring in an arid region of the southwestern United States, which receives both winter storm track and summer monsoon precipitation, is investigated. Bimodal precipitation and vegetation growth provide an opportunity to assess multiple climate mechanisms and their impact on hydroclimate and ecosystems. We detect multiple shifts from wet to drier conditions in the observational record and land surface model output. Focusing on the recent dry period, a shift in the late 1990s resulted in earlier and greater spring soil moisture draw down, and later and reduced spring vegetation green-up, compared to a prior wet period (1979–97). A simple soil moisture balance model shows this shift is driven by changes in winter precipitation. The recent post-1999 dry period and an earlier one from 1948 to 1966 are both related to the cool tropics phase of Pacific decadal variability, which influences winter precipitation. In agreement with other studies for the southwestern United States, we find the recent drought cannot be explained in terms of precipitation alone, but also is due to the rising influence of temperature, thus highlighting the sensitivity of this region to warming temperatures. Future changes in the spring dry season will therefore be affected by how tropical decadal variability evolves, and also by emerging trends due to human-driven warming.

Groundwater potential recharge estimation in bare soil using three soil moisture accounting models: field evaluation for a semi-arid foothill region

Performances of conventional and improved soil moisture balance as well as locally calibrated empirical models were evaluated in simulating potential recharge (R) and soil moisture content for a semi-arid foothill region. Models comparison with observed values using lysimeter data during [(2011–2012), (2012–2013)] reveal poor performance of conventional soil moisture balance model, underestimating annual R values. Improved soil moisture balance model provided acceptable estimation of annual R for 2011–2012 by considering the wetting of the near surface soil storage. However, it produced the worst simulation for daily soil moisture content once rainy season was over. Sensitivity analysis revealed that the precision degree of initial soil moisture deficit value would strongly influence estimation of R by improved soil moisture balance model, which can be viewed as a limiting factor. Additionally, locally calibrated model produced the best estimation of annual R and daily soil moisture content, which is suggested for the study region.

Building a traceable climate model hierarchy with multi-level emulators

Abstract. To study climate change on multi-millennial timescales or to explore a model's parameter space, efficient models with simplified and parameterised processes are required. However, the reduction in explicitly modelled processes can lead to underestimation of some atmospheric responses that are essential to the understanding of the climate system. While more complex general circulations are available and capable of simulating a more realistic climate, they are too computationally intensive for these purposes. In this work, we propose a multi-level Gaussian emulation technique to efficiently estimate the outputs of steady-state simulations of an expensive atmospheric model in response to changes in boundary forcing. The link between a computationally expensive atmospheric model, PLASIM (Planet Simulator), and a cheaper model, EMBM (energy–moisture balance model), is established through the common boundary condition specified by an ocean model, allowing for information to be propagated from one to the other. This technique allows PLASIM emulators to be built at a low cost. The method is first demonstrated by emulating a scalar summary quantity, the global mean surface air temperature. It is then employed to emulate the dimensionally reduced 2-D surface air temperature field. Even though the two atmospheric models chosen are structurally unrelated, Gaussian process emulators of PLASIM atmospheric variables are successfully constructed using EMBM as a fast approximation. With the extra information gained from the cheap model, the multi-level emulator of PLASIM's 2-D surface air temperature field is built using only one-third the amount of expensive data required by the normal single-level technique. The constructed emulator is shown to capture 93.2 % of the variance across the validation ensemble, with the averaged RMSE of 1.33 °C. Using the method proposed, quantities from PLASIM can be constructed and used to study the effects introduced by PLASIM's atmosphere.

The Impact of Urbanization on Moisture Excess in Hong Kong

Urban and rural atmospheric humidity differences were analysed and studied based on the hourly average data collected in two representative meteorology stations (TKL, 15m, 22°31’43 “N, 114°09’24 “E and HKO, 32m, 22°18’07 “N, 114°10’27 “E) in Hong Kong during the period of 1994 to 2009. It was found that in winter season (December and January), the urban areas were more humid than rural areas with the highest UME value of 2.28hPa while thus phenomenon was rarely significant in the summer season which is coordinate with UHI phenomenon. In addition, an urban moisture balance model, based on urban surface hydrology and urban atmospheric moisture balance, was developed to assess the different factors on the temporal behaviour of urban moisture environment. The performance of the urban moisture balance model was also discussed. We conclude that the impact of precipitation on urban moisture environment is important for the high-compact and high-rise city with limited vegetation ratio. Moreover, urban moisture environment is affected by urban morphology, anthropogenic moisture and weather conditions.

Simulation of Potential Groundwater Recharge from the Jaffna Peninsula of Sri Lanka using HYDRUS-1D Model

In drier regions, accurate knowledge of groundwater recharge is important for the sustainable management of scare water resources. Thirunelvely in Jaffna Peninsula is an area where groundwater is being utilized for domestic, agricultural and municipal water supply. Further the groundwater in this area also contaminated with nitrogenous fertilizer application due to intensive agriculture, as post war conditions in the Peninsula encourage farmers to engage in intensive agricultural activities. Very few or no studies have been conducted in the recent past on groundwater recharge or solute transport such a fertilizer leaching in this area. HYDRUS-1D is a Windows-based modelling environment for analysis of water flow and solute transport in variably saturated porous media. HYDRUS-1D is just as quick and cheap as other soil moisture balance models but more physically based and flexible as it allows for building up complexity as data are available whether for solute transport or non-equilibrium flow etc. Therefore the main objective of this paper is to simulate potential groundwater recharge using HYDRUS-1D and compare it with the results obtained in Thirunelvely using soil moisture balance and water table fluctuation methods. Results have shown that the HYDRUS-1D simulated potential groundwater recharge (41.8 cm) has close agreement with that estimated by other methods with high coefficient of determination (R2 = 0.95). Further runoff, soil moisture storage and bottom pressure head simulated by HYDRUS-1D too have good agreement with field observation. Therefore HYDRUS-1D is capable of simulating potential groundwater recharge close to the previously estimated values in Thirunelvely as it has good agreement with the water table fluctuation measured in the study site and the bottom head pressure at the 1 m soil profile simulated in the HYDRUS-1D model. Now that it has been demonstrated that HYDRUS-1D adequately reproduces the water fluxes predicted by other methods, it could be used for groundwater recharge with more confidence and to investigate pollution in soil zone and groundwater. DOI: http://dx.doi.org/10.4038/ouslj.v7i0.7307 OUSL Journal Vol.7 2014: 43-65

Using a Remote Sensing Driven Model to Analyze Effect of Land Use on Soil Moisture in the Weihe River Basin, China

In-depth study of the soil moisture mechanisms and understanding of the soil moisture transport law has an important practical significance for regional water resources management and the challenge of the water resources scarcity. Using traditional methods of soil moisture monitoring, deep soil layers can be monitored, but continuous monitoring of soil moisture at the regional level cannot be achieved. Although remote sensing simulation models can meet regional scale needs, these models are confined to the surface soil layer, and research on deep soil moisture inversion is still lacking. This paper focuses on these two issues, and investigates a remote sensing-driven soil moisture monitoring model for the Weihe River Basin. Considering water resource management needs in the Weihe River Basin, we improved the structure of the soil moisture balance model and optimized model parameters to build the remote sensing driven soil moisture balance model (RS-SWBM). Based on soil moisture modeling, the effect of vegetation on soil moisture in the Weihe River Basin was analyzed. The RS-SWBM developed for the Weihe River Basin was validated with observational data and Global Land Data Assimilation System (GLDAS) soil moisture data products. Based on the correlation analysis, correlation coefficients were all above 0.80, reflecting the effectiveness of the model. The effects of different vegetation types on soil moisture dynamics and consumption efficiency were analyzed. The results indicated that different vegetation types experienced different seasonal variations, vertical patterns, and consumption efficiencies, with strong correlations existing between these parameters and land use as well as precipitation.

Drip water isotopes in semi-arid karst: Implications for speleothem paleoclimatology

We report the results of the first multi-year monitoring and modelling study of the isotopic composition of drip waters in a semi-arid karst terrane. High temporal resolution drip rate monitoring combined with monthly isotope drip water and rainfall sampling at Cathedral Cave, Australia, demonstrates that drip water discharge to the cave occurs irregularly, and only after occasional long duration and high volume rainfall events, where the soil moisture deficit and evapotranspiration is overcome. All drip waters have a water isotopic composition that is heavier than the weighted mean annual precipitation, some fall along the local meteoric water line, others trend towards an evaporation water line. It is hypothesised that, in addition to the initial rainfall composition, evaporation of unsaturated zone water, as well as the time between infiltration events, are the dominant processes that determine infiltration water isotopic composition. We test this hypothesis using a soil moisture balance and isotope model. Our research reports, for the first time, the potential role of sub-surface evaporation in altering drip water isotopic composition, and its implications for the interpretation of speleothem δO18 records from arid and semi-arid regions.

Spatial climate models for Canada’s forestry community

We summarize ongoing efforts at the Canadian Forest Service to produce spatial climate models for Canada and the United States. Our models, which encompass a wide range of variables and spatiotemporal extents, typically employ thin plate smoothing splines to interpolate and extrapolate climate station values as a function of latitude, longitude and elevation. The resulting surfaces can be resolved as grids (i.e., maps) or as point estimates at locations of interest. Recent efforts, detailed here include: updated models for the most recent 30-year normal period (i.e., 1981–2010), moisture balance models, future climate projections using the latest round of general circulation model (GCM) outputs and emissions scenarios, lake ice freeze/thaw models, and growing season models. These models are available to the Canadian forest community and beyond via the internet ( http://cfs.nrcan.gc.ca/projects/3 ) or by contacting the senior author.

Linking soil moisture balance and source-responsive models to estimate diffuse and preferential components of groundwater recharge

Abstract. Results are presented of a detailed study into the vadose zone and shallow water table hydrodynamics of a field site in Shropshire, UK. A conceptual model is presented and tested using a range of numerical models, including a modified soil moisture balance model (SMBM) for estimating groundwater recharge in the presence of both diffuse and preferential flow components. Tensiometry reveals that the loamy sand topsoil wets up via preferential flow and subsequent redistribution of moisture into the soil matrix. Recharge does not occur until near-positive pressures are achieved at the top of the sandy glaciofluvial outwash material that underlies the topsoil, about 1 m above the water table. Once this occurs, very rapid water table rises follow. This threshold behaviour is attributed to the vertical discontinuity in preferential flow pathways due to seasonal ploughing of the topsoil and to a lower permeability plough/iron pan restricting matrix flow between the topsoil and the lower outwash deposits. Although the wetting process in the topsoil is complex, a SMBM is shown to be effective in predicting the initiation of preferential flow from the base of the topsoil into the lower outwash horizon. The rapidity of the response at the water table and a water table rise during the summer period while flow gradients in the unsaturated profile were upward suggest that preferential flow is also occurring within the outwash deposits below the topsoil. A variation of the source-responsive model proposed by Nimmo (2010) is shown to reproduce the observed water table dynamics well in the lower outwash horizon when linked to a SMBM that quantifies the potential recharge from the topsoil. The results reveal new insights into preferential flow processes in cultivated soils and provide a useful and practical approach to accounting for preferential flow in studies of groundwater recharge estimation.

Recharge estimation methodologies employed by the Environment Agency of England and Wales for the purposes of regional groundwater resource modelling

Abstract Recharge calculations based on daily soil moisture balance models define the resource available for most regional-scale groundwater models used by the environmental regulator in England and Wales. A switch in recent years from the Penman–Grindley methodology to the Food and Agricultural Organization approach has improved the representation of soil properties in these calculations. A new Meteorological Office algorithm for calculating potential evapotranspiration inputs has also been adopted and rain-gauge data processing on individual models are currently being streamlined towards the use of nationally derived grids. A range of infiltration, bypass and runoff–recharge mechanisms have been conceptualized and modelled incorporating simple representation of unsaturated zone storage and flow processes. This paper reviews the recent changes adopted and considers future challenges.

Nonlinearity of Land Carbon Sensitivities in Climate Change Simulations

In the climate-carbon cycle system, the terrestrial ecosystem feedback is significant. In studies on feedback analysis, the ecosystem feedback is divided into the sensitivity of carbon storage to atmospheric CO2 concentration (βL), and temperature change (γL). Although ecosystems include many nonlinear processes, the scenario-and time-dependency of βL and βL have not been explicitly discussed. To check the validity of this simplification and its robustness, we carried out two, 1% per year (p.a.) increase and RCP4.5 scenario, experiments, using a process-based terrestrial ecosystem model forced by an existing GCM output, combined with an energy moisture balance model for the latter experiment, with 300 ensemble members perturbing twelve important and a priori unconstrained parameters. In the 1% p.a. experiment, βL peaked around 500 ppm and then gradually decreased with increasing CO2 level, while βL decreased with some inter-annual variability as temperature increases. The time-dependency of βL was small (at least for CO2 level > 550 ppm), but that of βL was significant, and the effect of this was larger than that of the nonlinear term (i.e., combined effect of CO2 and temperature change). The scenario-dependency is also significant, but the effect in the estimated carbon uptake was smaller than that by the time-dependency. By investigating the background of this effect, we found that in the 1% p.a. CO2 increase scenario, the maximum photosynthesis rate and specific leaf area (SLA, leaf area per unit dry mass) had the most significant contribution to both of βL and βL, and the contributions are dependent on the climate state (i.e., temperature and atmospheric CO2 level). For carbon uptake in both experiments, SLA and coefficient of plant respiration were most significant. We also attempted to constrain the ensemble members, and found that for net primary production, soil carbon and soil respiration, the default parameter set was already well-tuned, while observations of leaf area index (LAI) strongly constrains βL, βL, airborne fraction and ecosystem carbon balance as the default model overestimated the LAI.

Estimation of Groundwater Recharge in Limestone Aquifer using an Improved Soil Moisture Balance Method: A Case Study in Jaffna District

Estimation of recharge is extremely important for proper management of groundwater systems. The main purpose of this paper is to study the possibility of estimation of potential recharge in limestone aquifer as a case study in Thirunelvely and Kondavil area of Jaffna district, Sri Lanka using an improved soil moisture balance model (SAMBA). This model was used to estimate the groundwater recharge for a permanent grass and a commonly cultivated vegetable crop chilli for the years 2007 and 2008 for which soil properties, crop characters and climatic conditions were considered. The new concept of near surface soil moisture storage was included in the model and it is used to represent continuing evaporation on the days following heavy rainfall even though the soil moisture deficit is high. Uncertainties and variation in parameter values were explored using sensitivity analysis. The potential recharge resulted from the model was compared with the real field conditions of actual recharge which was derived from the water table fluctuation method. DOI: http://dx.doi.org/10.4038/tar.v21i1.2586 Tropical Agricultural Research Vol. 21(1): 51-61 (2009)

The importance of preferential flow in controlling groundwater recharge in tropical Africa and implications for modelling the impact of climate change on groundwater resources

An improved water table fluctuation technique for estimating recharge is applied to a sustained (10-year) groundwater level monitoring record in Uganda, a rare dataset for tropical Africa, and compared against results from soil moisture balance models (SMBMs) and unsaturated flow models. The results show that recharge is directly proportional to rainfall (long-term average rainfall is around 1200 mm/a), even during times when high soil moisture deficits are anticipated. This indicates that preferential and/or localized flow mechanisms dominate the recharge behaviour. SMBMs and unsaturated flow models, based on uniform flow governed by the Richards equation, are shown to be inappropriate for estimating recharge in this location underlain by lateritic soils. Given the large spatial coverage of lateritic soils both globally and in tropical Africa, and despite the convenience of physically based uniform flow models and, in particular, SMBMs, concern is raised over the use of such models for recharge estimation, and thus for exploring future trends due to climate or land use change, unless backed up by sufficient hydraulic data to enable the recharge processes to be confirmed. More research is needed to assess how widespread preferential flow may be within other major soil groups and climate zones.

Meridional Density Gradients Do Not Control the Atlantic Overturning Circulation

Abstract A wide body of modeling and theoretical scaling studies support the concept that changes to the Atlantic meridional overturning circulation (AMOC), whether forced by winds or buoyancy fluxes, can be understood in terms of a simple causative relation between the AMOC and an appropriately defined meridional density gradient (MDG). The MDG is supposed to translate directly into a meridional pressure gradient. Here two sets of experiments are performed using a modular ocean model coupled to an energy–moisture balance model in which the positive AMOC–MDG relation breaks down. In the first suite of seven model integrations it is found that increasing winds in the Southern Ocean cause an increase in overturning while the surface density difference between the equator and North Atlantic drops. In the second suite of eight model integrations the equation of state is manipulated so that the density is calculated at the model temperature plus an artificial increment ΔT that ranges from −3° to 9°C. (An increase in ΔT results in increased sensitivity of density to temperature gradients.) The AMOC in these model integrations drops as the MDG increases regardless of whether the density difference is computed at the surface or averaged over the upper ocean. Traditional scaling analysis can only produce this weaker AMOC if the scale depth decreases enough to compensate for the stronger MDG. Five estimates of the depth scale are evaluated and it is found that the changes in the AMOC can be derived from scaling analysis when using the depth of the maximum overturning circulation or estimates thereof but not from the pycnocline depth. These two depth scales are commonly assumed to be the same in theoretical models of the AMOC. It is suggested that the correlation between the MDG and AMOC breaks down in these model integrations because the depth and strength of the AMOC is influenced strongly by remote forcing such as Southern Ocean winds and Antarctic Bottom Water formation.