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DOE OSTI2022

Statistical framework to assess long-term spatio-temporal climate changes: East River mountainous watershed case study

Abstract Evaluation of long-term temporal and spatial climatic change in mountainous regions is a critical challenge because of the interactive effects of multiple land and climatic factors and processes. Here we present the application of the statistical framework to the assessment of changes of climatic conditions, using data from 17 meteorological stations across the East River watershed near Crested Butte, Colorado, USA, and spanning the period from 1966 to 2021. The framework is developed based on (1) a time-series analysis of daily, monthly, and yearly averaged meteorological parameters (temperature, relative humidity, precipitation, wind speed, etc.), (2) evaluation and time series analysis of potential evapotranspiration (ET o ), actual evapotranspiration (ET), aridity index (AI), standard precipitation index (SPI) and standard precipitation-evapotranspiration index (SPEI), and (3) a temporal-spatial climatic zonation of the studied area based on the hierarchical clustering and PCA analysis of the SPEI, because the SPEI can be considered an integrative characteristic of the changes of climatic conditions. The Budyko model, with the application of the Penman–Monteith equation for the estimation of ET o , was used to determine the ET. The time series analysis of the AI is used to identify the periods with energy limited and water limited conditions. Hierarchical clustering of site locations for the three temporal segments of the SPEI showed a significant temporal-spatial shifts, indicating that dynamic climatic processes drive zonation patterns. Therefore, the watershed climatic zonation requires periodic re-evaluation based on the structural time series analysis of meteorological and water balance data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

The fate of water and water-soluble toxic wastes in the subsurface is of high importance for many scientific and practical applications. Although solute transport is proportional to water flow rates, theoretical and experimental studies show that heavy-tailed (power-law) solute transport distribution can cause chemical transport retardation, prolonging clean-up time-scales greatly. However, no consensus exists as to the physical basis of such transport laws. In percolation theory, the scaling behavior of such transport rarely relates to specific medium characteristics, but strongly to the dimensionality of the connectivity of the flow paths (for example, two- or three-dimensional, as in fractured-porous media or heterogeneous sediments), as well as to the saturation characteristics (i.e., wetting, drying, and entrapped air). In accordance with the proposed relevance of percolation models of solute transport to environmental clean-up, these predictions also prove relevant to transport-limited chemical weathering and soil formation, where the heavy-tailed distributions slow chemical weathering over time. The predictions of percolation theory have been tested in laboratory and field experiments on reactive solute transport, chemical weathering, and soil formation and found accurate. Recently, this theoretical framework has also been applied to the water partitioning at the Earth’s surface between evapotranspiration, ET, and run-off, Q, known as the water balance. A well-known phenomenological model by Budyko addressed the relationship between the ratio of the actual evapotranspiration (ET) and precipitation, ET/P, versus the aridity index, ET 0 /P, with P being the precipitation and ET 0 being the potential evapotranspiration. Existing work was able to predict the global fractions of P represented by Q and ET through an optimization of plant productivity, in which downward water fluxes affect soil depth, and upward fluxes plant growth. In the present work, based likewise on the concepts of percolation theory, we extend Budyko’s model, and address the partitioning of run-off Q into its surface and subsurface components, as well as the contribution of interception to ET. Using various published data sources on the magnitudes of interception and information regarding the partitioning of Q, we address the variability in ET resulting from these processes. The global success of this prediction demonstrated here provides additional support for the universal applicability of percolation theory for solute transport as well as guidance in predicting the component of subsurface run-off, important for predicting natural flow rates through contaminated aquifers.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1979

Variational formulation of Budyko-Sellers climate models

A class of simple climate models including those of the Budyko-Sellers type are formulated from a variational principle. A functional is constructed for the zonally averaged mean annual temperature field such that extrema of the functional occur when the climate satisfies the usual energy-balance equation. Local minima of the functional correspond to stable solutions while saddle points correspond to unstable solutions. The technique can be used to construct approximate solutions from trial functions and to carry out finite-amplitude stability analyses. A spectral example is given in explicit detail.

North, G. R.↗

DOE OSTI2021

An Improved Zhang's Dynamic Water Balance Model Using Budyko-Based Snow Representation for Better Streamflow Predictions

Understanding the water balance of a catchment in relation to its regional climate forcings and catchment characteristics is critical for predicting current and future water resources amid changing climate and land cover. This study intends to improve Zhang's monthly water balance model (a physics-based conceptual hydrologic model) that reflects the physical partitioning process of the hydrological cycle at the basin level based on regional climate and catchment characteristics. The existing model does not include snow process and has confronted evident limitations in snow-affected areas, which is a critical aspect since snowmelt water has been a significant source of water resources for many regions, especially in the temperate and frigid zones. We introduce a snow module based on surface energy balance and Budyko-limits on melting and combine it with the existing water balance equations. Moreover, monthly parameterization is applied to the model to better explain the time-varying hydrological characteristics of a catchment. The proposed model involves five different monthly parameters, which determine the physical partitioning process of the hydrological cycle, and they are regionally calibrated and validated under Budyko-type constraints. The model is applied to 1,210 basins across the continental United States (CONUS), and the simulated streamflow is compared to the observed data. The proposed model significantly outperformed the original model, improving the median NSE by 31% (from 0.51 to 0.67) and increasing the number of catchments with an acceptable NSE by 58%. The spatial variability of the basin characteristics across the CONUS is also investigated based on the calibrated parameters.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1982

A simple method to compute the change in earth-atmosphere radiative balance due to a stratospheric aerosol layer

A computer code was developed in terms of a three-layer model for the earth-atmosphere system, using a two-stream approximation for the troposphere and stratosphere. The analysis was limited to variable atmosphere loading by solar radiation over an unperturbed section of the atmosphere. The scattering atmosphere above a Lambertian ground layer was considered in order to derive the planar albedo and the spherical albedo. Attention was given to the influence of the aerosol optical thickness in the stratosphere, the single scattering albedo and asymmetry factor, and the sublayer albedo. Calculations were performed of the zonal albedo and the planetary radiation balance, taking into account a stratospheric aerosol layer containing H2SO4 droplets and volcanic ash. The resulting ground temperature disturbance was computed using a Budyko (1969) climate model. Local decreases in the albedo in the summer were observed in high latitudes, implying a heating effect of the aerosol. An accompanying energy loss of 23-27 W/sq m was projected, which translates to surface temperature decreases of either 1.1 and 0.45 C, respectively, for background and volcanic aerosols.

Lenoble, J.↗

NASA NTRS1979

Elementary analytic models of climate. 1: The mean global heat balance

Climate models based on global radiative equilibrium are normally so complicated that they require extensive computer codes to provide adequate accuracy. However, by simply modifying the concept of a gray atmosphere, a reasonably correct mean global temperature is obtained. This elementary model is then used to estimate the effects of changes in the abundances of minor infrared absorbers and changes in the solar constant or earth albedo. When applied to a Budyko-Sellers zonally averaged model, the quasi-gray model could give a physical basis for the latitude dependence of outgoing radiation and of opacity due to H2O vapor content. The latter effect constitutes an important positive feedback on surface temperature.

Chamberlain, J. W.↗

NASA NTRS1982

The seasonal CO2 cycle on Mars - An application of an energy balance climate model

Energy balance climate models of the Budyko-Sellers variety are applied to the carbon-dioxide cycle on Mars. Recent data available from the Viking mission, in particular the seasonal pressure variations measured by Viking landers, are used to constrain the models. No set of parameters was found for which a one-dimensional model parameterized in terms of ground temperature gave an adequate fit to the observed pressure variations. A modified, two-dimensional model including the effects of dust storms and the polar hood reasonably reproduces the pressure curve, however. The implications of these results for Martian climate changes are discussed.

James, P. B.↗

NASA NTRS1979

Differences between seasonal and mean annual energy balance model calculations of climate and climate sensitivity

The paper extends a simple Budyko-Sellers mean annual energy balance climate model with diffusive transport to include a seasonal cycle. In the model the latitudinal distribution of the zonal average surface temperature is represented by Legendre polynomials and its time-dependence by a Fourier sine-cosine series, and it has three parameters adjusted so that the observed amplitudes of the Northern Hemisphere zonal mean surface temperature are recovered. The seasonal model is used to reveal how the annual mean climate and the sensitivity to changes in incident radiation differ from the predictions obtained with the corresponding mean annual model. The distribution of the incident solar radiation in the models is shown to be insensitive to changes in the eccentricity and the longitude of perihelion and sensitive only to changes in the obliquity of the earth, and for past orbital changes both the seasonal and the mean annual model fail to produce glacial advances of the magnitude that are thought to have occurred.

North, G. R.↗

NASA NTRS1981

Predictability in a solvable stochastic climate model

A highly idealized atmospheric model is presented for the purpose of examining the limits of predictability for the large scales of the temperature field. The model is of the semiempirical type introduced by Budyko (1968, 1969) and Sellers (1969), but forced by a white noise heating term. The advantage of the considered model is its simplicity and the fact that analytical methods can be used throughout so that each assumption and simplification can be examined explicitly. On the other hand, the model lacks many features expected to be important in the real geophysical system. The predictability problem is illustrated by considering first a simple model for the global temperature. The characteristic time for the decay of a global temperature anomaly is determined by the ratio of the associated heat storage to the radiative loss rate.

North, G. R.↗

NASA NTRS1980

Comments on 'Some realistic modifications of simple climate models'

Lindzen and Farrell (LF) in 1977 argued that the eddy diffusion is not a good parameterization of meridional heat flux in tropical latitudes and that model sensitivity could be altered drastically if a more 'realistic' (nondiffusive) parameterization of tropical transports were included. LF suggested modifications to the heat transport term in Budyko's (1969) zonal energy-balance climate model. The authors do not believe that the modifications suggested by LF are necessarily more realistic than the original formulation, and thus it is not believed that the quantitative results offered by LF can be demonstrated as more realistic than those they replace. Reasons for the belief are discussed.

Warren, S. G.↗

DOE OSTI2023

The Budyko shape parameter as a descriptive index for streamflow loss

Increases in evapotranspiration (ET) from global warming are decreasing streamflow in headwater basins worldwide. However, these streamflow losses do not occur uniformly due to complex topography. To better understand the heterogeneity of streamflow loss, we use the Budyko shape parameter (ω) as a diagnostic tool. We fit ω to 37-year of hydrologic simulation output in the Upper Colorado River Basin (UCRB), an important headwater basin in the US. We split the UCRB into two categories: peak watersheds with high elevation and steep slopes, and valley watersheds with lower elevation and gradual slopes. Our results demonstrate a relationship between streamflow loss and ω. The valley watersheds with greater streamflow loss have ω higher than 3.1, while the peak watersheds with less streamflow loss have an average ω of 1.3. This work highlights the use of ω as an indicator of streamflow loss and could be generalized to other headwater basin systems.

large scale analysis↗

NASA NTRS1980

Latitude-dependent sensitivity to stationary perturbations in simple climate models

The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are: (1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and (2) the indirect feedback effect produces an enhanced response in polar latitudes.

Salmun, H.↗

NASA NTRS2012

Hydroclimatic Controls over Global Variations in Phenology and Carbon Flux

The connection between phenological and hydroclimatological variations are quantified through joint analyses of global NDVI, LAI, and precipitation datasets. The global distributions of both NDVI and LAI in the warm season are strongly controlled by three quantities: mean annual precipitation, the standard deviation of annual precipitation, and Budyko's index of dryness. Upon demonstrating that these same basic (if biased) relationships are produced by a dynamic vegetation model (the dynamic vegetation and carbon storage components of the NCAR Community Land Model version 4 combined with the water and energy balance framework of the Catchment Land Surface Model of the NASA Global Modeling and Assimilation Office), we use the model to perform a sensitivity study focusing on how phenology and carbon flux might respond to climatic change. The offline (decoupled from the atmosphere) simulations show us, for example, where on the globe a given small increment in precipitation mean or variability would have the greatest impact on carbon uptake. The analysis framework allows us in addition to quantify the degree to which climatic biases in a free-running GCM are manifested as biases in simulated phenology.

Koster, Randal↗

DOE OSTI2020

Assessing Shifts in Regional Hydroclimatic Conditions of U.S. River Basins in Response to Climate Change over the 21st Century

Characterization of shifts in regional hydroclimatic conditions helps reduce negative consequences on agriculture, environment, economy, society, and ecosystem. This study assesses shifts in regional hydroclimatic conditions across the conterminous United States in response to climate change over the 21 st Century. The hydrological responses of five downscaled climate models from the Multivariate Adaptive Constructed Analogs (MACA) dataset ranging from the driest to wettest and least warm to hottest were simulated using the Variable Infiltration Capacity (VIC) model. Shifts in regional hydroclimatic conditions at 8-digit hydrologic unit scale (HUC8) were evaluated by the magnitude and direction of movements in the Budyko space. HUC8 river basins were then clustered into seven unique hydroclimatic behavior groups using the K-means method. A tree classification method was proposed to illustrate the relationships between hydroclimatic behavior groups and regional characteristics. The results indicate that hydroclimatic responses may vary from a river basin to another, but basins in the same neighborhood follow a similar movement in the Budyko space. The systematic hydroclimatic behavior of river basins is highly associated with their regional landform, climate, and ecosystem characteristics. Most HUC8s with Mountain, Plateau and Basin landform types will likely experience less arid conditions. However, most HUC8s with Plain landform type behave differently according to the regional ecosystem and climate. This study provides a potential roadmap of shifts in regional hydroclimatic conditions of U.S. river basins, which can be used to improve regional preparedness and ability of various sectors to mitigate or adapt to the impacts of future hydroclimate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

One-Parameter Analytical Derivation in Modified Budyko Framework for Unsteady-State Streamflow Elasticity in Humid Catchments

The changes in climate and catchment properties have altered the hydrological processes significantly at different spatiotemporal scales around the world. In particular for finer time scales, changes in water storage, which has been commonly neglected for long-term temporal scales, may play an important role on hydrological processes. Nevertheless, few studies addressed this question in modifying the Budyko framework, with most of them remaining a steady-state assumption on catchment characteristics. Here, in this work, we derive new analytical formulas of unsteady-state streamflow elasticity in a modified Budyko framework, incorporating both storage change and one specific parameter for catchment properties. We study 78 humid catchments in the USA with simulation data of daily hydrological processes from a probability-distribution-based hydrological model (the modified HyMOD). As indicated by results, the annual storage change ratio is linearly correlated with the annual aridity index, and this relationship can be used to estimate elasticity coefficients with our formulas. The estimated elasticity coefficients perform well in simulating the annual streamflow with the power-law model. For different catchments, variability of the unsteady-state elasticity is higher than that of the steady-state elasticity. Unsteady-state streamflow coefficients show significant linear correlation with catchment properties, such as the average slope, average elevation, and catchment area. This study provides a new analytical approach to investigate the interannual stability of catchments with varying climate and catchment properties.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Shifts in hydroclimatology of US megaregions in response to climate change

Most of the population and economic growth in the United States occurs in megaregions as the clustered metropolitan areas, whereas climate change may amplify negative impacts on water and natural resources. This study assesses shifts in regional hydroclimatology of fourteen US megaregions in response to climate change over the 21st century. Hydroclimatic projections were simulated using the Variable Infiltration Capacity (VIC) model driven by three downscaled climate models from the Multivariate Adaptive Constructed Analogs (MACA) dataset to cover driest to wettest future conditions in the conterminous United States (CONUS). Shifts in the regional hydroclimatolgy and basin characteristics of US megaregions were represented as a combination of changes in the aridity and evaporative indices using the Budyko framework and Fu's equation. Changes in the climate types of US megaregions were estimated using the Fine Gaussian Support Vector Machine (SVM) method. The results indicate that Los Angeles, San Diego, and San Francisco are more likely to experience less arid conditions with some shifts from Continental to Temperate climate type while the hydroclimatology of Houston may become drier with some shifts from Temperate to Continental climate type. Additionally, water yield is likely to decrease in Seattle. Change in the hydroclimatology of Denver and Phoenix highly depends on the selected climate model. However, the basin characteristics of Phoenix have the highest sensitivity to climate change. Overall, the hydroclimatic conditions of Los Angeles, San Diego, Phoenix, Denver, and Houston have the highest sensitivity to climate change. Understanding of future shifts in hydroclimatology of megaregions can help decision-makers to attenuate negative consequences by implementing appropriate adaptation strategies, particularly in the water-scare megaregions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Energy‐Water Asynchrony Principally Determines Water Available for Runoff From Snowmelt in Continental Montane Forests

ABSTRACT Changes in the volume, rate, and timing of the snowmelt water pulse have profound implications for seasonal soil moisture, evapotranspiration (ET), groundwater recharge, and downstream water availability, especially in the context of climate change. Here, we present an empirical analysis of water available for runoff using five eddy covariance towers located in continental montane forests across a regional gradient of snow depth, precipitation seasonality, and aridity. We specifically investigated how energy‐water asynchrony (i.e., snowmelt timing relative to atmospheric demand), surface water input intensity (rain and snowmelt), and observed winter ET (winter AET) impact multiple water balance metrics that determine water available for runoff (WAfR). Overall, we found that WAfR had the strongest relationship with energy‐water asynchrony (adjusted r 2 = 0.52) and that winter AET was correlated to total water year evapotranspiration but not to other water balance metrics. Stepwise regression analysis demonstrated that none of the tested mechanisms were strongly related to the Budyko‐type runoff anomaly (highest adjusted r 2 = 0.21). We, therefore, conclude that WAfR from continental montane forests is most sensitive to the degree of energy‐water asynchrony that occurs. The results of this empirical study identify the physical mechanisms driving variability of WAfR in continental montane forests and are thus broadly relevant to the hydrologic management and modelling communities.

Webb, Ryan William↗

NASA NTRS1993

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

Mintz, Y.↗