skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, October 10 until 2:00 AM ET on Friday, October 11 due to maintenance. We apologize for the inconvenience.


Title: Hydrological Basis of Different Budyko Equations: The Spatial Variability of Available Water for Evaporation
Abstract

The available water for evaporation within a catchment is spatially variable. However, how the spatial variability of available water affects mean annual evaporation is not fully understood. For a specific catchment, a suitable distribution function defined for non‐negative random variables can be determined through statistical methods to represent the spatial variability of the available water when the point‐scale data are available. This article proposes that the distribution function representing the spatial variability of available water for evaporation determines the functional form of Budyko equation based on the one‐stage precipitation partitioning concept. Specifically, the available water for evaporation following a single‐parameter distribution function leads to a deterministic Budyko equation; whereas a two‐parameter distribution function of available water for evaporation leads to a single‐parameter Budyko equation. We identified the property of distribution function for symmetric Budyko equation, which suggests that precipitation partitioning and energy partitioning in the hydrological cycle follow the same functional form with respect to aridity index and humidity index, respectively. The lower bound of Budyko curve is explained as a result of probable distributions of available water for evaporation due to catchment co‐evolution.

 
more » « less
Award ID(s):
1804770
NSF-PAR ID:
10442581
Author(s) / Creator(s):
 ;  
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
Water Resources Research
Volume:
58
Issue:
2
ISSN:
0043-1397
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The long‐term water balance of catchments is given by precipitation partitioned into either runoff or evaporation. Understanding precipitation partitioning controls is a critical focus of hydrology and water resources management. A useful theoretical framework that serves their understanding is the Budyko Framework. Our purpose is to understand how Budyko's n parameter is related to different controls and what is its relevance to precipitation partitioning. We investigated the relative importance of the dryness index and the Budyko parameter for precipitation partitioning, then applied partial correlation analysis and multivariate regressions to find out which were the principal partitioning controls. We focused our research in the central Appalachian mountains located in the eastern United States, considered as water towers to metropolitan areas in the eastern and mid‐western US (e.g., Pittsburgh, Washington DC), and selected a set of catchments characterized by minimal human disturbance and with large proportions of temperate forests. We found that climate controls such as mean annual temperature and fraction of precipitation falling in the form of snow exert a higher influence on partitioning than landscape controls (e.g., forest cover, Normalized Difference Vegetation Index, and slope). Thus, the importance of vegetation as a primary driver of partitioning could not be confirmed based on regional or basin‐wide characteristics. On the other hand, the influence of topography, and elevation in particular, was highly ranked as important. Our study highlights that partitioning controls could differ between basins in the same climate region, especially in a complex, mountainous topography setting.

     
    more » « less
  2. Understanding the process of precipitation partitioning into evapotranspiration and streamflow is fundamental for water resource planning. The Budyko framework has been widely used to evaluate the factors influencing this process. Still, its application has primarily focused on studying watersheds with minimal human influence and on a relatively small number of factors. Furthermore, there are discrepancies in the literature regarding the effects of climatic factors and land use changes on this process. To address these gaps, this study aims to quantify the influence of climate and anthropogenic activities on streamflow generation in the contiguous United States. To accomplish this, we calibrated an analytical form of the Budyko curve from 1990 to 2020 for 383 watersheds. We developed regional models of , a free parameter introduced to account for controls of precipitation partitioning not captured in the original Budyko equation, within different climate zones. We computed 49 climatic and landscape factors that were related to using correlation analysis and stepwise multiple linear regression. The findings of this study show that human activities explained a low variance of the spatial heterogeneity of compared with the watershed slope and the synchronization between precipitation and potential evapotranspiration, nevertheless, urban development emerged as a factor in temperate climates, whereas irrigated agriculture emerged in cold climates. In arid climates, mean annual precipitation explains less than 20% of the spatial variability in mean annual streamflow; furthermore, this climate is the most responsive to changes in . These results provide valuable insights into how land use and climate interact to impact streamflow generation differently in the contiguous United States contingent on the regional climate, explaining discrepancies in the literature. 
    more » « less
  3. Abstract

    For evaluating the climatic and landscape controls on long‐term baseflow, baseflow index (BFI, defined as the ratio of baseflow to streamflow) and baseflow coefficient (BFC, defined as the ratio of baseflow to precipitation) are formulated as functions of climate aridity index, storage capacity index (defined as the ratio of average soil water storage capacity to precipitation), and a shape parameter for the spatial variability of storage capacity. The derivation is based on the two‐stage partitioning framework and a cumulative distribution function for storage capacity. Storage capacity has a larger impact on BFI than on BFC. When storage capacity index is smaller than 1, BFI is less sensitive to storage capacity index in arid regions compared to that in humid regions; whereas, when storage capacity index is larger than 1, BFI is less sensitive to storage capacity index in humid regions. The impact of storage capacity index on BFC is only significant in humid regions. The shape parameter plays an important role on fast flow generation at the first‐stage partitioning in humid regions and baseflow generation at the second‐stage partitioning in arid regions. The derived formulae were applied to more than 400 catchments where storage capacity index was found to follow a logarithmic function with climate aridity index. The role of climate forcings at finer timescales on baseflow were quantified, indicating that seasonality in climate forcings has a significant control especially on BFI.

     
    more » « less
  4. Abstract

    A three‐stage precipitation partitioning framework is proposed to study the climate controls on mean annual groundwater evapotranspiration (GWET) for 33 gauged watersheds in west‐central Florida. Daily GWET, total evapotranspiration (ET), groundwater recharge, base flow, and total runoff are simulated by the Integrated Hydrologic Model, which dynamically couples a surface water model (HSPF) and a groundwater flow model (MODFLOW). The roles of GWET on long‐term water balance are quantified by four ratios. The ratios of GWET to total available water, watershed wetting, ET, and recharge decrease exponentially with watershed aridity index (WAI), which is defined as the ratio of potential evapotranspiration to total available water. In the one‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and available water for ET (i.e., they‐axis of Budyko curve) decreases with WAI. In the two‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and watershed wetting (i.e., Horton index) decreases with WAI. The changes in GWET caused by intra‐monthly (IM) climate variability are the highest among the temporal scales of climate variability investigated to understand controls on GWET. The inter‐annual, intra‐annual, and IM climate variabilities lead to increase of GWET; but the sub‐daily climate variability results in decrease of GWET. For the third stage of partitioning, given the same ratio of potential GWET to available water for GWET, higher percentage of forest and wetland and lower percentage of impervious land contribute to higher ratio of GWET to available water for GWET.

     
    more » « less
  5. Abstract. Following the Budyko framework, the soil wetting ratio (the ratio betweensoil wetting and precipitation) as a function of the soil storage index (theratio between soil wetting capacity and precipitation) is derived from theSoil Conservation Service Curve Number (SCS-CN) method and the variableinfiltration capacity (VIC) type of model. For the SCS-CN method, the soilwetting ratio approaches 1 when the soil storage index approaches ,due to the limitation of the SCS-CN method in which the initial soil moisturecondition is not explicitly represented. However, for the VIC type of model,the soil wetting ratio equals the soil storage index when the soil storageindex is lower than a certain value, due to the finite upper bound of thegeneralized Pareto distribution function of storage capacity. In this paper,a new distribution function, supported on a semi-infinite interval x[0,), is proposed for describing the spatial distribution of storagecapacity. From this new distribution function, an equation is derived for therelationship between the soil wetting ratio and the storage index. In thederived equation, the soil wetting ratio approaches 0 as the storage indexapproaches 0; when the storage index tends to infinity, the soil wettingratio approaches a certain value (≤1) depending on the initial storage.Moreover, the derived equation leads to the exact SCS-CN method when initialwater storage is 0. Therefore, the new distribution function for soil waterstorage capacity explains the SCS-CN method as a saturation excess runoffmodel and unifies the surface runoff modeling of the SCS-CN method and theVIC type of model.

     
    more » « less