A NONSTATIONARY UNCERTAINTY FRAMEWORK FOR CLIMATE CHANGE IMPACT PROJECTIONS – TRADING SPACE-FOR-TIME TO UNDERSTAND STREAMFLOW ELASTICITY

ABSTRACT

Watershed models are used to simulate the streamflow for a given climatic scenarios and also for ungauged basins. They have become increasingly important to predict the behavior of watersheds under the expected climate change where the watersheds will experience climates which will be much different from their historical climate. Most of the waterheds models require a simulation based approach to arrive at optimal parameter sets. One of the major problems is dependence of watershed models on calibration, whose outcome is dependent on the climatic regime of the calibration data, or on a priori parameter estimates, which often perform poorly even in reproducing historical data. In addition there is an urgent need to for the estimation of uncertainty in climate change impact assessment.

Streamflow elasticity is defined as the percent change in streamflow for a percent change in precipitation or temperature. It is an indicator of the sensitivity of streamflow to climate change. Elasticity can be derived from historical observations or from watershed model simulations.

In this study we develop a new uncertainty framework utilizing trading-space-fortime to establish model constraints that reduce predictive uncertainty while accounting for the impact of climate nonstationarity on parameter estimates. The driving hypothesis is that observed spatial gradients in watershed signatures such as runoff ratio, baseflow index etc can be used as a proxy for temporal gradients. Thus, relationships developed over vast spatial extent spanning a variety of watersheds and climate, can be used to predict the nature of a watershed as it moves to climates that it never experienced before.

The main conclusion of the study is that as we move towards more extreme climates, the importance of including nonstationarity in parameters increases. Moreover, drier climates are more sensitive to climate change than wetter climates for most of the watersheds considered in the study. The latter scenario is likely to be the case for many less developed countries, which typically already lie in regions where water availability is lower and climate variability is higher. The results shown here suggest that previously used frameworks will likely underestimate the hydrologically-controled risks posed by climate change!

 

                                                 

 

                                     TABLE OF CONTENTS

LIST OF FIGURES ………………………………………………………………………………………………….. v

LIST OF TABLES …………………………………………………………………………………………………… vii

ACKNOWLEDGEMENTS ………………………………………………………………………………………. viii

• Introduction ………………………………………………………………………………………………………….. 1
  • Global problem of understanding climate change impact .. …….. ………………………… 1       2 Approaches used until now and their drawbacks ……………………………………………….. 3       1.3  Objectives and scope of the study …………………………………………………………………… 5
• Model ………………………………………………………………………………………………………………….. 7
• Methods ……………………………………………………………………………………………………………….. 9
• Data . …………………………………………………………………………………………………………………… 13
• Results and Discussion …………………………………………………………………………………………… 17
  • Testing the value of signatures as constraints …………………………………………….. 17
  • Regionalization of Signatures ………………………………………………………………….. 17
  • Application of methodology for changing climatic scenarios ……………………….. 19
  • Change in constraints with changing climate ……………………………………………… 19
  • Matrix of Ensemble streamflow predictions ………………………………………………. 20
  • Comparison of matrix for different watersheds ………………………………………….. 27
  • Elasticity of streamflow ………………………………………………………………………….. 28 5.8 Contours of change in streamflow ……………………………………………………………. 32

5.9 Change of model parameters with climate……………………………………37

• Conclusion ……………………………………………………………………………………………………………. 41 References ………………………………………………………………………………………………………………. 43

Chapter 1

 

Introduction

Global problem of understanding climate change impacts

Global climate change is posing a challenge to hydrological science. Since its impacts are likely to alter freshwater resources availability in many regions of the world, there is therefore an urgent need to understand how climate change will propagate into regional hydrology, i.e. the scale of decision-making [Wagener et al., 2010].  To manage water resources in the context of high hydrologic variability, potentially changes in mean flows and an increasing occurrence of extremes, we are interested in predicting the response of environmental systems with respect to any hydrologically-controlled endpoints relevant for the management of water resources or to understand aquatic ecosystem health and biodiversity. For developing management strategies for water resources we need credible tools to make such projections at relevant scales including estimates of uncertainty for effective risk assessment and adaptation.

To aid the management strategies we need characterization tools to assess the extremity of expected impact. One measure to quantify the sensitivity of hydrological systems to climate change is streamflow elasticity. In one of the first studies of its kind, Schaake and Nemek (1982) forced a hydrologic model calibrated on historical period with a changed precipitation and temperature forcing to estimate runoff sensitivity and concluded that sensitivity is higher for arid areas as compared to humid. Several studies followed which attempted to give a theoretical definition to elasticity and applying them to outputs from a hydrologic model to evaluate elasticity values for given watersheds. Schaake and Liu (1989) developed a map of streamflow elasticity due to precipitation change for the United States in such a manner. Other studies that also derived predictions of elasticity using hydrologic models include Nash and Gleick[1990] ,Jones et al.[2006] andFu et al.[2007] . These studies include both numerical estimates of elasticity and contour maps developed across a range of climate change regimes.  The studies byDooge[1992] andDooge et al.[1999] focused on analytical methods of obtaining elasticity as a function of climate. Some studies likeVogel et al.[1999] evaluate elasticity based on regression models.Risbey and Entekhabi[1996] developed contour plots of elasticity for the Sacremento river basin by using data records of 100 years. They computed elasticity directly from historical records. An extensive study on the different definitions of elasticity and their applicability has been carried out by

Sankarasubramanian et al.[2001] . They compared various methods of obtaining elasticity. One of their important conclusions is that elasticity is a model dependent quantity. They showed that estimates of precipitation elasticity depends on both model choice and model calibration by evaluating elasticity by different models. Elasticity, in general, is computed from output derived from hydrologic model or from observed records. The basic definition is given bySchaake and Liu[1989] :

(1)

Where, Q is the historical mean flow and δQ is the departure from this historical value due; X can be precipitation or evapotranspiration; δX is the departure from the historical value of X. Therefore  can be precipitation elasticity or evapotranspiration elasticity of streamflow. It is to be noted that this definition is general and can be applied to both simulated and observed runoff. However, recent methods to obtain the value of elasticity focus on forcing a hydrologic model calibrated on historical regime with changed inputs as expected from climate change since it allows for an assessment of a wider climatic range. In this paper, we focus on the derivation of elasticity from simulated streamflow.

 

 

 

 

 

Approaches used until now and their drawbacks

But also outside the goal of obtaining elasticity estimates, we ultimately depend on the use of watershed models to achieve continuous streamflow predictions since statistical approaches will not allow us to extrapolate under nonstationary conditions [Milly et al.,

2008]. Many studies have used watershed scale models for climate change impact assessment

[Zheng et al., 2009; Jha et al., 2004; Legesse et al., 2010; Knowles, 2002, Chiew et al., 2009]. The general approach adopted in these studies is to force a watershed model with downscaled climate change projections of precipitation and temperature. Most do not yet include a feedback from the hydrological model to the atmosphere. Current limitations of this approach, among other things, include in many cases a lack of consideration of uncertainty and of the nonstationarity in the parameters of the hydrological model as well. This non stationarity has been observed in several studies and has been discussed in detail in the subsequent text.The need for the inclusion of uncertainties in these projections has been motivated elsewhere and will not be repeated here [e.g. Buytaert et al., 2009; Maurer et al., 2005; Ghosh et al., 2009]. These studies have focused on the impact of input data uncertainty arising from the use of different GCM models and downscaling techniques. However, uncertainties also stem from nonuniqueness of parameters and from errors in hydrologic model structures. The study by Wilby et al.[2006] attempted at incorporating hydrologic model uncertainty along with GCM uncertainties in a probabilistic framework. They found that uncertainty in the streamflow prediction due to uncertainty in hydrologic model parameters was significant and could not be neglected. However, they only attempt to quantify this uncertainty, we still need to find a method to assess the impact of changing climate on model parameters.  It is expected that climate change impact projections will be even more uncertain than simulations driven by historical observations which makes it unlikely that deterministic change impact projections will be very robust and a good basis for risk assessment or decision-making. Although different sources of uncertainty will affect such impact projections; here we will focus on the uncertainty introduced through the model parameters under nonstationary conditions.

Parameters in watershed models are generally derived via two strategies: calibration on historical observations or through a priori parameter estimation.

• A priori estimates of parameters are derived by relating model parameters to physical characteristics of the watershed such as soil, vegetation etc. However, studies have shown that a priori parameter estimates have a high degree of uncertainty attached to them, lack robustness and can often produce low performance [Duan et.al, 2006; van Werkhoven et al. 2009; Hughes and Kapangaziwiri, 2009]. Hence, model calibration has generally been found to produce more reliable estimates of parameters.
• During calibration, the parameter set that produces the best fit between simulated and observed streamflow is identified. Different strategies have been developed to consider the uncertainty in this identification process when historical observations are used or when the model is applied to ungauged watersheds [Clark and Vrugt, 2006; Khadam and Kaluarachchi, 2004].

More recently it has been observed that the climatic regime of the time period in which the calibration data have been observed leaves an imprint in the parameter estimates [e.g. Van Werkhoven et al., 2008; Vaze et al., 2009]. A recent study by Merz et. al [2010] for example analyzes how calibrated parameters might change with  climate. They found that the parameters used for their model showed clear time trends when calibrated on different periods. In other words, parameters were found to be function climate regime of the period of calibration. They suggest that explicitly accounting for non-stationary model parameters is one of the potential solutions for assessing climate change impact on streamflows. This implies that the parameter set obtained by calibrating over a wet period can be different than what we obtain by calibrating over a dry period and vice versa. This has potential implications for climate change impact studies where the climate is by definition different from historical observations. Vaze et al. [2009] carried out a study to examine the validity of using historically calibrated rainfall runoff models for future climate change predictions. Their modeling study quantifies the departure from mean rainfall after which the applicability of historical model parameters becomes unsuitable for the new climate regime.  Again, they point out to the problem of nonstationarity of parameters but we still need to identify a methodology to deal with this.Van Werkhoven et al. [2008] also point out that calibrated parameters depend on the period of record used for calibration and that the sensitivity of the parameters varies with climate. Hence, the functional behavior of the model also varies. We therefore hypothesize that a nonstationary uncertainty framework is needed to account for the required change of watershed model parameters in a changing climate.

The observed nonstationarity can be caused either by a change in the processes occurring in the watershed or by a change in the parameters of the model. In order to distinguish between the causes of nonstationarity either as a change in process or change in parameter or both, we need to compare across a wide range of models. However, in this study we focus on a single model to understand what the impacts are of changing the parameter sets according to the future climate regime.

Objectives and scope of study

In this study we propose and evaluate a novel nonstationary uncertainty framework for obtaining streamflow projections under a changing climate. The hypothesis we put forward is twofold:

• The parameters of a given model obtained through calibration on historical records will change in a changing climate and thus, new sets of parameters need to be obtained for simulating future climate scenarios instead of using the parameters obtained by calibration to historical data.
  • To address this issue we adopt the method of ‘trading-space-for-time’. It extends the use of regionalization for predicting flow in ungaged basins to predicting flow in a changing climatic scenario. Regionalization [Yadav et

al., 2007] involves development of a relationship between a watershed response characteristic and its climatic/physical characteristics.

• The second part of our hypothesis is that, the parameter estimation process does not result in a unique parameter set, but has uncertainty attached to it and that it is important to quantify this uncertainty in order to make more robust decisions.
  • We demonstrate in this paper a way to do this by accepting an ensemble of parameter values satisfying our performance criteria instead of using just one best parameter set.

We introduce this method and demonstrate its application on four watersheds located in climatically different parts of the United States.  As introduced earlier, the concept of climate elasticity can be used to quantify the sensitivity of streamflow to climate change. Here, the introduction of uncertainty and nonstationarity provides us with a tool to analyze the climate dependence of streamflow elasticity. We demonstrate how elasticity estimates will depend on how a watershed model is used and also allow for uncertainty in the same. Also, the estimates of elasticity derived from the approach developed in this paper and from the traditional approach are compared in order to reveal the difference in the results obtained.

It has been mentioned earlier that the source of nonstationarity can be both the model used and the parameters. One of the limitations of this study is that we use only one model and therefore focus only on the change of parameters with climate and not on the change of processes within the watershed as the climate changes. Another assumption of the study is that the regression relationships developed for using spatial gradients as a proxy for temporal gradients accurately define how watersheds will change with time.

A NONSTATIONARY UNCERTAINTY FRAMEWORK FOR CLIMATE CHANGE IMPACT PROJECTIONS – TRADING SPACE-FOR-TIME TO UNDERSTAND STREAMFLOW ELASTICITY

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